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// The first argument is array of length <math>2^q</math> for some natural number $q$. If the numeration of elements of the array begins with zero, and the n

Let ''k''₁, ''k''₂, ..., ''k''_m be [[natural number]]s giving a [[Partition (mathematics)|partition]] of ''n'':

...r is conventionally denoted by ''Z'' and is by definition a non-negative [[natural number]]. For instance, the element [[carbon]] is characterized by ''Z'' = 6 and t

...<math>X^2=\left(0,0,1,0,0,\dots\right)</math>. More generally, for each [[natural number]] <math>n</math>, one can verify that the <math>n</math>-th power of <math>

sometimes also called '''highest common factor''') of two or more [[natural number]]s

...the [[chemical element]]s can be characterized uniquely by non-negative [[natural number]]s, always denoted by ''Z''. For instance, the element [[carbon]] is charac

...how that the relation of divisibility is a [[partial order]] in the set of natural number &nbsp;<math>\mathbb{N},</math>&nbsp; and also in <math>\mathbb{Z}_+</math>

For a given natural number <math>N</math> operator <math>\mathrm{DCTIII}_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

For the discrete approximation of this operator, assume some large natural number <math>N</math>. Let <math>x_n=\sqrt{\pi/N}~ n</math>. Assume some large natural number <math>N</math>. Let <math>\displaystyle x_n=\frac{\pi}{N} n</math>. For app

...ation]] as follows: A number <math>\scriptstyle p \in \mathbb{N}</math> ([[natural number]]) is prime if for any <math>\scriptstyle a, b \in \mathbb{N}</math> such t

...ably many sets of the form treated in G ("7" being replaced with arbitrary natural number). Still a Borel set!

...scribed above as the set of ''R''-valued functions on the set '''N''' of [[natural number]]s (including zero) and defining the ''[[support (mathematics)|support]]''

The grid points <math>x_j</math>, <math>j=0..N</math> are chosen for [[natural number]] <math>~j~</math>; <math>~0\!\le \! j \!<\! N</math> in the following way It is convenient to chose <math>N=2^m</math> for some natural number <math>m</math>; then the fast implementation of such a summation is especia

Every natural number <math>\scriptstyle N > 1</math> can be written as a product of prime factor ...ation]] as follows: A number <math>\scriptstyle p \in \mathbb{N}</math> ([[natural number]]) is prime if for any <math>\scriptstyle a, b \in \mathbb{N}</math> such t

[[Natural number]]

* Let ''M'' be the [[natural number]]s (including zero) with addition as the operation. The corresponding conv

...;∧&nbsp; ''n''&nbsp;>2&nbsp;&nbsp;⇔&nbsp; ''n''&nbsp;= 3 when ''n'' is a [[natural number]]. ...&nbsp;∨&nbsp; ''n''&nbsp;≤ 2&nbsp;&nbsp;⇔ ''n''&nbsp;≠ 3 when ''n'' is a [[natural number]].

; If n is a natural number, we define the factorial of n as:

:: This is true for links like [[Natural Number]], but not if you search for "Natural Number" in the search box at the top of the page. [[User:Peter Schmitt|Peter Schmi

Let ''n'' be a natural number and denote by Small(''<u>n</u>'') a sentence whose intended meaning is ''"a On the other hand from these formulas given any natural number ''n'', by applying MP (Modus Ponens) rule several times we can prove that a