DIALOG:
What is the meaning of Fixed-point theorem?
- Fixed-point theorem In mathematics, a fixed-point theorem is a result saying that a function "F" will have at least one fixed point (a point "x" for which "F"("x") = "x"), under some conditions on "F" that can be stated in general terms.
- What is the significance of this result?
- Results of this kind are amongst the most generally useful in mathematics.
- Are there any other interesting aspects about this article?
- The Banach fixed-point theorem gives a general criterion guaranteeing that, if it is satisfied, the procedure of iterating a function yields a fixed point.
- What is the difference between the two?
- By contrast, the Brouwer fixed-point theorem is a non-constructive result: it says that any continuous function from the closed unit ball in "n"-dimensional Euclidean space to itself must have a fixed point, but it doesn't describe how to find the fixed point (See also Sperner's lemma).
- What are some examples of the theorems?
- 
Next turn: For example, the cosine function is continuous in [−1,1] and maps it into [−1, 1], and thus must have a fixed point.


Problem: What could be the response? DIALOG:
What is the difference between a fire episode and a rocket power episode
- 
A: List of Rocket Power episodes This is a list of "Rocket Power" episodes.


QUESTION: Write another turn of this conversation. DIALOG:
What happened in 2014 with Sanki King?
- In 2014, Sanki worked for the first time with a local designer brand "Zeb-Tan".
- What happened in 2015 with Sanki King?
- He collaborated with The House of Arsalan Iqbal for the collection ‘Desirably Distressed’, which came out in March 2015.
- What happened in 2012 with Sanki King?
- He said, “In 2012, I painted a shutter in Arsalan Iqbal’s store.
- What happened in 2011 with Sanki King?
- Since Iqbal travels a lot, he finds graffiti very inspiring.
- What happened in 2010 with Sanki King?
- Then in May 2014 we worked on a collaborative venture for the next 10 months” Another collection of footwear and jewellery incorporating his designs "Devolution Chic" was showcased a month later at the 8th PFDC Sunsilk Fashion Week 2015.
- Are there any other interesting aspects about this article?
- 
ANS: King is one of the early leaders of b-boying and parkour in Pakistan.


question: Write a response. DIALOG:
When did the UN retreat from North Korea take place?
- UN retreat from North Korea The UN retreat from North Korea was the withdrawal of United Nations (UN) forces from North Korea that took place from 2–25 December 1950.
- What happened?
- 
response: On 30 September Republic of Korea Army (ROK) forces crossed the 38th Parallel, the de facto border between North and South Korea on the east coast of the Korean peninsula and this was followed by a general UN offensive into North Korea to pursue the shattered North Korean Korean People's Army (KPA).


Q: See the conversation. DIALOG:
What happened in the 2015 Berlin Marathon?
- 2015 Berlin Marathon The 2015 Berlin Marathon was the 42nd edition of the Berlin Marathon.
- When did the marathon happen?
- The marathon took place in Berlin, Germany, on 27 September 2015 and was the fourth World Marathon Majors race of the year.
- Who won the race?
- 
****
Next: The men's race was won by Kenyan athlete Eliud Kipchoge in 2:04:00 hours and the women's race was won by Gladys Cherono of Kenya in a time of 2:19:25 hours.


Read the dialog and predict the next turn. DIALOG:
What is the music video of Picture to Burn?
- Swift is sitting on a brown couch, sporting a black tank top, black leather pants and a beehive hairdo, as the band ransacks the house.
- What happens when the band runssacks the house?
- They throw darts at photographs of Swift's ex, envelop all of his furniture with toilet paper, mess his mirror with the word "loser", lick his utensils and spit into his mouthwash.
- Are there any other interesting aspects about this article?
- Suddenly, the ex-boyfriend and the woman are shown approaching the house, and, seeing this, Anderson informs Swift and the band via handheld transceiver.
- What happens next?
- 


He enters the house and discovers it was ransacked, and repeats the name "Taylor".