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The first ordinal number that is not a natural number is expressed as ω; this is also the ordinal number of the set of natural numbers itself. 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 .
The Natural Area Code, this is the smallest base such that all of 1 / 2 to 1 / 6 terminate, a number n is a regular number if and only if 1 / n terminates in base 30. 32: Duotrigesimal: Found in the Ngiti language. 33: Use of letters (except I, O, Q) with digits in vehicle registration plates of Hong Kong. 34
The Frobenius number exists as long as the set of coin denominations is setwise coprime. There is an explicit formula for the Frobenius number when there are only two different coin denominations, and , where the greatest common divisor of these two numbers is 1: . If the number of coin denominations is three or more, no explicit formula is known.
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1: 4: 3: 110 2 =6 10: I take 2 from B 1: 2: 3: 000 2 =0 10: You take 1 from C 1: 2: 2: 001 2 =1 10: I take 1 from A 0: 2: 2: 000 2 =0 10: You take 1 from C 0: 2: 1: 011 2 =3 10: The normal play strategy would be to take 1 from B, leaving an even number (2) heaps of size 1. For misère play, I take the entire B heap, to leave an odd number (1 ...
In mathematics, the notion of number has been extended over the centuries to include zero (0), [3] negative numbers, [4] rational numbers such as one half (), real numbers such as the square root of 2 and π, [5] and complex numbers [6] which extend the real numbers with a square root of −1 (and its combinations with real numbers by adding or ...