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...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

{{r|Natural number}}

{{r|Natural number}}

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The '''integers''' ([[Latin]] word ''integer'' means "untouched") are the [[natural number]]s ([[1 (number)|1]], [[2 (number)|2]], [[3 (number)|3]], &hellip;), their ...is a set ℤ⁺ ∈ ℤ which contains only positive numbers (same as [[natural number]]s);

'''Is zero a natural number?''' <br> Whether [[zero (mathematics)|0]] is a natural number or not is not a mathematical question

...r.htm#carmichael (2003-11-22) Generic Carmichael Numbers]</ref>. If, for a natural number ''n'', the three numbers <math>\scriptstyle 6n+1\ </math>, <math>\scriptsty

...tural numbers<ref>[http://en.citizendium.org/wiki/Natural_number Notation] Natural number</ref>

if its elements can be "numbered" using the [[natural number|natural numbers]].

if its elements can be "numbered" using the [[natural number|natural numbers]].

...itself. '''But''', for example, '''is''' <math>\mathbb N</math> the set of natural number, or isn't it only a symbol that can (and is) sometimes changed, and could m

If the natural number <math>\scriptstyle p\ </math> is a [[prime number]] then it holds that

The [[natural number]]s with the usual order form a directed set, and so a [[sequence]] is a spe

...the equation ''x'' + 1 = 0 has no solutions if ''x'' is supposed to be a [[natural number]], but it does have a solution

{{r|Natural number}}

...direct from "Countability (mathematics)" is, of course, possible. (We say "natural number", "rational number" not "naturality" or "rationality", and it should not be

For a given natural number <math>N</math>, operator <math>\mathrm{DCTII}_N</math> converts any array < For the simple and efficient implementation, <math>N=2^q</math> for some natural number <math>q</math>. Note that the size of the arrays is for unity smaller than

...2, 3} and {a, b, c, d, e}, the elements may be counted to give a unique [[natural number]] for each set, here 3 and 5 respectively, called the size of the set. 5 is ...long as neither is 0 (if both are finite then cardinal arithmetic is just natural number arithmetic).

# The [[natural number]]s (<math> \scriptstyle \mathbb{N} </math>) are used to count things (e.g., ...nd "+"). This applies to any numeral, as long as it does not represent a [[natural number]].