National Lottery (Ireland) their five main EuroMillions numbers in an additional draw for a fixed, non-rolling prize of €500,000. Players can also win fixed prizes of €2,000 for a match-4 and €20 for a match-3. The first Plus drawing was held on 15 June 2007. 76 percent of EuroMillions players now play Plus. Sales of Plus were €44.6 million in 2012, an increase of 3.7 percent over the previous year. In September 2012, the National Lottery introduced Daily Million to replace both Monday Million (a draw game with prizes up to €1 million, held once weekly on Monday nights) and All Or Nothing
Construction of the real numbers For convenience we may take the lower set formula_1 as the representative of any given Dedekind cut formula_2, since formula_3 completely determines formula_4. By doing this we may think intuitively of a real number as being represented by the set of all smaller rational numbers. In more detail, a real number formula_5 is any subset of the set formula_6 of rational numbers that fulfills the following conditions: As an example of a Dedekind cut representing an irrational number, we may take the positive square root of 2. This can be defined by the set formula_49. It can be seen from