1 yen note, Government and National Bank Notes, National Bank Notes (1873-1880)
National fiat banknotes are also referred to as new national bank notes (新国立銀行券) as they differ from their older counterparts in place of origin. These notes were produced domestically rather than the more difficult task of outsourcing them to the United States for printing. One yen fiat notes measure 74mm x 156mm in size, and are commonly known as sailor one-yen (水兵1円) due to the design. This obverse design depicts two sailors along with seals from the corresponding bank of issuance. The reverse side meanwhile features the Japanese god of fishermen and luck (Ebisu).


1 yen note, Government and National Bank Notes, National Bank Notes (1873-1880)
In July 1877 then prime minister Ōkuma Shigenobu realized that keeping Japan on a gold standard was pointless given the low price of silver. The silver one yen coin was thus brought into domestic commerce on May 27, 1878 switching Japan to a de facto silver standard. This did little good for fiat currency as it continued to lose its value against silver coinage. The issuance of national fiat banknotes was ultimately suspended in 1880 by then prime minister Matsukata Masayoshi.


1 yen note, Government and National Bank Notes, National Bank Notes (1873-1880)
During this time Matsukata introduced a policy of fiscal restraint that resulted in what has come to be called the "Matsukata Deflation". The most significant of these policies established a centralized banking system through the "Bank of Japan Regulation" on June 27, 1882 by proclamation No. 32. In order to decrease inflation all of the old notes were to be collected and exchanged by notes from the central bank. The first step of this process came with an amendment to the regulation in May 1883, which provided the redemption and retirement of national bank notes.


1 yen note, Government and National Bank Notes, National Bank Notes (1873-1880)
As the amount of paper currency in circulation decreased, the amount of silver reserves increased. This drove up the value of paper currency until it was about equal to that of silver coins by the end of 1885. The National Bank Act was amended again in March 1896, providing for the dissolution of the national banks on the expiration of their charters. This amendment also prohibited national bank notes from circulating after December 31, 1899. The ongoing redemption process took additional time as national bank notes were not fully removed from circulation until 1904.


1 yen note, Government and National Bank Notes, Modified "Jingū" Banknotes (1881-1886)
Previous Meiji Tsūhō one yen notes were printed using western technology which had its disadvantages in terms of quality. Over time these fragile notes became discolored easily due to the climate of Japan. Counterfeiting was another issue as these thieves eventually found a way around the elaborate Meiji Tsūhō design. The Japanese government took action by releasing a new series referred to as modified banknotes (改造紙幣). Notes for this particular denomination measure 77mm x 131mm in size, and are commonly referred to as Empress Jingu 1-yen notes (神功皇后1円札) because of their design.


1 yen note, Government and National Bank Notes, Modified "Jingū" Banknotes (1881-1886)
These notes feature an artist's representation of Empress Jingū that was commissioned by Italian engraver Edoardo Chiossone. This design is notable for being the first portrait on a Japanese banknote, and the only female depicted in the history of Japanese paper currency. Also present on the obverse are counterfeit penalties which were later expanded in the Meiji era. The reverse side meanwhile features inscriptions from the Ministry of Finance, and displays the Treasurer's seal. One yen modified banknotes were released in February 1881 (year 14 of Meiji), and were intended to be exchanged for old Meiji Tsuho notes.


1 yen note, Government and National Bank Notes, Modified "Jingū" Banknotes (1881-1886)
During this time inflation hit an all time high due to the amount of non convertible paper currency in circulation (see section above). Measures were put into place which included the establishment of a centralized bank known as the Bank of Japan in 1882. All of the paper money in circulation was to be retired in favor of either silver coinage or newly printed Bank of Japan notes. One yen modified banknotes notes were redeemed for silver starting in January 1886 as production decreased for the series.


1 yen note, Government and National Bank Notes, Modified "Jingū" Banknotes (1881-1886)
The Japanese government adopted the gold standard on March 26, 1897 which switched over the redemption of government banknotes from silver to gold. This was followed by a deadline set in June 1898 to prohibit circulation of government notes by the end of the century. Modified one yen "Jingū" banknotes were abolished by the set deadline on December 31, 1899.


1 yen note, Bank of Japan Notes, Daikokuten Notes (1885-1958)
During the early 1880s, then prime minister Matsukata Masayoshi was dealing with a serious inflation problem. The value of inconvertible Government and National Bank Notes was devalued as too many notes were in circulation. In response, Masayoshi suspended the issuance of these notes and established a centralized banking system through the "Bank of Japan Regulation" on June 27, 1882. The Bank of Japan commenced operations on October 10, 1882 with the authority to print banknotes that could be exchanged for the old Government and National Bank Notes.


1 yen note, Bank of Japan Notes, Daikokuten Notes (1885-1958)
The first step of this process came with an amendment to the regulation in May 1883, which provided the redemption and retirement of national bank notes. No new banknotes could be issued during this time as there was an imbalance between existing coins and notes in regards to silver. Redeeming old paper currency was eventually effective at stabilizing the price of silver alloy. The Japanese government stablished a convertible bank note system by Dajo-kwan Notification No. 18 in May 1884. Concurrently, the amount of old paper currency in circulation decreased allowing the amount of silver reserves to grow.


1 yen note, Bank of Japan Notes, Daikokuten Notes (1885-1958)
This drove up the value of paper currency until it was about equal to that of silver coins by the end of 1885. There is a disagreement among sources on the exact release date of the new Bank of Japan notes. Older sources give a date somewhere in "May 1885" with one source specifically pointing to May 9, 1885. Newer sources on the other hand such as the Bank of Japan website officially give a release date of September 8, 1885 for the notes. In either case Japan was placed on a silver standard with laws enacted to issue silver for the notes starting in January 1886.


1 yen note, Bank of Japan Notes, Daikokuten Notes (1885-1958)
One yen notes from this series are commonly called Daikoku 1 yen (大黒一円札) after the lucky god Daikokuten featured in the design. Officially they are referred to as former convertible banknotes (旧兌換銀行券) in relation to events that occurred since their release. One yen notes measure 78mm X 135mm in size and were designed by Italian engraver Edoardo Chiossone. Daikokuten is featured on the obverse with the inscription NIPPON GINKO Promises to Pay the Bearer on Demand One Yen in Silver (此券引きかへ尓銀貨壹圓相渡可申候也). The reverse meanwhile features a colored pattern with the value written in English, and counterfeit penalties written in Kanji.


1 yen note, Bank of Japan Notes, Daikokuten Notes (1885-1958)
Security features include a character watermark that reads "Bank of Japan Note" when held up to a light source. One yen Daikoku notes were only printed for a few years due to problems involving the design. One of these defects involved the addition of "konjac powder" to increase the strength of the bill. This powder wound up attracting rats and insects which would easily damage the bills by chewing on them. Another issue had to due with the "blue ink" in the watermark that was used to prevent counterfeiting.


1 yen note, Bank of Japan Notes, Daikokuten Notes (1885-1958)
The ink used was mixed with white lead as a pigment causing it to turn black when it reacted with hydrogen sulfide in hot spring areas. When the Japanese government adopted an official gold standard in 1897, the silver yen was abolished. One yen Daikoku notes were gradually withdrawn afterwards in exchange for subsidiary silver currency. The notes though were not suspended from issuance (de jure) until October 1, 1958 (year 33 of Shōwa). These notes are still legal tender today making them the oldest valid currency in Japan. They remain unused in circulation as their collector's value far exceeds their face value.


1 yen note, Bank of Japan Notes, Modified Convertible Banknotes (1889-1958)
On May 1, 1889 (22nd year of Meiji) the Bank of Japan printed new one yen silver certificates to replace the old "Daikokuten" notes. This action had to be undertaken to address design flaws which caused the latter series to be eaten and discolored. Modified one yen notes are now officially referred to as former convertible banknotes (旧兌換銀行券) in relation to events that occurred since their release. This series is broken up into two different varieties called Kanji one yen (漢数字1円) and Arabic one yen (アラビア数字一円) aka Taishō one yen banknotes (大正兌換銀行券1円).


1 yen note, Bank of Japan Notes, Modified Convertible Banknotes (1889-1958)
Kanji one yen notes were the first variety to be released as the serial numbers are written in kanji. Notes from this series all measure 85mm X 145mm in size, and feature legendary Japanese hero-statesman Takenouchi no Sukune on the obverse. With this legendary figure are inscriptions in three circles that reference the convertible wording, the Dajo-kwan Notification of 1884 (year 17 of Meiji), and counterfeit penalties. The reverse side of the notes meanwhile feature a contemporary one yen silver coin with the convertible wording written in English.


1 yen note, Bank of Japan Notes, Modified Convertible Banknotes (1889-1958)
Security features include paulownia watermarks, and the words "Silver Standard One Yen Bill" when held up to a light source. Originally these notes were intended to be silver certificates that could be converted through a bank transaction into a one yen silver coin. Problems arose when foreign countries left the silver standard leading to a large increase in worldwide silver production. As the price of silver dropped the value of the silver yen went along with it causing inflation. The Japanese government was now eager to drop the silver standard in favor of something more sustainable.


1 yen note, Bank of Japan Notes, Modified Convertible Banknotes (1889-1958)
An opportunity for change came in the aftermath of the First Sino-Japanese War as the Japanese government received a large compensation. This compensation was used to mint gold coins as the government switched from a silver standard to a gold standard. Japan officially switched to this adopted gold standard on October 1, 1897 (year 30) and all of the silver one yen coins were demonetized. Kanji one yen notes were gradually withdrawn afterwards in exchange for subsidiary silver currency.


1 yen note, Bank of Japan Notes, Modified Convertible Banknotes (1889-1958)
The second variety of notes were issued during Emperor Taishō's reign due to effects caused by World War I. More banknotes were needed during this time as a booming economy caused the demand for Japanese products to increase. Arabic or Taishō one yen notes were issued on August 15, 1916 (year 5 of Taishō) with no changes other than the Arabic printed serial numbers. These notes were convertible to silver only in practice as no silver was present in the bank's note reserve.


1 yen note, Bank of Japan Notes, Modified Convertible Banknotes (1889-1958)
The effects of the war caused a silver subsidiary coin shortage which prompted the issuance of fractional currency in denominations of 10, 20, and 50 sen notes. One yen silver coins were "practically nonexistent" by this time as larger sums in yen were negotiated by banknotes. It was recorded on November 17, 1917 that one yen notes in particular were hoarded due to the scarcity of subsidiary coinage. At some point in time these notes were not de facto issued anymore as they were replaced by a new series in 1943. Modified convertible one yen banknotes were ultimately suspended from issuance (de jure) on October 1, 1958 (year 33 of Shōwa). While these notes are still legal tender today, they remain unused in circulation as their collector's value far exceeds their face value.


1 yen note, Bank of Japan Notes, First issue series (1943-1958)
The "Bank of Japan Act" was promulgated on February 24, 1942 allowing the Bank of Japan to be re-organized to reflect the reality of World War II. This act empowered the Bank of Japan to release nonconvertible notes in denominations of 1, 5, 10, and eventually 100 yen as fiat currency. These notes are part of the First issue series (い号券), which is a collective term for notes issued after the Bank of Japan was re-organized.


1 yen note, Bank of Japan Notes, First issue series (1943-1958)
One yen notes from this series measure 81 mm x 142 mm in size, and are also called Chuo Takenouchi one yen (中央武内1円) after their design. This design features Japanese hero-statesman Takenouchi no Sukune on the obverse, and Ube shrine on the reverse. Chuo Takenouchi one yen notes were released into circulation on December 15, 1943 (18th year of Shōwa). These notes were manufactured in poor condition due to budget cuts made in preparation for the war. Changes to production included a shift from mitsumata paper material to pulp as mitsumata required more time and labor to manufacture.


1 yen note, Bank of Japan Notes, First issue series (1943-1958)
Other changes involved the simplification of printing, raw materials, and design patterns as personnel and materials were in short supply. Security features were added in the form of  paulownia watermarks when held up to a light source. Overall, the issuance of fiat currency was strongly criticized by the public as the Japanese government abandoned its promise to convert paper money to gold.


1 yen note, Bank of Japan Notes, First issue series (1943-1958)
As the war intensified the Japanese government tried drastically to reduce costs by simplifying the notes even more. This effort created a second variety as the serial numbers were omitted on November 20, 1944 (year 19) to save labor in printing. Notes from the second variety are virtually identical to the ones issued in 1943 other than a missing serial number. Non visible changes involved the printing of the symbols with the bank seals for efficiency with a simplified watermark. The overall amount of Bank of Japan notes in circulation after the war became an issue due to rampant inflation.


1 yen note, Bank of Japan Notes, First issue series (1943-1958)
In order to control the situation a process known as new yen switching (新円切替) was implemented by the Shidehara Cabinet. By March 9, 1946 it was reported by the International Monetary Fund that all notes issued by the Bank of Japan had been surrendered for a one to one conversion into new yen notes. Chuo Takenouchi one yen notes remained legal tender as they were not invalidated with the other denominations. In either case the re-introduction of the one yen coin in 1948 (year 23) was the beginning of the end for the one yen note. This series was eventually suspended from issuance (de jure) on October 1, 1958 (year 33) when the amount of coins in circulation became sustainable. While these notes are still legal tender today, they remain unused in circulation as their collector's value exceeds their face value.


1 yen note, Bank of Japan Notes, A series (1946-1958)
Notes from the "A series" (A号券) were the last denomination of "one yen" to be issued as paper currency in Japan. When World War II  ended the amount of banknotes issued compared to before the war had more than tripled. This was due to factors such as wartime compensation, payment of retirement allowances to veterans, and refunds due to forced deposits and savings made during the war. All of these things had a negative effect on the Japanese economy due to rampant inflation and the devaluation of the yen.


1 yen note, Bank of Japan Notes, A series (1946-1958)
In order to control the situation a process known as new yen switching (新円切替) was implemented by the Shidehara Cabinet. The "A series" acted as renewal currency when banknotes were issued in denominations of 1, 5, 10, and 100 yen throughout 1946 (21st year of Shōwa). One yen notes are also referred to as "Ninomiya 1-yen banknotes" (買取価格が高い二宮1円) as the obverse features agricultural leader Ninomiya Sontoku. The reverse side meanwhile uses a colored pattern ripple design with "1 Yen" written in English. This design had to be approved by the Supreme Commander for the Allied Powers (GHQ) before it was implemented for use. These notes were issued both by the Bank of Japan and the Japanese government in name only, as production and printing was outsourced to the private sector.


1 yen note, Bank of Japan Notes, A series (1946-1958)
By March 9, 1946 it was reported by the International Monetary Fund that all notes issued by the Bank of Japan had been surrendered for a one to one conversion into new yen notes. One yen notes from the "A series" measure 68mm x 124mm in size and were poorly made due to post-war conditions. When the notes were released into circulation on March 19, 1946 they were prone to counterfeiting as there were no protective watermarks. To make matters worse, there were quality differences depending on where the notes were printed and produced which helped forgery to spread.


1 yen note, Bank of Japan Notes, A series (1946-1958)
The notes were not in circulation for long before Japanese coinage was reformed in 1948 (year 23) with the issue of a brass one-yen coin. Inflation was gradually stabilized by a monetary tightening policy called "Dodge Line", which was announced on March 7, 1949. One yen notes from the "A series" were eventually discontinued in 1956 (year 31) as aluminum one yen coins were now circulating. They were finally suspended from issuance (de jure) on October 1, 1958 (year 33) when the amount of coins in circulation became sustainable. While one yen notes from the "A series" are still legal tender today, they remain unused in circulation as their collector's value exceeds their face value.


1 yen note, Watermarks
Daikoku one yen bill with watermark reading: "Bank of Japan note" (read from right to left)


1 yen note, Watermarks
Remodeled one yen bill showing Paulownia and "Silver Standard One Yen Bill" watermarks


1 yen note, Collecting
The value of any given banknote is determined by survivability rate and condition as collectors in general prefer original notes with bright rich coloring. In contrast to this are notes with ink stains, missing pieces, and evidence of repairs which can all impact their value. Exceptions to this include extremely rare banknotes where there are few surviving examples (ex: National Gold Bank Note). The oldest one yen notes include the Meiji Tsūhō series which were first issued in 1872 and later abolished in 1899.


1 yen note, Collecting
These were mostly made in Germany with a print run of 39,814,943 notes from in Frankfurt, and 5,394,916 notes made in Japan during their fifteen year use in commerce. This combined figure is the third highest print run after the smaller denomination Meiji Tsūhō 10 and 20 sen notes. Notes from the one yen denomination are thus easier to obtain as they were made in relatively large amounts. Many of the surviving examples are in better conditions due to a portion being made domestically.


1 yen note, Collecting
These notes can be obtained in average condition for 6,000+ yen (~$60+ USD), with prices reaching 100,000 yen (~$1,000 USD) for examples in top conditions. Professional grading is recommended for this series as "many" counterfeit notes exist on the market. The next series are National Bank Notes issued from 1873 to 1880 in two different varieties. Both of these "old" and "new" national one yen banknote varieties are now rare due to events surrounding the aftermath of the Satsuma Rebellion in 1877.


1 yen note, Collecting
In order to pay for this event a large amount of banknotes were printed and released into circulation as a way to ease the economic situation. This wound up having a negative effect in the form of rampant inflation which caused National banknotes to be actively collected by officials. These are now popular banknotes among collectors which are rarely seen on the marketplace. When they are up for the sale, one yen national bank notes sell in the hundreds of thousands of yen ($1,000s USD) in average condition.


1 yen note, Collecting
It is recommended that ungraded notes be checked for authenticity given their rarity. The final government series include one yen Modified "Jingū" Banknotes issued from 1881 to 1886. These are also popular as they are Japan's first portrait-filled banknote. "Jingū" one yen notes are scarcely valued in the tens to hundreds of thousands of yen ($100s-$1000s USD) depending on condition as they were not issued for a long period of time.


1 yen note, Collecting
Daikokuten one yen notes were part of the first series to be issued by the newly formed Bank of Japan in 1885. These were not in circulation for long as they suffered from design defects which later prompted the issuance of replacement notes. As these were the first notes released by the bank of Japan they now boast a considerable premier element. The value of "Daikokuten" one yen notes range from the tens of thousands of yen in average condition ($100s USD), to hundreds of thousands of yen in top conditions.


1 yen note, Collecting
Replacement modified convertible banknotes were issued from 1889 to 1917 in two different varieties by serial number appearance. One yen notes from the first series are called Kanji one yen (漢数字1円), and are often sold on the market in average condition. These notes become rare when found in uncirculated grades with values in the hundreds of thousands of yen ($1,000s USD). The second variety is referred to as Taishō one yen banknotes (大正兌換銀行券1円), and are valued by their block numbers (ex: "{254}"). Notes with low block numbers are valued the most when compared to those with "{200}" and higher.


1 yen note, Collecting
The next series is known as the "First issue" which was released during World War II in two different varieties. These notes are inexpensive and are commonly collected with the exception of "SPECIMEN" notes. Finally, notes from the last "A series" are valued according to their serial number in a matter similar to 50 sen "B series" notes. The most valuable notes have serial numbers ending in "13", "32", "42" and "44". Notes issued on behalf of the Bank of Japan have "1" as the first serial digit, while government issued notes use the first digit "2". Spending one yen banknotes issued by the Bank of Japan is not advised due to the financial loss incurred by doing so.


1 µm process
The 1 μm process refers to the level of MOSFET semiconductor process technology that was commercialized around the 1984–1986 timeframe, by leading semiconductor companies like NTT, NEC, Intel and IBM. It was the first process where CMOS was common (as opposed to NMOS).


1 µm process
The earliest MOSFET with a 1 μm NMOS channel length was fabricated by a research team led by Robert H. Dennard, Hwa-Nien Yu and F.H. Gaensslen at the IBM T.J. Watson Research Center in 1974.


1 × 1
1 × 1 (One Times One, sometimes stylized I × I) is a 1944 book of poetry by American poet E. E. Cummings. Cummings's biographer Richard S. Kennedy described the theme of the book, Cummings's ninth, as "oneness and the means (one times one) whereby that oneness is achieved—love". The book contains 54 poems, including portraits of people important to Cummings, and antiwar poems. It received the Shelley Memorial Award in 1945, and was reissued by publisher Harcourt Brace in 1954.


1 Şişe Aşk
1 Şişe Aşk (1 Bottle of Love) is the first studio album by Cypriot-Turkish singer Buray. It was released on 14 August 2015 by Sony Music.


1 Şişe Aşk, Release and content
1 Şişe Aşk is Buray's first album. It contains 8 songs in total. Bahadır Tanrıvermiş served as the album's music director. All of the pieces in the album were written by Gözde Ançel, and composed by Buray together with Ançel. Buray arranged all of the songs in the album.


1 Şişe Aşk, Release and content
Buray explained the production of the album as follows: "My album 1 Şişe Aşk is a result of a 2-year project. Out of hundreds of compositions that we prepared, I chose the ones that were close to my own style and kneaded with my own soul. All of the arrangements were done by me. The lyrics are by Gözde Ançel, and most of the music was made through our collaboration with Gözde. At first, I had no intention of making an album. I had a very enjoyable way of life in Australia and I didn't want to leave it at first. 2 years ago I felt the right time was coming and I let the events flow."


1 − 1 + 2 − 6 + 24 − 120 + ...
is a divergent series, first considered by Euler, that sums the factorials of the natural numbers with alternating signs. Despite being divergent, it can be assigned a value of approximately 0.596347 by Borel summation.


1 − 1 + 2 − 6 + 24 − 120 + ..., Euler and Borel summation
This series was first considered by Euler, who applied summability methods to assign a finite value to the series. The series is a sum of factorials that are alternately added or subtracted. One way to assign a value to this divergent series is by using Borel summation, where one formally writes


1 − 1 + 2 − 6 + 24 − 120 + ..., Euler and Borel summation
If summation and integration are interchanged (ignoring that neither side converges), one obtains:


1 − 1 + 2 − 6 + 24 − 120 + ..., Euler and Borel summation
The summation in the square brackets converges when x<1{\displaystyle x<1}, and for those values equals 11+x{\displaystyle {\tfrac {1}{1+x}}}. The analytic continuation of 11+x{\displaystyle {\tfrac {1}{1+x}}} to all real x{\displaystyle x} leads to a convergent integral for the summation:


1 − 1 + 2 − 6 + 24 − 120 + ..., Euler and Borel summation
where E1(z) is the exponential integral. This is by definition the Borel sum of the series.


1 − 1 + 2 − 6 + 24 − 120 + ..., Connection to differential equations
The solution with stable equilibrium at (x,y) = (0,0) as t → ∞ has y(t) = 1/t, and substituting it into the first equation gives a formal series solution


1 − 1 + 2 − 6 + 24 − 120 + ..., Connection to differential equations
On the other hand, the system of differential equations has a solution


1 − 1 + 2 − 6 + 24 − 120 + ..., Connection to differential equations
By successively integrating by parts, the formal power series is  recovered as an asymptotic approximation to this expression for x(t). Euler argues (more or less) that since the formal series and the integral both describe the same solution to the differential equations, they should equal each other at t=1{\displaystyle t=1}, giving


1 − 2 + 3 − 4 + ⋯
In mathematics, 1 − 2 + 3 − 4 + ··· is an infinite series whose terms are the successive positive integers, given alternating signs. Using sigma summation notation the sum of the first m terms of the series can be expressed as∑n=1mn(−1)n−1. {\displaystyle \sum _{n=1}^{m}n(-1)^{n-1}.}


1 − 2 + 3 − 4 + ⋯
The infinite series diverges, meaning that its sequence of partial sums, (1, −1, 2, −2, ...), does not tend towards any finite limit. Nonetheless, in the mid-18th century, Leonhard Euler wrote what he admitted to be a paradoxical equation:1−2+3−4+⋯=14. {\displaystyle 1-2+3-4+\cdots ={\frac {1}{4}}.}


1 − 2 + 3 − 4 + ⋯
A rigorous explanation of this equation would not arrive until much later. Starting in 1890, Ernesto Cesàro, Émile Borel and others investigated well-defined methods to assign generalized sums to divergent series—including new interpretations of Euler's attempts. Many of these summability methods easily assign to 1 − 2 + 3 − 4 + ... a "value" of 1/4. Cesàro summation is one of the few methods that do not sum 1 − 2 + 3 − 4 + ..., so the series is an example where a slightly stronger method, such as Abel summation, is required.


1 − 2 + 3 − 4 + ⋯
The series 1 − 2 + 3 − 4 + ... is closely related to Grandi's series 1 − 1 + 1 − 1 + .... Euler treated these two as special cases of the more general sequence 1 − 2n + 3n − 4n + ..., where n = 1 and n = 0 respectively. This line of research extended his work on the Basel problem and leading towards the functional equations of what are now known as the Dirichlet eta function and the Riemann zeta function.


1 − 2 + 3 − 4 + ⋯, Divergence
The series' terms (1, −2, 3, −4, ...) do not approach 0; therefore 1 − 2 + 3 − 4 + ... diverges by the term test. Divergence can also be shown directly from the definition: an infinite series converges if and only if the sequence of partial sums converges to limit, in which case that limit is the value of the infinite series. The partial sums of 1 − 2 + 3 − 4 + ... are:


1 − 2 + 3 − 4 + ⋯, Divergence
1 − 2 = −1,1 − 2 + 3 = 2,1 − 2 + 3 − 4 = −2,1 − 2 + 3 − 4 + 5 = 3,1 − 2 + 3 − 4 + 5 − 6 = −3,


1 − 2 + 3 − 4 + ⋯, Divergence
The sequence of partial sums shows that the series does not converge to a particular number: for any proposed limit x, there exists a point beyond which the subsequent partial sums are all outside the interval [x−1, x+1]), so 1 − 2 + 3 − 4 + ... diverges.


1 − 2 + 3 − 4 + ⋯, Divergence
The partial sums include every integer exactly once—even 0 if one counts the empty partial sum—and thereby establishes the countability of the set Z{\displaystyle \mathbb {Z} } of integers.


1 − 2 + 3 − 4 + ⋯, Heuristics for summation, Stability and linearity
Since the terms 1, −2, 3, −4, 5, −6, ... follow a simple pattern, the series 1 − 2 + 3 − 4 + ... can be manipulated by shifting and term-by-term addition to yield a numerical value. If it can make sense to write s = 1 − 2 + 3 − 4 + ... for some ordinary number s, the following manipulations argue for s = 1⁄4:4s=(1−2+3−4+⋯)+(1−2+3−4+⋯)+(1−2+3−4+⋯)+(1−2+3−4+⋯)=(1−2+3−4+⋯)+1+(−2+3−4+5+⋯)+1+(−2+3−4+5+⋯)+(1−2)+(3−4+5−6⋯)=(1−2+3−4+⋯)+1+(−2+3−4+5+⋯)+1+(−2+3−4+5+⋯)−1+(3−4+5−6⋯)=1+(1−2+3−4+⋯)+(−2+3−4+5+⋯)+(−2+3−4+5+⋯)+(3−4+5−6⋯)=1+[(1−2−2+3)+(−2+3+3−4)+(3−4−4+5)+(−4+5+5−6)+⋯]=1+[0+0+0+0+⋯]4s=1{\displaystyle {\begin{array}{rclllll}4s&=&&(1-2+3-4+\cdots )&{}+(1-2+3-4+\cdots )&{}+(1-2+3-4+\cdots )&{}+(1-2+3-4+\cdots )\\&=&&(1-2+3-4+\cdots )&{}+1+(-2+3-4+5+\cdots )&{}+1+(-2+3-4+5+\cdots )&{}+(1-2)+(3-4+5-6\cdots )\\&=&&(1-2+3-4+\cdots )&{}+1+(-2+3-4+5+\cdots )&{}+1+(-2+3-4+5+\cdots )&{}-1+(3-4+5-6\cdots )\\&=&1+&(1-2+3-4+\cdots )&{}+(-2+3-4+5+\cdots )&{}+(-2+3-4+5+\cdots )&{}+(3-4+5-6\cdots )\\&=&1+[&(1-2-2+3)&{}+(-2+3+3-4)&{}+(3-4-4+5)&{}+(-4+5+5-6)+\cdots ]\\&=&1+[&0+0+0+0+\cdots ]\\4s&=&1\end{array}}}


1 − 2 + 3 − 4 + ⋯, Heuristics for summation, Stability and linearity
Although 1 − 2 + 3 − 4 + ... does not have a sum in the usual sense, the equation s = 1 − 2 + 3 − 4 + ... = 1⁄4 can be supported as the most natural answer if such a sum is to be defined. A generalized definition of the "sum" of a divergent series is called a summation method or summability method. There are many different methods and it is desirable that they share some Divergent series#Properties of summation methodsproperties of ordinary summation.


1 − 2 + 3 − 4 + ⋯, Heuristics for summation, Stability and linearity
What the above manipulations actually prove is the following: Given any summability method that is linear and stable and sums the series 1 − 2 + 3 − 4 + ..., the sum it produces is 1⁄4. Furthermore, since2s=(1−2+3−4+⋯)+(1−2+3−4+⋯)=1+(−2+3−4+⋯)+1−2+(3−4+5⋯)=0+(−2+3)+(3−4)+(−4+5)+⋯2s=1−1+1−1⋯{\displaystyle {\begin{array}{rcllll}2s&=&&(1-2+3-4+\cdots )&+&(1-2+3-4+\cdots )\\&=&1+{}&(-2+3-4+\cdots )&{}+1-2&{}+(3-4+5\cdots )\\&=&0+{}&(-2+3)+(3-4)+(-4+5)+\cdots \\2s&=&&1-1+1-1\cdots \end{array}}}such a method must also sum Grandi's series as 1 − 1 + 1 − 1 + ... = 1⁄2.


1 − 2 + 3 − 4 + ⋯, Heuristics for summation, Cauchy product
In 1891, Ernesto Cesàro expressed hope that divergent series would be rigorously brought into calculus, pointing out, "One already writes (1 − 1 + 1 − 1 + ...)2 = 1 − 2 + 3 − 4 + ... and asserts that both the sides are equal to 1⁄4." For Cesàro, this equation was an application of a theorem he had published the previous year, which is the first theorem in the history of summable divergent series. The details on his summation method are below; the central idea is that 1 − 2 + 3 − 4 + ... is the Cauchy product (discrete convolution) of 1 − 1 + 1 − 1 + ... with 1 − 1 + 1 − 1 + ....


1 − 2 + 3 − 4 + ⋯, Heuristics for summation, Cauchy product
The Cauchy product of two infinite series is defined even when both of them are divergent. In the case where an = bn = (−1)n, the terms of the Cauchy product are given by the finite diagonal sumscn=∑k=0nakbn−k=∑k=0n(−1)k(−1)n−k=∑k=0n(−1)n=(−1)n(n+1). {\displaystyle {\begin{array}{rcl}c_{n}&=&\displaystyle \sum _{k=0}^{n}a_{k}b_{n-k}=\sum _{k=0}^{n}(-1)^{k}(-1)^{n-k}\\[1em]&=&\displaystyle \sum _{k=0}^{n}(-1)^{n}=(-1)^{n}(n+1).\end{array}}}


1 − 2 + 3 − 4 + ⋯, Heuristics for summation, Cauchy product
The product series is then∑n=0∞(−1)n(n+1)=1−2+3−4+⋯. {\displaystyle \sum _{n=0}^{\infty }(-1)^{n}(n+1)=1-2+3-4+\cdots .}


1 − 2 + 3 − 4 + ⋯, Heuristics for summation, Cauchy product
Thus a summation method that respects the Cauchy product of two series — and assigns to the series 1 − 1 + 1 − 1 + ... the sum 1/2 — will also assign to the series 1 − 2 + 3 − 4 + ... the sum 1/4. With the result of the previous section, this implies an equivalence between summability of 1 − 1 + 1 − 1 + ... and 1 − 2 + 3 − 4 + ... with methods that are linear, stable, and respect the Cauchy product.


1 − 2 + 3 − 4 + ⋯, Heuristics for summation, Cauchy product
Cesàro's theorem is a subtle example. The series 1 − 1 + 1 − 1 + ... is Cesàro-summable in the weakest sense, called (C, 1)-summable, while 1 − 2 + 3 − 4 + ... requires a stronger form of Cesàro's theorem, being (C, 2)-summable. Since all forms of Cesàro's theorem are linear and stable, the values of the sums are as calculated above.


1 − 2 + 3 − 4 + ⋯, Specific methods, Cesàro and Hölder
To find the (C, 1) Cesàro sum of 1 − 2 + 3 − 4 + ..., if it exists, one needs to compute the arithmetic means of the partial sums of the series. The partial sums are:


1 − 2 + 3 − 4 + ⋯, Specific methods, Cesàro and Hölder
This sequence of means does not converge, so 1 − 2 + 3 − 4 + ... is not Cesàro summable.


1 − 2 + 3 − 4 + ⋯, Specific methods, Cesàro and Hölder
There are two well-known generalizations of Cesàro summation: the conceptually simpler of these is the sequence of (H, n) methods for natural numbers n. The (H, 1) sum is Cesàro summation, and higher methods repeat the computation of means. Above, the even means converge to 1⁄2, while the odd means are all equal to 0, so the means of the means converge to the average of 0 and 1⁄2, namely 1⁄4. So 1 − 2 + 3 − 4 + ... is (H, 2) summable to 1⁄4.


1 − 2 + 3 − 4 + ⋯, Specific methods, Cesàro and Hölder
The "H" stands for Otto Hölder, who first proved in 1882 what mathematicians now think of as the connection between Abel summation and (H, n) summation; 1 − 2 + 3 − 4 + ... was his first example. The fact that 1⁄4 is the (H, 2) sum of 1 − 2 + 3 − 4 + ... guarantees that it is the Abel sum as well; this will also be proved directly below.


1 − 2 + 3 − 4 + ⋯, Specific methods, Cesàro and Hölder
The other commonly formulated generalization of Cesàro summation is the sequence of (C, n) methods. It has been proven that (C, n) summation and (H, n) summation always give the same results, but they have different historical backgrounds. In 1887, Cesàro came close to stating the definition of (C, n) summation, but he gave only a few examples. In particular, he summed 1 − 2 + 3 − 4 + ..., to 1⁄4 by a method that may be rephrased as (C, n) but was not justified as such at the time. He formally defined the (C, n) methods in 1890 in order to state his theorem that the Cauchy product of a (C, n)-summable series and a (C, m)-summable series is (C, m + n + 1)-summable.


1 − 2 + 3 − 4 + ⋯, Specific methods, Abel summation
In a 1749 report, Leonhard Euler admits that the series diverges but prepares to sum it anyway:


1 − 2 + 3 − 4 + ⋯, Specific methods, Abel summation
... when it is said that the sum of this series 1 − 2 + 3 − 4 + 5 − 6 etc. is 1⁄4, that must appear paradoxical. For by adding 100 terms of this series, we get −50, however, the sum of 101 terms gives +51, which is quite different from 1⁄4 and becomes still greater when one increases the number of terms. But I have already noticed at a previous time, that it is necessary to give to the word sum a more extended meaning ...


1 − 2 + 3 − 4 + ⋯, Specific methods, Abel summation
Euler proposed a generalization of the word "sum" several times. In the case of 1 − 2 + 3 − 4 + ..., his ideas are similar to what is now known as Abel summation:


1 − 2 + 3 − 4 + ⋯, Specific methods, Abel summation
... it is no more doubtful that the sum of this series 1 − 2 + 3 − 4 + 5 etc. is 1⁄4; since it arises from the expansion of the formula 1⁄(1+1)2, whose value is incontestably 1⁄4. The idea becomes clearer by considering the general series 1 − 2x + 3x2 − 4x3 + 5x4 − 6x5 + &c. that arises while expanding the expression 1⁄(1+x)2, which this series is indeed equal to after we set x = 1.


1 − 2 + 3 − 4 + ⋯, Specific methods, Abel summation
There are many ways to see that, at least for absolute values |x| < 1, Euler is right in that1−2x+3x2−4x3+⋯=1(1+x)2. {\displaystyle 1-2x+3x^{2}-4x^{3}+\cdots ={\frac {1}{(1+x)^{2}}}.} One can take the Taylor expansion of the right-hand side, or apply the formal long division process for polynomials. Starting from the left-hand side, one can follow the general heuristics above and try multiplying by (1 + x) twice or squaring the geometric series 1 − x + x2 − .... Euler also seems to suggest differentiating the latter series term by term.


1 − 2 + 3 − 4 + ⋯, Specific methods, Abel summation
In the modern view, the generating function 1 − 2x + 3x2 − 4x3 + ... does not define a function at x = 1, so that value cannot simply be substituted into the resulting expression. Since the function is defined for all |x| < 1, one can still take the limit as x approaches 1, and this is the definition of the Abel sum:limx→1−∑n=1∞n(−x)n−1=limx→1−1(1+x)2=14. {\displaystyle \lim _{x\rightarrow 1^{-}}\sum _ {n=1}^{\infty } n(-x)^{n-1}=\lim _ {x\rightarrow 1^{-}}{\frac {1}{(1+x)^{2}}}={\frac {1}{4}}.}


1 − 2 + 3 − 4 + ⋯, Specific methods, Euler and Borel
Euler applied another technique to the series: the Euler transform, one of his own inventions. To compute the Euler transform, one begins with the sequence of positive terms that makes up the alternating series—in this case 1, 2, 3, 4, .... The first element of this sequence is labeled a0.


1 − 2 + 3 − 4 + ⋯, Specific methods, Euler and Borel
Next one needs the sequence of forward differences among 1, 2, 3, 4, ...; this is just 1, 1, 1, 1, .... The first element of this sequence is labeled Δa0. The Euler transform also depends on differences of differences, and higher iterations, but all the forward differences among 1, 1, 1, 1, ... are 0. The Euler transform of 1 − 2 + 3 − 4 + ... is then defined as12a0−14Δa0+18Δ2a0−⋯=12−14. {\displaystyle {\frac {1}{2}}a_{0}-{\frac {1}{4}}\Delta a_{0}+{\frac {1}{8}}\Delta ^{2}a_{0}-\cdots ={\frac {1}{2}}-{\frac {1}{4}}.}


1 − 2 + 3 − 4 + ⋯, Specific methods, Euler and Borel
In modern terminology, one says that 1 − 2 + 3 − 4 + ... is Euler summable to 1⁄4.


1 − 2 + 3 − 4 + ⋯, Specific methods, Euler and Borel
The Euler summability also implies Borel summability, with the same summation value, as it does in general.


1 − 2 + 3 − 4 + ⋯, Specific methods, Separation of scales
Saichev and Woyczyński arrive at 1 − 2 + 3 − 4 + ... = 1⁄4 by applying only two physical principles: infinitesimal relaxation and separation of scales. To be precise, these principles lead them to define a broad family of "φ-summation methods", all of which sum the series to 1⁄4:


1 − 2 + 3 − 4 + ⋯, Specific methods, Separation of scales
This result generalizes Abel summation, which is recovered by letting φ(x) = exp(−x). The general statement can be proved by pairing up the terms in the series over m and converting the expression into a Riemann integral. For the latter step, the corresponding proof for 1 − 1 + 1 − 1 + ... applies the mean value theorem, but here one needs the stronger Lagrange form of Taylor's theorem.


1 − 2 + 3 − 4 + ⋯, Generalization
The threefold Cauchy product of 1 − 1 + 1 − 1 + ... is 1 − 3 + 6 − 10 + ..., the alternating series of triangular numbers; its Abel and Euler sum is 1⁄8. The fourfold Cauchy product of 1 − 1 + 1 − 1 + ... is 1 − 4 + 10 − 20 + ..., the alternating series of tetrahedral numbers, whose Abel sum is 1⁄16.


1 − 2 + 3 − 4 + ⋯, Generalization
Another generalization of 1 − 2 + 3 − 4 + ... in a slightly different direction is the series 1 − 2n + 3n − 4n + ... for other values of n. For positive integers n, these series have the following Abel sums:1−2n+3n−⋯=2n+1−1n+1Bn{\displaystyle 1-2^{n}+3^{n}-\cdots ={\frac {2^{n+1}-1}{n+1}}B_{n}}where Bn are the Bernoulli numbers. For even n, this reduces to1−22k+32k−⋯=0,{\displaystyle 1- 2^{2k}+3^{2k}-\cdots =0,}which can be interpreted as stating that negative even values of the Riemann zeta function are zero. This sum became an object of particular ridicule by Niels Henrik Abel in 1826:


1 − 2 + 3 − 4 + ⋯, Generalization
Divergent series are on the whole devil's work, and it is a shame that one dares to found any proof on them. One can get out of them what one wants if one uses them, and it is they which have made so much unhappiness and so many paradoxes. Can one think of anything more appalling than to say that


1 − 2 + 3 − 4 + ⋯, Generalization
where n is a positive number. Here's something to laugh at, friends.


1 − 2 + 3 − 4 + ⋯, Generalization
Cesàro's teacher, Eugène Charles Catalan, also disparaged divergent series. Under Catalan's influence, Cesàro initially referred to the "conventional formulas" for 1 − 2n + 3n − 4n + ... as "absurd equalities", and in 1883 Cesàro expressed a typical view of the time that the formulas were false but still somehow formally useful. Finally, in his 1890 Sur la multiplication des séries, Cesàro took a modern approach starting from definitions.


1 − 2 + 3 − 4 + ⋯, Generalization
The series are also studied for non-integer values of n; these make up the Dirichlet eta function. Part of Euler's motivation for studying series related to 1 − 2 + 3 − 4 + ... was the functional equation of the eta function, which leads directly to the functional equation of the Riemann zeta function. Euler had already become famous for finding the values of these functions at positive even integers (including the Basel problem), and he was attempting to find the values at the positive odd integers (including Apéry's constant) as well, a problem that remains elusive today.


1 − 2 + 3 − 4 + ⋯, Generalization
The eta function in particular is easier to deal with by Euler's methods because its Dirichlet series is Abel summable everywhere; the zeta function's Dirichlet series is much harder to sum where it diverges. For example, the counterpart of 1 − 2 + 3 − 4 + ... in the zeta function is the non-alternating series 1 + 2 + 3 + 4 + ..., which has deep applications in modern physics but requires much stronger methods to sum.


1 − 2 + 4 − 8 + ⋯
This is the current revision of this page, as edited by 73.168.5.183 (talk) at 04:44, 3 April 2020 (→P-adic numbers). The present address (URL) is a permanent link to this version.


1 − 2 + 4 − 8 + ⋯
In mathematics, 1 − 2 + 4 − 8 + ⋯ is the infinite series whose terms are the successive powers of two with alternating signs. As a geometric series, it is characterized by its first term, 1, and its common ratio, −2.


1 − 2 + 4 − 8 + ⋯
As a series of real numbers it diverges, so in the usual sense it has no sum. In a much broader sense,  the series is associated with another value besides ∞, namely 1/3, which is the limit of the series using the 2-adic metric.


1 − 2 + 4 − 8 + ⋯, Historical arguments
Gottfried Leibniz considered the divergent alternating series 1 − 2 + 4 − 8 + 16 − ⋯ as early as 1673. He argued that by subtracting either on the left or on the right, one could produce either positive or negative infinity, and therefore both answers are wrong and the whole should be finite:


1 − 2 + 4 − 8 + ⋯, Historical arguments
Now normally nature chooses the middle if neither of the two is permitted, or rather if it cannot be determined which of the two is permitted, and the whole is equal to a finite quantity


1 − 2 + 4 − 8 + ⋯, Historical arguments
Leibniz did not quite assert that the series had a sum, but he did infer an association with 1/3 following Mercator's method. The attitude that a series could equal some finite quantity without actually adding up to it as a sum would be commonplace in the 18th century, although no distinction is made in modern mathematics.


1 − 2 + 4 − 8 + ⋯, Historical arguments
After Christian Wolff read Leibniz's treatment of Grandi's series in mid-1712, Wolff was so pleased with the solution that he sought to extend the arithmetic mean method to more divergent series such as 1 − 2 + 4 − 8 + 16 − ⋯. Briefly, if one expresses a partial sum of this series as a function of the penultimate term, one obtains either 4m + 1/3 or −4n + 1/3. The mean of these values is 2m − 2n + 1/3, and assuming that m = n at infinity yields 1/3 as the value of the series.


1 − 2 + 4 − 8 + ⋯, Historical arguments
Leibniz's intuition prevented him from straining his solution this far, and he wrote back that Wolff's idea was interesting but invalid for several reasons. The arithmetic means of neighboring partial sums do not converge to any particular value, and for all finite cases one has n = 2m, not n = m. Generally, the terms of a summable series should decrease to zero; even 1 − 1 + 1 − 1 + ⋯ could be expressed as a limit of such series. Leibniz counsels Wolff to reconsider so that he "might produce something worthy of science and himself."


1 − 2 + 4 − 8 + ⋯, Modern methods, Geometric series
Any summation method possessing the properties of regularity, linearity, and stability will sum a geometric series


1 − 2 + 4 − 8 + ⋯, Modern methods, Geometric series
In this case a = 1  and r = −2, so the sum is 1/3.


1 − 2 + 4 − 8 + ⋯, Modern methods, Euler summation
In his 1755 Institutiones, Leonhard Euler effectively took what is now called the Euler transform of 1 − 2 + 4 − 8 + ⋯, arriving at the convergent series 1/2 − 1/4 + 1/8 − 1/16 + ⋯. Since the latter sums to 1/3, Euler concluded that 1 − 2 + 4 − 8 + ... = 1/3. His ideas on infinite series do not quite follow the modern approach; today one says that 1 − 2 + 4 − 8 + ... is Euler summable and that its Euler sum is 1/3.


1 − 2 + 4 − 8 + ⋯, Modern methods, Euler summation
The Euler transform begins with the sequence of positive terms:


1 − 2 + 4 − 8 + ⋯, Modern methods, Euler summation
which is just the same sequence. Hence the iterated forward difference sequences all start with Δna0 = 1 for every n. The Euler transform is the series


1 − 2 + 4 − 8 + ⋯, Modern methods, Euler summation
This is a convergent geometric series whose sum is 1/3 by the usual formula.


1 − 2 + 4 − 8 + ⋯, Modern methods, Borel summation
The Borel sum of 1 − 2 + 4 − 8 + ⋯ is also 1/3; when Émile Borel introduced the limit formulation of Borel summation in 1896, this was one of his first examples after 1 − 1 + 1 − 1 + ⋯


1 − 2 + 4 − 8 + ⋯, Modern methods, P-adic numbers
The sequence of partial sums associated with 1−2+4−8…{\displaystyle 1-2+4-8\ldots } in the 2-adic metric is


1 − 2 + 4 − 8 + ⋯, Modern methods, P-adic numbers
and the limit of this sequence is 01¯1=13{\displaystyle {\overline {01}}1={\frac {1}{3}}} in the 2-adic metric. Thus 1−2+4−8… =13{\displaystyle 1-2+4-8\ldots ={\frac {1}{3}}}.


1! 2! 3! 4! Yoroshiku!
1! 2 ! 3! 4! Yoroshiku! (１！２！３！４！ヨロシク！) is the 4th single by Japanese girl group SKE48. It reached the 2nd place on the weekly Oricon Singles Chart and, as of February 6, 2012 (issue date), has sold 175,027 copies.


1! 2! 3! 4! Yoroshiku!
This was last full version music video featured on SKE48 official channel (YouTube); starting from "Banzai Venus" only short versions are featured.


1% (South Park)
"1%" is the twelfth episode of the fifteenth season of the American animated television series South Park, and the 221st episode overall. It first aired on Comedy Central in the United States on November 2, 2011. In the episode, Cartman feels persecuted after he is blamed for causing his school to attain a low score on a national fitness test. As he confides in his sapient stuffed animals, they end up becoming targeted for mutilation.


1% (South Park)
The episode was written by series co-creator Trey Parker, and is a parody of the Occupy Wall Street movement and the late-2000s recession.


1% (South Park), Plot
The assembled student body of South Park Elementary is informed that they have scored the lowest in the entire country on the Presidential Fitness Test due to Eric Cartman's extremely poor health, which single-handedly ruined what would have been the school's otherwise acceptable average; as punishment, the students are forced to alternate physical education in place of recess for four weeks.


1% (South Park), Plot
When they rebuke Cartman for this, he accuses them of being "the 99%" that is "ganging up" on him, the 1%, but when Craig Tucker dismissively tells him to go home and cry to his stuffed animals as usual, Cartman does just that. As he commiserates with his five stuffed animals, he carries on an imaginary conversation with them. When the toys "tell" him that the Fitness Test is Barack Obama's fault, Cartman concludes that he is being blamed because it is politically incorrect to blame a black president, even accusing the student-filled cafeteria of being a "99% rally" being held against him.


1% (South Park), Plot
This inspires Butters Stotch and Jimmy Valmer to form a 99% club to protest their being punished for Cartman's poor health. An angry group of fifth graders agrees, saying that it is time to make Cartman suffer.


1% (South Park), Plot
When the head of the Colorado Division of the President's Council on Fitness, Sports, and Nutrition refuses to drop Cartman's test scores from the school's average, Butters and Jimmy stage a two-man protest outside his office that despite its size, attracts the attention of the police, who create a two square mile perimeter around them, and the news media, who mistakenly report that they are occupying the Red Robin two doors down from the Council office.


1% (South Park), Plot
Meanwhile, Cartman discovers his beloved stuffed animals being mutilated and destroyed one by one, beginning with his long-beloved Clyde Frog, nailed to a tree with his stuffing ripped out, and the word "VENGEANCE" written beneath him. Cartman regards his animals' destruction as their "murders", and even holds a funeral service for Clyde Frog.


1% (South Park), Plot
When Stan Marsh, Kyle Broflovski, and Kenny McCormick ask the fifth-graders whether they are behind the mutilations, they do not give a straightforward answer, but state that Cartman has had a comeuppance coming his way for a long time, and that because Stan and the other fourth-graders have failed to rein in Cartman's problematic behavior, the fifth-graders have something big planned to remedy the problem, in which they warn Stan and his friends not to interfere. When Peter Panda, another of Cartman's toys, is destroyed by a fire set in Cartman's bedroom one night, he seeks refuge with his three surviving stuffed animals at Token Black's house, because, according to Cartman, black people are not subject to criticism or harassment.


1% (South Park), Plot
Meanwhile, the fifth-graders stage an "83%" protest right next to Butters and Jimmy's 99% protest, proclaiming that as the 83%, they are tired of being punished for the fourth grade class. This begins an argument between the two groups that degenerates into a physical altercation that media characterize as "class warfare".


1% (South Park), Plot
Despite being at Token's mansion, Cartman discovers Muscle Man Marc melted in a boiling pot of water and Rumper Tumpskin chained to a wall with explosives, which Cartman triggers with a tripwire. He finds the remaining toy, a doll named Polly Prissypants, sitting in an armchair with a revolver, claiming responsibility for all the toy "murders". Polly "explains" that she did this because his friends were right when they said that he needed to grow up.


1% (South Park), Plot
Unbeknownst to him, Cartman's stunned friends watch the bizarre scene unfold from a balcony, as do Cartman's mother and Token's parents from outside a window. Cartman is incredulous that Polly murdered her friends, but Polly explains they were holding her and Cartman back, and that now, with the latter deaths occurring at Token's house, the blame will fall on him, while she and Cartman can grow up together.


1% (South Park), Plot
When Cartman points out that black people cannot be blamed for anything any more, Polly realizes her catastrophic error, and convinces Cartman to shoot her to death in order to escape blame himself, which Cartman tearfully does. Shocked at what they have just witnessed, Stan asks "what the hell?" Kyle, knowing how psychologically disturbed Cartman is, explains that "we told him to grow up so he got rid of his stuffed animals".


1% (South Park), Plot
The protests eventually fall apart, as the 99% and 83% are replaced by various smaller percentages, according to a reporter, who then rushes away when he is informed that protestors are now "occupying" a Macaroni Grill.


1% (South Park), Production
According to the DVD commentary, the episode was based on cut footage from the season 14 episode "201" in which Cartman holds a tea party with his stuffed animals, and discusses the identity of his father with his mother. The episode included Marc Jacobs as one of Cartman's dolls because Jacobs has a real life tattoo of Cartman's Clyde Frog and Rumpertumskin dolls. Jacobs commemorated the reference by getting a Marc Jacobs doll tattoo on his arm.


1% (South Park), Reception
Ryan McGee of The A.V. Club graded the episode an "A−", stating: "What worked in this episode didn't really have much to do with what was funny about it. While there were a few laughs to be had, humor wasn't really the focus. The focus instead lay on the twisted mind of Eric Cartman actually going through a potentially life-changing part of his existence."


1% (South Park), Reception
Ramsey Isler of IGN gave the episode a "Great" rating of 8 out of 10, noting the "clever bait-and-switch" on the part of Matt Stone and Trey Parker, who indicated in their pre-air press that the episode would parody the Occupy Wall Street movement, only to focus more on Cartman's psychological growth. Though Isler felt it followed past formula for Cartman, he thought it enhanced the episode's theme, lent itself to memorable humor, and found Cartman's maturation, much like the plot of "You're Getting Old", to be surprising and interesting, if not exceptionally funny.


1% (South Park), Reception
Katia McGlynn of The Huffington Post, who found the episode's themes funny, praised Parker and Stone for their ability to make a topical episode in only six days, and to use the fourth grade class as a microcosm to parody current events.


1% (South Park), Reception
Asawin Suebsaeng of Mother Jones stated that despite Parker and Stone's libertarian leanings and their tendency to skewer orthodoxies in general and the political left and right in particular, the episode's "blatant" analogs did not merely target the Occupy Wall Street movement, but what Suebsaeng calls "the whiners, paranoid excuse-makers, and irrational Obama-blamers", as well as overreaction on the part of police and the media, and panic over class warfare. According to Suebsaeng, this underscores Parker and Stone's formula for mining politics for crude, contrarian humor rather than taking it too seriously.


1% (South Park), Reception
Ken Tucker of Entertainment Weekly did not find the episode particularly funny, owing to what he felt was its uncharacteristically mild obviousness, and the number of different targets of its parody, which he felt rendered the humor mostly aimless and "flimsy".


1% (film)
1% (also known as Outlaws) is a 2017 Australian biker film directed by Stephen McCallum and starring Ryan Corr, Abbey Lee and Matt Nable, who also wrote the film. It premiered at the 2017 Toronto International Film Festival in September 2017 where the film was acquired by A24 for North American distribution.


1% (film), Premise
Set within the primal underworld of outlaw motorcycle club gangs, the film follows the heir to the throne of a motorcycle club, who has to save his brother's life by betraying his president.


1% (film), Release
1% had its world premiere in the Discovery section at the 2017 Toronto International Film Festival on 9 September 2017. A24 and DirecTV Cinema subsequently acquired the North American distribution rights to the film, for a tentative 2019 wide release.


1% (film), Reception, Box office
The film grossed $76,151 in worldwide theatrical box office, all within Australia.


1% (film), Reception, Critical response
On review aggregator website Rotten Tomatoes, the film holds an approval rating of 47% based on 17 reviews and an average rating of 3.68/10. On Metacritic, the film has a weighted average score of 24 out of 100, based on 4 critics, indicating "generally unfavorable reviews".


1% (song)
"1%" is the fourth solo single by Tomomi Itano (a Japanese idol, a member of AKB48). It was released in Japan on June 12, 2013, on the label You, Be Cool! (a subsidiary of King Records).


1% (song)
The physical CD single reached fourth place in the Japanese Oricon weekly singles chart.


1% (song), Background
The single was released in four versions: Type A, Type B, a regular edition, and a theater edition.


1% rule (Internet culture)
In Internet culture, the 1% rule is a rule of thumb pertaining to participation in an internet community, stating that only 1% of the users of a website add content, while the other 99% of the participants only lurk. Variants include the 1–9–90 rule (sometimes 90–9–1 principle or the 89:10:1 ratio), which states that in a collaborative website such as a wiki, 90% of the participants of a community only consume content, 9% of the participants change or update content, and 1% of the participants add content.


1% rule (Internet culture)
Similar rules are known in information science; for instance, the 80/20 rule known as the Pareto principle states that 20 percent of a group will produce 80 percent of the activity, however the activity is defined.


1% rule (Internet culture), Definition
According to the 1% rule, about 1% of Internet users are responsible for creating content, while 99% are merely consumers of that content. For example, for every person who posts on a forum, generally about 99 other people view that forum but do not post. The term was coined by authors and bloggers Ben McConnell and Jackie Huba, although earlier references to the same concept did not use this name.


1% rule (Internet culture), Definition
The terms lurk and lurking, in reference to online activity, are used to refer to online observation without engaging others in the community.


1% rule (Internet culture), Definition
A 2005 study of radical Jihadist forums found 87% of users had never posted on the forums, 13% had posted at least once, 5% had posted 50 or more times, and only 1% had posted 500 or more times.


1% rule (Internet culture), Definition
A 2014 peer-reviewed paper entitled "The 1% Rule in Four Digital Health Social Networks: An Observational Study" empirically examined the 1% rule in health oriented online forums. The paper concluded that the 1% rule was consistent across the four support groups, with a handful of "Superusers" generating the vast majority of content. A study later that year, from a separate group of researchers, replicated the 2014 van Mierlo study in an online forum for depression. Results indicated that the distribution frequency of the 1% rule fit followed Zipf's Law, which is a specific type of a power law.


1% rule (Internet culture), Definition
The "90–9–1" version of this rule states that for websites where users can both create and edit content, 1% of people create content, 9% edit or modify that content, and 90% view the content without contributing.


1% rule (Internet culture), Definition
The actual percentage is likely to vary depending upon the subject matter. For example, if a forum requires content submissions as a condition of entry, the percentage of people who participate will probably be significantly higher than one percent, but the content producers will still be a minority of users. This is validated in a study conducted by Michael Wu, who uses economics techniques to analyze the participation inequality across hundreds of communities segmented by industry, audience type, and community focus.


1% rule (Internet culture), Definition
The 1% rule is often misunderstood to apply to the Internet in general, but it applies more specifically to any given Internet community. It is for this reason that one can see evidence for the 1% principle on many websites, but aggregated together one can see a different distribution. This latter distribution is still unknown and likely to shift, but various researchers and pundits have speculated on how to characterize the sum total of participation.


1% rule (Internet culture), Definition
Research in late 2012 suggested that only 23% of the population (rather than 90 percent) could properly be classified as lurkers, while 17% of the population could be classified as intense contributors of content. Several years prior, results were reported on a sample of students from Chicago where 60 percent of the sample created content in some form.


1% rule (Internet culture), Participation inequality
A similar concept was introduced by Will Hill of AT&T Laboratories and later cited by Jakob Nielsen; this was the earliest known reference to the term "participation inequality" in an online context. The term regained public attention in 2006 when it was used in a strictly quantitative context within a blog entry on the topic of marketing.


1% rule (aviation medicine)
In the field of aviation medicine, the 1 percent rule is a risk threshold that is applied to the medical fitness of pilots. The 1 percent rule states that a 1% per annum risk (See also Risk management) of medical incapacitation is the threshold between acceptable and unacceptable. In other words:


1% rule (aviation medicine)
Applying this 1 percent rule would result in an airline pilot being denied a medical certificate if their risk of a medical incapacitation (e.g. heart attack, convulsion, stroke, faint etc) was determined as being greater than 1% during the year.


1% rule (aviation medicine)
This 1 percent rule began in the late 1980s and early 1990s in a series of British and then European aviation cardiology workshops. The application of this "1 percent rule" has subsequently spread beyond the domain of aviation cardiology to all potential causes of medical incapacitation.


1% rule (aviation medicine)
The reasoning that was used in the development of the original aviation medical 1 percent rule is well described in Flight Safety and Medical Incapacitation Risk of Airline Pilots (see references). In this article the authors argue that changes in the underlying assumptions, that were the basis of the 1 percent rule, have been such that a 2 percent rule may be an appropriate modern analogue.


1% rule (aviation medicine)
The application of this one percent rule is controversial. The civil aviation regulatory authorities of some nations employ such numerical risk thresholds while others do not. Of those that use numerical risk criteria there are differences in the levels of measured / calculated risk that are applied (1% per annum, 2% per annum etc.). There is also debate concerning the application of population statistics to an individual pilot and the utility and validity of the risk screening tools that are used by the civil aviation regulatory authorities (e.g. data from the Framingham Heart Study).


1%Club
The 1%Club is a non-profit organization which uses an online platform to connect people with ideas in developing countries with people, money and knowledge around the world. The basic idea is that people or organizations can offer 1% of their time, knowledge and income directly to a development project of their own choice. These projects need to be sustainable projects that stimulate the self-reliance of individuals anywhere in the world and improve their standard of living.


1%Club, Founders
The 1%Club was founded by Anna Chojnacka and Bart Lacroix who both have backgrounds in development cooperation. Anna Chojnacka began as youth representative on the General Meeting at the United Nations in 2003. She also worked as campaign leader at Fair Trade Original. Besides that Anna is a member of the Worldconnectors think tank, a think tank for international cooperation. Bart Lacroix worked in Tanzania as business and marketing manager at VSO. Furthermore, he was online marketing consultant for Africa Interactive and he worked as project manager for Butterfly Works They both specialized in applying Web 2.0 in order to increase participation, democracy and empowerment of disadvantaged groups worldwide.


1%Club, History
1%Club was established in 2008. The Dutch website was launched on April 1, 2008. The international website was launched on March 12, 2010. Anna Chojnacka developed the vision that money intended for development could be better spent, especially because internet was developing into a big cooperation system where people who never even met each other were able to create things together, for example Wikipedia! That is why she wondered what could happen if such a system would be used for developmental issues.


1%Club, History
Bart Lacroix also came up with the idea that people nowadays want to have a personal influence on development cooperation and that they want to see what happens with their money. The Manifesto International Cooperation 2.0 was written. This manifesto states that we live in a world where economic means are very unequally divided. The '1.0' way of dealing with this would hold that authorities come up with a fixed policy for a couple of years to fight poverty. In International Cooperation 2.0 the people have the power.


1%Club, History
Internet has become available all over the world through which we have become the first generation that has the knowledge and means to collaborate on a global scale. That is why an online marketplace platform was designed where projects can be started and people can personally choose which projects they want to direct their money, time or knowledge to. This website combines social media sites: both the people who created a project as the members introduce themselves in an interactive way and explain why they support certain projects with their gifts or time.


1%Club, International co-operation 2.0
'International co-operation 2.0’ is characterized by massive collaboration, self organisation, open-source marketing, collective intelligence and crowd sourcing. Anna Chojnacka and Bart Lacroix decided to apply this concept to development co-operation. In essence, the person itself is at the centre and can create his or her own world. The idea behind this is that participants of the marketplace become owners of the process, instead of it being directed from the top, this way trying to solve poverty together. By connecting people’s energy, passion, means, experience and knowledge on a world-wide scale, a structure comes into being where worldwide one to one development co-operation is possible. People can come together, publish small pieces of information online, share specific knowledge, ask specific questions and offer concrete expertise and solutions.


1%Club, Organizational structure
The 1%Club is a foundation with a Board that consists of five people. Furthermore, the 1%Club has a Recommendation Committee in the Netherlands consisting of prominent people who are concerned with the poverty problems and who are supportive of the goals of the 1%Club. The members of this Recommendation Committee are former minister-president Ruud Lubbers, rabbi Awraham Soetendorp, lawyer and professor Tineke Lambooy and lawyer Naema Tahir. At the moment 6 people work at the 1%Club offices in Amsterdam and Nairobi (Kenya). They are supported by volunteers, interns and partners (e.g. Accenture).


1%Club, Financing
The 1%Club calculates a service fee of 1% per donation from individuals and 5% from businesses. Sponsors and grants further cover 1%Club’s own costs. The 1%Club has developed the first version of the website with a start-up grant from NCDO. For 2009 and 2010 the 1%Club received a grant from the Dutch Ministry of Foreign Affairs in the category ‘young and renewing'. The 1%Club receives MFSII from 2011 till 2016. Therefore the 1%Club has joined the IMPACT alliance (‘Innovative Mitigation of Poverty Actions’). Also Oxfam Novib, Butterfly Works, Somo, Hirda and Fairfood joined this alliance.


1%Club, Projects
Within the 1%Club individual responsibility and trust are of importance. Members have their own profile page and can choose which projects they want to support. All people can see where the projects stand for, where the money, knowledge or time goes to and what the progress is. It can be monitored what went well and what went wrong. Ultimately it can be seen whether or not the project is completed.


1%Club, Projects
The people who run the projects are responsible for the outcome of the project and they have to demonstrate who they are, what they do and why they are doing it. All knowledge and information about the projects have to be available directly for everyone. A few of the conditions to become a 1%Club project are:


1&1 Drillisch
1&1 Drillisch AG (formerly known as: Drillisch AG) is a German telecommunication service provider listed on the TecDAX. Since 2017 it has been part of United Internet AG.


1&1 Drillisch, Infrastructure
The mobile network of the Drillisch company uses the network infrastructure provided by Telefónica Germany and Vodafone Germany. Based on regulations by the Competition regulator regarding the fusion of E-Plus and Telefónica Germany, Drillisch was able to secure 20% of the network's capacities for their uses. Due to historical reasons, the company still resorts to networks of other carriers for Digital subscriber line and Glass fiber in addition to their own 1&1 Versatel network. With 1&1 Versatel, the parent company United Internet holds their own network infrastructure and keeps adding customer connections to their broadband provisional services. In 2019, the company gained a bonus for setting up their own mobile network at the auction of 5G frequencies which is planned for 2021.


1&1 Drillisch, Infrastructure, Divisions
The core business Mobile telephony is handled by the wholly owned subsidiaries


1&1 Drillisch, Infrastructure, Divisions
The brands that are part of the Drillisch subsidiaries mostly market Mobile virtual network operators to private customers, but in addition to that also M2M products to business customers. The products use either the Telefónica or the Vodafone mobile networks, the latter generally reach a higher price average than those using the Telefónica network. The private customers business amounts to about 20 percent of the overall business. The business guidelines for the subsidiaries are generally centrally determined, so most brands show a similar structured portfolio of tariffs.


1&1 Drillisch, Infrastructure, Divisions
On April 1, 2014, a new selection of tariffs was introduced by all different providers. IQ-optimize Software AG mainly provides technical services for the parent group but also provides similar services of a smaller scope to business customers. Besides pure services, IQ-optimize Software AG also distributes licenses for their internally developed “workflow-management”-software called “Mapito”. In September 2014, Drillisch announced that in addition to the usage of 30 percent of the network capacities of the corporation they fused with (O2/E-Plus) in 2015, they also plan to create or take over up to 600 O2/E-Plus shops in Germany. In  an interview released on January 22, 2015, it was clarified, that the shops would be running under the new label "Yourfone".


1&1 Drillisch, Infrastructure, Divisions
Within the scope of internal restructuring, the operative businesses of the Eteleon AG and the MS Mobile Services GmbH were transferred over to the Drillisch Telecom GmbH on April 1, 2015. Based on a fusion contract, on March 17. 2015 the Eteleon AG was fused with MSP Holding GmbH on  and MS Mobile Services GmbH was absorbed directly by the Drillisch Telecom GmbH. Yourfone will be established as the stationary premium label and Smartmobil as the online premium label.


1&1 Drillisch, Infrastructure, Divisions
On May 27, 2015, Drillisch's plans to take over about 300 Telefónica retail shops in Germany were made public. The subsidiary Drillisch Telecom Gmbh changed their legal form to an AG and from then on operated under the name Drillisch Online AG. On December 28, 2017, Heiko Hambückers, Managing Director of Drillisch Online AG, announced the sale of the shops to Aptus.


1&1 Drillisch, Recent news
It was announced in May 2015 that the company would take over more than 300 shops and 300 employees from Telefónica Deutschland.


1&1 Ionos
1&1 Ionos (styled as 1&1 IONOS, formerly 1&1 Internet), is a web hosting company. It was founded in Germany in 1988 and is currently owned by United Internet. In addition to web hosting, it also provides domain registration, SSL certificates, email services, website builder packages and cloud hosting, as well as virtual private servers and dedicated servers. The company has two headquarters, one in Montabaur, Germany, and the other in Chesterbrook, Pennsylvania. It has approximately 2,000 employees in 40 countries, with eight million customers, ten data centers and over 90,000 servers. The company's CEO is Achim Weiss.


1&1 Ionos
1&1 in Germany also operates as an ISP through 1&1 Telecommunication (de), as a MVNE through 1&1 Drillisch, and as an own-brand MVNO using the O2 network.


1&1 Ionos, History
In 2000, the company changed its name to United Internet and moved its product business to 1&1 Internet AG. In the same year, 1&1 began operating in the United Kingdom, and three years later began serving United States customers. One of the company's biggest North American data centers is located in Lenexa, Kansas, which houses more than 40,000 servers.


1&1 Ionos, History
In 2018, 1&1 merged with cloud infrastructure specialists ProfitBricks (founded by Achim Weiss) and rebranded as 1&1 Ionos. The rebrand involved a name change and a slightly redesigned Web site, but the service offerings and prices initially stayed the same. However, 1&1 Ionos introduced some new services the following year, including a personal consultant service for customers. As of September 2019, 1&1 Ionos held second place in a ranking of the market share of global Web hosting providers.


1&1 Ionos, History
"As this new company is more than just a hosting provider, we have opted for a new name — and Ionos fits perfectly. It is inspired by the ionosphere; the upper part of the Earth's atmosphere that contains a high concentration of ions and free electrons. It is inspiring to look at, whether viewing from down on Earth, or up in outer space and is, of course, situated in the clouds."


1&1 Ionos, Eco-friendly efforts
1&1 Ionos uses sustainable methods to reduce carbon emissions, including the use of 100% renewable energy in data centers and administrative buildings in the UK and Germany. The carbon is offset in other locations across the world with green certificates or by using local renewable sources.


1&1 Ionos, Server outages
In April 2019, customers in the  United Kingdom complained of lengthy server outages due to a malfunctioning uninterruptible power supply (UPS), which resulted in Web sites being offline. Call center staff were also unable to answer customer questions due to support tools not functioning properly. 1&1 Ionos eventually fixed and addressed the issue, stating: "For when such cases occur, we have UPS systems and emergency power generators that ensure power supply is uninterrupted during an emergency.


1&1 Ionos, Server outages
One of the five UPS systems in the affected data center suffered a technical malfunction, which meant several servers suffered a temporary loss of power and had to be restarted. As file systems had to be repaired after the power failure, some servers were not immediately available again. We're continuing to look into the cause of the error of the affected UPS system, however all UPS systems are working properly again."


1+1 (Grin album)
1+1 is a 1972 album by Grin, featuring songs by their guitarist Nils Lofgren. As well as being an album in its own right, this was released by CBS in the UK as part of a 1976 double album set along with its predecessor Grin. The original LP was a gatefold. It had a photo of Nils on the front, with Bob & Bob on the back. The inside features triple exposure photos of the band members performing, giving the impression of motion. The Sides are not labelled 1 & 2. The first side is labelled "Rockin' Side" and the flip side is labelled "Dreamy Side".


1+1 (Herbie Hancock and Wayne Shorter album)
1 + 1 is a duet studio album by Herbie Hancock (piano) and Wayne Shorter (soprano saxophone).


1+1 (Herbie Hancock and Wayne Shorter album), Overview
Hancock and Shorter perform 10 compositions on the album, including the Grammy Award-winning "Aung San Suu Kyi", named after the Burmese pro-democracy activist of the same name; "Joanna's Theme", which originally was on Hancock's original soundtrack to the film Death Wish; and "Diana", originally recorded for Shorter's album Native Dancer. It is Hancock's forty-first album and Shorter's twenty-first.


1+1 (TV channel)
1+1 (Ukrainian: один плюс один, odyn plyus odyn) is a national Ukrainian-language TV channel, owned by 1+1 Media Group. It has the second largest geographic reach of any channel in Ukraine, covering 95% of Ukraine's territory.


1+1 (TV channel), History
1+1 TV channel was founded in August 1995, headed by its original President Alexander Rodnyansky who also was its general director from 1996 to 2002. In 2002 he joined STS Media and since 2004 he has been the president of that Delaware-registered Russian company.


1+1 (TV channel), History
It immediately became a major force in the Ukrainian TV industry, even though in the very beginning the channel's programming consisted solely of movie broadcasts. Its first broadcast was within two months of its founding, in September 1995, and since 1997 has been broadcasting continuously on the second channel of the Ukrainian national TV network UT-2 (Ukrainian: Другий загальнонаціональний канал (УТ-2), liter. : "Druhyj zagalnonatsionalnyj kanal"), with an appropriate license of the Ukrainian National Television and Radio Council.


1+1 (TV channel), History
From the start, the channel was very successful, despite its initial  limited programming. Until 2004 1+1 broadcast only for 15 hours. Its program schedule was from 7 AM until 10 AM, followed by a break for four hours with the UT-2 channel from 10 AM until 1+1 backs, and then from 2 PM until 2AM. Beginning on 30 June 2004 the channel was given official permission to broadcast 24 hours each day. Since then, 1+1 has been able to create a complete round-the-clock broadcast schedule.


1+1 (TV channel), Programming and current schedule
1+1 was the first TV project in Ukraine to start actively inviting popular TV stars and other celebrities to take part in their live shows. The following is a list of most popular programmes currently being offered to 1+1 viewers:


1+1 (TV channel), Programming and current schedule
Television Service of News (TSN) is a news service programme, which has been operating on the channel from the start, and even its presenters have mainly remained the same. Such names as Ala Mazur (on TSN since January 3, 1997; in 1996, 1998, 1999, and 2001 was awarded the best news presenter of the year), Ljudmyla Dobrovolska, Oles Tereshenko and some others are very familiar to those who live in Ukraine, and according to the research, these people have the highest level of trust among news viewers. The TSN series air daily at 7:30 pm except Saturday. Oles Tereshenko leads the concluding TSN series of a day at 00:00 and a week as well every Sunday at 7:30 pm with the overview of political, social, and cultural life of Ukraine and the world.


1+1 (TV channel), Programming and current schedule
Breakfast with 1+1Working actively since 2002, Breakfast is the early morning programme, offering viewers a fun way to spend the morning. Originally, it was the Monday to Friday Breakfast, but since 2006 a weekend breakfast has been "cooked" as well, adding such activities to its "menu" as "Fitness", "Fashion Stuffs", "Relax! ", and "Don't sleep and travel". The programme offers an interactive area on its website.


1+1 (TV channel), Programming and current schedule
The Voice Of UkraineA reality talent show. Holos Krainy is part of the international syndication The Voice based on the reality singing competition launched in the Netherlands as The Voice of Holland, created by Dutch television producer John de Mol.


1+1 (TV channel), Programming and current schedule
Reality television programme, part of international syndication Wife Swap. Two families, usually from different social classes and lifestyles, swap wives/mothers  – and sometimes husbands – for two weeks.


1+1 (TV channel), Programming and current schedule
Reality television programme, based on the UK version of the same name. Four brides attend each other's weddings and rate them on their Dress, Ceremony, Food and Reception out of thirty marks.


1+1 (TV channel), Programming and current schedule
Dance competition television series, part of international syndication of the same name. The format of the show consists of a celebrity paired with a professional dancer. Each couple performs predetermined dances and competes against the others for judges' points and audience votes. The couple receiving the lowest combined total of judges' points and audience votes is eliminated each week until only the champion dance pair remains.


1+1 (TV channel), Programming and current schedule
Comedy series created by Volodymyr Zelensky. The members of comedy team of the same name tell the audience jokes, perform comedy numbers in a satire manner.


1+1 (TV channel), Awards and recognitions
The brand of the channel has become a traditional sign of quality in Ukrainian TV industry. The company's work and separate presenters have been recognized and highly evaluated not only by national specialists and experts in TV production, but also by many international experts and at TV forums.


1+1 (TV channel), Criticism
In 1999, after 1+1 had been broadcasting on UT-2 24h per day for two years with an appropriate license, the channel sent a claim to the Supreme Court of Ukraine requesting the TV company AITI, who used to hire UT-2 4 hours of broadcasting time earlier before, to give up its license as it had stopped its programming for a year. In the year 2000 the claim was decided for the 1+1 preference.


1+1 (TV channel), Criticism
Channel 1+1 has been the subject of continuing criticism during the 2004 presidential election, when it was heavily criticized for twisting information in favor of Viktor Yanukovych (Prime Minister of Ukraine at the time). Such behavior was typical for a Ukrainian-wide channel, because all of the media were under heavy pressure from the Administration of the President of President Kuchma. Furthermore, critics accused the channel of being part of the Social Democratic Party of Ukraine empire.


1+1 (TV channel), Criticism
In late November 2004 several journalists left the channel in protest against this pressure and almost all leading presenters had refused to report news. Those actions altogether with similar actions on other channels marked the beginning of the Orange revolution.


1+1 (TV channel), Criticism
In October 2006 Alexander Rodnyansky, the General Producer of Studio 1+1, won a hard appeal process in the Supreme Court of Ukraine, after the court gave ownership of 70% of the company's shares to Ihor Kolomyyskyy, and as he had claimed, in June 2005 there was an agreement signed between himself and Rodnyansky, that 70% of the company's shares were sold to Kolomyyskyy (for ~US$70 million).


1+1 (TV channel), Criticism
On the 2014-2015 New Year night the 80th Disco TV program was shown on 1+1. Oleg Gazmanov participated in it. He is one of the signatories of the petition in support of Russian actions in Crimea and Eastern Ukraine in 2014. That caused a scandal in Ukrainian society. The National Council on Television and Radio of Ukraine promised to review all facts of violation of broadcast regulations by Ukrainian TV and radio companies on the New Year night.


1+1 (song)
"1+1" is a song recorded by American recording artist Beyoncé for her fourth studio album, 4 (2011). It was released by Columbia Records in the United States on May 25, 2011, as a promotional single. Serving as the opening track on 4, it was written and produced by The-Dream, Tricky Stewart and Beyoncé. "1+1" was originally titled "Nothing But Love" and The-Dream had initially planned to include it on his second studio album, Love vs. Money (2009). A down-tempo contemporary R&B and soul music power ballad, "1+1" Beyoncé expressing her endless love to her soul mate; the lyrics make strong statements about the power of the relationship.


1+1 (song)
"1+1" garnered acclaim from music critics, who noted its resemblance to the work of American singers Prince and Sam Cooke. It was also complimented for its subtle instrumentation, which provides emphasis on Beyoncé's vocals. "1+1" peaked at number 82 on the Canadian Hot 100 chart and at number 57 on the US Billboard Hot 100 chart. Its accompanying music video was directed by Beyoncé herself, alongside Lauren Briet and Ed Burke, and it premiered on August 26, 2011.


1+1 (song)
The video was a "different" direction in the sense that it does not incorporate the heavy dance routines Beyoncé is known for, and that it experiments with psychedelic visual effects as well as innovative lighting, which give the clip a cinematic feel. The clip met with generally positive reception from music critics, who praised its aesthetic and sexual theme and claimed that it will be remembered as one of Beyoncé's most iconic visuals.


1+1 (song)
Soon after Beyoncé's performance on American Idol, a video that surfaced online received considerable coverage from different media. It was filmed by Jay-Z with a camera phone and shows Beyoncé rehearsing "1+1" backstage at American Idol. The ballad was included on Beyoncé's set list for a free concert as part of Good Morning America's Summer Concert Series, the ITV special A Night With Beyoncé, and her revue, 4 Intimate Nights with Beyoncé, held at the Roseland Ballroom in New York City. Beyoncé's live performances of "1+1" have received positive reception; a writer from HuffPost described her live performance on American Idol as "an epic, emotionally-charged [one]." American singers Dondria and Tiffany Evans have performed covers of the ballad, with lyrical modifications.


1+1 (song), Conception and release
"1+1" was initially written and titled "Nothing but Love" for Terius "The-Dream" Nash, who intended to include it on his second studio album, Love King (2010). He later gave it to Beyoncé Knowles for her fourth studio album 4, where she and Christopher "Tricky" Stewart did some additional writing. The song was produced by the trio at the Studio at the Palms in Paradise, Nevada and Triangle Sound Studio in Atlanta, Georgia, where Beyoncé recorded the song. The-Dream and Stewart did the musical arrangements and Beyoncé worked on arranging the vocals.


1+1 (song), Conception and release
Lee Blaske, Nikki Gallespi and Pete Wolford played the instruments, while Brian Thomas alongside Pat Thrall assisted in recording the music. Jordan Young then recorded Beyoncé's vocals. Tony Maserati mixed the track with assistance from Val Brathwaite, and Jason Sherwood, Mark Gray, Steven Dennis and Wolford all assisted in the audio engineering.


1+1 (song), Conception and release
Shortly after "1+1" was released online, Beyoncé debuted the ballad by performing a piano version on the finale of the tenth season of American Idol on May 25, 2011. "1+1" was made available for download only a few hours after her performance; its cover art was photographed by Anthony Duran. The song was released through the iTunes Store as a promotional single from 4 in the United States. People who pre-ordered 4 at the iTunes Store received a free download of "1+1". The song was not sent for airplay in the US as "Best Thing I Never Had" was favored as the second single, following the release of the lead single "Run the World (Girls)".


1+1 (song), Composition and lyrical interpretation
"1+1" is a downtempo R&B and soul music power ballad with influences of indie rock music. The song features "a soft, almost non-existent" backing beat and makes use of a guitar and a piano as its foundation, while wind chimes, sprinkling strings, synthesizers, funk-influenced bass and a pipe organ are also present. "1+1" is set in 12/8 time with a slow tempo of 50 beats per minute and was written in the key of G♭ major. Beyoncé's voice spans from the low note of F#3 to the high note of C6.


1+1 (song), Composition and lyrical interpretation
"1+1" essentially demonstrates her "urgent" and "raw" vocals; in an interview with Ray Rogers of Billboard magazine, Beyoncé stated that she wanted to use her album 4 to showcase this side of her vocal abilities: "I used a lot of the brassiness and grittiness in my voice that people hear in my live performances, but not necessarily on my records." Nadine Cheung wrote that the subtle instrumentation allows Beyoncé'ss voice to emphasise the emotional lyrics Amos Barshad of New York magazine and Tim Finney of Pitchfork Media described the vocals as similar to those of Whitney Houston's work.


1+1 (song), Composition and lyrical interpretation
Several critics including Matthew Perpetua of Rolling Stone noted that "1+1" is comparable to Sam Cooke's 1960 song "Wonderful World" and Prince's 1984 song "Purple Rain". Brandon Soderberg of Pitchfork explained that "Wonderful World"'s line, "don't know much about algebra", was retained during the conception of "1+1" by its producers, who however accentuated its "love song sentiment". Soderberg further wrote that "1+1" bears resemblance to "Purple Rain" as they both have similar "delicate guitars, melodramatic piano, and [Beyoncé affects Prince's] high-register whimper a few times". Jillian Mapes of Billboard magazine wrote that the guitar solo is similar to the ones in Bon Jovi's power ballads.


1+1 (song), Composition and lyrical interpretation
"1+1" begins with a low fidelity indie rock arrangement which is brought about by distorted guitar arpeggios and a discreet pipe organ. Beyoncé sings a meandering melody as she alternately references the pleasures of love and sex. Using simple arithmetic to describe her undying love for her partner, she begins the first verse as she affirms to her romantic interest that the only thing she is sure about are her feelings for him, "I don't know much about algebra, but I know that one plus one equals two ...


1+1 (song), Composition and lyrical interpretation
If I ain't got something, I don't give a damn / 'Cause I got it with you". In the pre-chorus lines, Beyoncé expresses her reliance on her man without whom she believes to be incomplete as she sings, "And it's me and you, that's all we'll have when the world is through / Because baby we ain't got nothing without love / Darling, you got enough love for the both of us".


1+1 (song), Composition and lyrical interpretation
Brandon Soderberg of Pitchfork commented that Beyoncé mixes "vulnerability and confidence" while singing the chorus lines, where she repeatedly pleads her romantic interest, "Make love to me when my days look low / Pull me in close and don't let me go / Make love to me when the world's at war / That our love will heal us all", while the music stays steady and soft with only a few piano chords and a baseline plucked guitar riff.


1+1 (song), Composition and lyrical interpretation
As she continues to chant about making love in apocalyptic circumstances, "So when the world's at war / Let our love heal us all", she projects a universal "all you need is love" feeling, as noted by Jillian Mapes. In the second verse, Beyoncé sings, "Hey! I don't know much about guns but I ... I've been shot by you", as she pushes the final word "you" up at a full octave. She then continues: "Hey! And I don't know when I'm gonna die, but I hope that I'm gonna die by you / Hey!


1+1 (song), Composition and lyrical interpretation
And I don't know much about fighting, but I, I know I will fight for you / Hey! Just when I ball up my fist, I realize that I'm laying right next to you". According to Thomas Conner of the Chicago Sun-Times, these lines are intended to show that love conquers all. The song ends with an intense electric guitar solo.


1+1 (song), Critical reception
"1+1" was lauded by music critics, who complimented the effective display of Beyoncé's emotive vocals due to the use of light instrumentation, and approved that the ballad was the opening song on 4. AOL Music's Contessa Gayles called it "an achy, screechy ballad – in the best way possible" and Nadine Cheung from AOL Radio noted that the minimal instrumentation highlights the song's lyrics, and effectively show Beyoncé's "powerful voice and impressive control", further writing, "The professions are so intense that there's no need for a complicated bridge or dramatic key change."


1+1 (song), Critical reception
Brandon Soderberg from Pitchfork wrote, "she really digs in and sells the song's knotty qualities, and when that over-the-top guitar break appears exactly when it should, it's cathartic. At that precise moment, this passionate pastiche of timeless pop becomes a classic all its own." Ryan Dombal, writing for the same music webzine, commented that Adele's 'Someone Like You' is the only recent pop ballad which comes close to "the power" of "1+1". Michael Cragg of The Guardian called the song a "loved up ballad" and praised Beyoncé for showcasing her raw vocals.


1+1 (song), Critical reception
Describing "1+1" as "[having] no interest in [Beyoncé'ss] typical pursuit of forward-thinking, energetic fare, preferring to throw the emphasis on her radio-destroying vocal chords", David Amidon of PopMatters wrote that the song "is the best result of this, finally providing Beyoncé a song that can compete with the favorites of this generation's parents."


1+1 (song), Critical reception
Jocelyn Vena of MTV News wrote, "Beyoncé may not know a thing about algebra, but when it comes to the math of power ballads, she totally gets it."


1+1 (song), Critical reception
Matthew Perpetua of Rolling Stone wrote that "the album [4] opens with its most tender ballad, a slow-burning number that calls back to both Sam Cooke's 'Wonderful World' and Prince's 'Purple Rain' without sounding like a retread of either tune [...] it sounds best in the context of the album, where its slow, steady build to a cathartic guitar break is the perfect introduction to a set of mostly low-key tracks about love and heartbreak."


1+1 (song), Critical reception
Similarly considering "1+1" to be "the perfect opener" of 4, Joanne Dorken of MTV UK wrote that it exposes a more vulnerable side of Beyoncé and that it will remain "a classic stripped-back slow jam from the diva." Praising Beyoncé's vocals, Jon Caramainca of The New York Times stated that "['1+1'] requires a vocal muscle few singers possess, and even fewer would care to deploy."


1+1 (song), Critical reception
Writing for The Baltimore Sun, Wesley Case included "1+1" in his list of Five Great Songs and praised song's concept, writing that he began crying when he heard the album version and called it "gut-wrenching" and "gorgeous". Case appreciated Beyoncé's sensitivity and concluded that it "fades to black like an ellipsis and it's so damn beautiful."


1+1 (song), Critical reception
Cameron Adams of the Herald Sun wrote that "1+1" is an "amazing [and] arguably the most honest and tender Beyoncé has sounded, singing 'help me let my guard down, make love to me'". Similarly, Claire Suddath of Time magazine commented that "1+1" is probably the finest ballad Beyoncé has delivered in years. Amos Barshad of New York magazine described "1+1" as "a big grand love ballad".


1+1 (song), Critical reception
Andy Kellman of Allmusic picked "1+1" as one of the album's top songs, describing it as "a sparse and placid vocal showcase, [which] fades in with a somber guitar line, throws up occasional and brief spikes in energy, and slowly recedes." Chris Coplan of Consequence of Sound commented that in contrast to the geometry taught at school, there is something interesting in "1+1"; he further wrote that ballad focuses on Beyoncé's "amazing vocal range" as it is not upbeat like most of her previous offerings. Leah Collins of Canada's Dose described the song as a "melodramatic soul ballad".


1+1 (song), Critical reception
A reporter from The Huffington Post stated that "1+1" is a departure from "Run the World (Girls)", noting that Beyoncé replaces the defiance of Run the World (Girls) with devotion [in '1+1']". He added that it is one of the first representations that "Beyoncé is keeping her promise that a whole new array of sounds will make their way into 4." Similarly, Rap-Up favored the track stating that "If 'Run the World (Girls)' wasn't your thing, this should do the trick." By contrast, Katy Hasty from HitFix criticized the song's lyrics and wrote that it "seem[s] the lyrics to '1+1' were penned by a second-grader."