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...xtstyle (x + y)^n = \sum_{k=0}^n {n \choose k} x^k y^{n-k} </math> for any natural number ''n''.

...ole consisting of a numerator (an integer — the part) and a denominator (a natural number — the whole).

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like the set of [[natural number|natural numbers]] (or any other [[countable set|countably infinite set]]).

same operations on the integers). For any primes number p, and natural number n, there exists a unique finite field with pⁿ elements; this hence there is some minimal natural number N such that <math>\sum_{i=1}^N 1_F = 0</math>. Since F is a field, it has n

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is the traditional notation for the [[cardinality]] of the set of [[natural number]]s.

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Let ''f'' be a function on the [[natural number]]s. We say that the ''average order'' of ''f'' is ''g'' if

...h> (where there are <math>k</math> ones on the right-hand side). If such a natural number does not exist, then the characteristic of a field is taken to be 0. If the

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Let ''f'' be a function on the [[natural number]]s. We say that the ''normal order'' of ''f'' is ''g'' if for every &epsil

...notonic function is a [[sequence]] regarded as a function defined on the [[natural number]]s. So a sequence <math>a_n</math> is monotonic increasing if <math>m \le

Let (''a''_''n'') be a [[sequence]] indexed by the [[natural number]]s. The ''ordinary generating function'' may be defined purely formally as

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