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The mean number chosen when playing the "guess 2/3 of the average" game four consecutive rounds. Grosskopf and Nagel's investigation also revealed that most players do not choose 0 the first time they play this game. Instead, they realise that 0 is the Nash Equilibrium after some repetitions. [14]
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A leading zero is any 0 digit that comes before the first nonzero digit in a number string in positional notation. [1] For example, James Bond 's famous identifier, 007, has two leading zeros. [ 2 ] Any zeroes appearing to the left of the first non-zero digit (of any integer or decimal) do not affect its value, and can be omitted (or replaced ...
Entering the final day of the 1964–65 season, Hearts were two points ahead of nearest rivals Kilmarnock, with two points awarded for a win. Hearts played Kilmarnock at Tynecastle in the last game, with Kilmarnock needing a 2–0 victory to win the league championship on goal average. Hearts could afford to lose 1–0 or 2–1, but lost 2–0 ...
If n < 5, the inequality is satisfied by k = 0; in that case the sum is empty, giving the answer 0. The formula actually counts the number of factors 5 in n !, but since there are at least as many factors 2, this is equivalent to the number of factors 10, each of which gives one more trailing zero.
When written in base 10, all multiples of 2 will end in 0, 2, 4, 6, or 8. [3] 2 is the smallest and the only even prime number, and the first Ramanujan prime. [4] It is also the first superior highly composite number, [5] and the first colossally abundant number. [6]
All other four-digit numbers eventually reach 6174 if leading zeros are used to keep the number of digits at 4. For numbers with three identical digits and a fourth digit that is one higher or lower (such as 2111), it is essential to treat 3-digit numbers with a leading zero; for example: 2111 – 1112 = 0999; 9990 – 999 = 8991; 9981 – 1899 ...
The least ordinal of cardinality ℵ 0 (that is, the initial ordinal of ℵ 0) is ω but many well-ordered sets with cardinal number ℵ 0 have an ordinal number greater than ω. For finite well-ordered sets, there is a one-to-one correspondence between ordinal and cardinal numbers; therefore they can both be expressed by the same natural ...