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  • Peano axioms
    The '''Peano axioms''' are a set of [[axiom]]s that formally describes the [[natural number]]s (0, 1, 2, 3 ...). : There is a smallest natural number (either 0 or 1), starting from which all natural numbers can be reached by
    1 KB (167 words) - 15:43, 1 November 2010
  • Infinite/Definition
    Greater in size (number of elements, length, area, etc.) than any natural number
    117 bytes (16 words) - 00:12, 26 October 2009
  • Finite set/Definition
    The number of its elements is a natural number (0,1,2,3,...)
    97 bytes (12 words) - 18:46, 6 July 2009
  • Infinite set/Definition
    The number of its elements is larger than any natural number. (See: [[Finite set]].)
    121 bytes (17 words) - 19:09, 6 July 2009
  • Principal quantum number/Definition
    Atomic quantum number labeling atomic shells; usually denoted by the non-zero natural number ''n''.
    136 bytes (17 words) - 08:10, 18 September 2009
  • Finite/Definition
    Bounded (or limited) in size (length, area, etc., or number of elements) by a natural number
    129 bytes (19 words) - 23:57, 25 October 2009
  • User talk:Jason Potkanski/Locke Math
    The study of quantity starts with [[number]]s, first the familiar [[natural number]]s and [[integer]]s ("whole numbers") and arithmetical operations on them, | [[Natural number]]s|| [[Integer]]s || [[Rational number]]s || [[Real number]]s || [[Complex
    1 KB (209 words) - 21:20, 13 April 2007
  • Template:Natural number/Metadata
    | pagename = Natural number | abc = natural number
    681 bytes (59 words) - 19:22, 26 August 2009
  • Greatest common divisor/Definition
    The largest positive natural number which divides evenly all numbers given.
    112 bytes (14 words) - 18:35, 26 June 2009
  • Peano axioms/Definition
    A set of [[axiom]]s that completely describes the [[natural number]]s.
    106 bytes (15 words) - 05:59, 1 November 2010
  • Zero (mathematics)
    Whether zero is considered as a natural number is a matter of convention — often it is, but sometimes not. ...r, in modern mathematics, it is convenient and usual to consider zero as a natural number
    2 KB (326 words) - 18:28, 17 July 2009
  • Rational number/Related Articles
    {{r|Natural number}}
    1 KB (169 words) - 19:54, 11 January 2010
  • Erdős–Fuchs theorem
    ...t of the natural numbers and ''r''(''n'') denote the number of ways that a natural number ''n'' can be expressed as the sum of two elements of ''A'' (taking order in
    1 KB (199 words) - 10:50, 18 June 2009
  • Exponent/Related Articles
    {{r|Natural number}}
    203 bytes (25 words) - 18:31, 26 October 2008
  • Cantor's diagonal argument/Related Articles
    {{r|Natural number}}
    307 bytes (44 words) - 16:27, 26 July 2008
  • Aleph-0/Related Articles
    {{r|natural number}}
    189 bytes (21 words) - 16:20, 17 June 2009
  • Limit of a sequence
    [[if and only if]] for every [[real number]] &epsilon; > 0 there exists a [[natural number]] ''n''<sub>0</sub> such that for all ''n'' > ''n''<sub>0</sub> we have |'
    771 bytes (122 words) - 09:45, 28 November 2007
  • Divisibility
    ...'''divides''' a number ''n'', if ''n'' is the product of ''d'' and another natural number ''k''. Every natural number ''n'' has two divisors, 1 and ''n'',
    3 KB (515 words) - 21:49, 22 July 2009
  • Kurt Gödel/Definition
    ...st famous for proving that in any logical system rich enough to describe [[natural number|naturals]], there are always statements that are true but impossible to pro
    275 bytes (38 words) - 10:24, 7 June 2008
  • Standard (mathematics)
    * In [[set theory]], ''standard model'' of the [[natural number]]s usually refers to the set <math>\mathbb N</math> constructed inductively
    1 KB (212 words) - 21:14, 9 September 2020
  • Finite set
    In other words, if &mdash; from a given set with ''n'' elements (''n'' a natural number) &mdash;
    1 KB (222 words) - 16:36, 4 January 2013
  • Nature/Related Articles
    {{r|Natural number}}
    1 KB (169 words) - 16:45, 27 April 2010
  • Binomial theorem/Definition
    ...xtstyle (x + y)^n = \sum_{k=0}^n {n \choose k} x^k y^{n-k} </math> for any natural number ''n''.
    142 bytes (24 words) - 06:53, 15 July 2008
  • Fraction (mathematics)/Definition
    ...ole consisting of a numerator (an integer — the part) and a denominator (a natural number — the whole).
    217 bytes (33 words) - 08:31, 2 June 2008
  • Integer/Related Articles
    {{r|Natural number}}
    2 KB (247 words) - 17:28, 11 January 2010
  • Multiplication/Related Articles
    {{r|Natural number}}
    969 bytes (124 words) - 18:42, 11 January 2010
  • Talk:Integer
    ...gers? Things like the difference between "integer" and "whole number" and "natural number", probably. Ways in which integers are important - in divisibility/factoriz
    2 KB (284 words) - 19:33, 3 November 2007
  • Distributivity/Related Articles
    {{r|Natural number}}
    626 bytes (79 words) - 16:01, 11 January 2010
  • Zero (mathematics)/Related Articles
    {{r|Natural number}}
    165 bytes (18 words) - 19:20, 12 November 2009
  • Euclidean algorithm/Related Articles
    {{r|Natural number}}
    618 bytes (80 words) - 16:24, 11 January 2010
  • Hilbert's hotel
    like the set of [[natural number|natural numbers]] (or any other [[countable set|countably infinite set]]).
    2 KB (360 words) - 09:07, 17 June 2009
  • Finite field
    same operations on the integers). For any primes number p, and natural number n, there exists a unique finite field with p<sup>n</sup> 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
    2 KB (406 words) - 20:45, 8 February 2010
  • Number theory/Related Articles
    {{r|Natural number}}
    2 KB (262 words) - 19:07, 11 January 2010
  • Aleph-0
    is the traditional notation for the [[cardinality]] of the set of [[natural number]]s.
    1 KB (214 words) - 13:35, 6 July 2009
  • Peano axioms/Related Articles
    {{r|Natural number}}
    113 bytes (13 words) - 06:03, 1 November 2010
  • Average order of an arithmetic function
    Let ''f'' be a function on the [[natural number]]s. We say that the ''average order'' of ''f'' is ''g'' if
    2 KB (254 words) - 08:27, 19 December 2011
  • Field (mathematics)
    ...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
    3 KB (496 words) - 22:16, 7 February 2010
  • Sequence/Related Articles
    {{r|Natural number}}
    421 bytes (51 words) - 18:51, 10 January 2010
  • Countable set/Related Articles
    {{r|Natural number}}
    267 bytes (32 words) - 19:16, 17 June 2009
  • Normal order of an arithmetic function
    Let ''f'' be a function on the [[natural number]]s. We say that the ''normal order'' of ''f'' is ''g'' if for every &epsil
    2 KB (276 words) - 16:53, 6 December 2008
  • Monotonic function
    ...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
    1 KB (211 words) - 17:02, 7 February 2009
  • Generating function
    Let (''a''<sub>''n''</sub>) be a [[sequence]] indexed by the [[natural number]]s. The ''ordinary generating function'' may be defined purely formally as
    1 KB (148 words) - 13:24, 19 December 2009
  • Mathematical induction/Related Articles
    {{r|Natural number}}
    535 bytes (68 words) - 18:22, 11 January 2010
  • Easter/Related Articles
    {{r|Natural number}}
    667 bytes (90 words) - 16:09, 11 January 2010
  • Mesoamerica/Related Articles
    {{r|Natural number}}
    709 bytes (94 words) - 18:27, 11 January 2010
  • Integer
    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<sup>+</sup> ∈ ℤ which contains only positive numbers (same as [[natural number]]s);
    10 KB (1,566 words) - 08:34, 2 March 2024
  • Natural number
    '''Is zero a natural number?''' <br> Whether [[zero (mathematics)|0]] is a natural number or not is not a mathematical question
    16 KB (2,562 words) - 00:45, 13 October 2009
  • Carmichael number
    ...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
    4 KB (576 words) - 12:00, 1 January 2013
  • Omega (Greek letter)
    ...tural numbers<ref>[http://en.citizendium.org/wiki/Natural_number Notation] Natural number</ref>
    3 KB (474 words) - 15:58, 19 March 2022
  • Countable set
    if its elements can be "numbered" using the [[natural number|natural numbers]].
    10 KB (1,462 words) - 17:25, 25 August 2013
  • Countable set/Citable Version
    if its elements can be "numbered" using the [[natural number|natural numbers]].
    10 KB (1,462 words) - 17:24, 25 August 2013
  • Talk:Aleph-0
    ...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
    4 KB (722 words) - 19:10, 19 June 2009
  • Lucas sequence
    If the natural number <math>\scriptstyle p\ </math> is a [[prime number]] then it holds that
    4 KB (776 words) - 20:44, 20 February 2010
  • Net (topology)
    The [[natural number]]s with the usual order form a directed set, and so a [[sequence]] is a spe
    1,002 bytes (167 words) - 17:12, 7 February 2009
  • Equation (mathematics)
    ...the equation ''x'' + 1 = 0 has no solutions if ''x'' is supposed to be a [[natural number]], but it does have a solution
    6 KB (951 words) - 05:01, 8 December 2009
  • Computer science/Related Articles
    {{r|Natural number}}
    3 KB (353 words) - 03:48, 24 September 2013
  • Talk:Countable set/Draft
    ...direct from "Countability (mathematics)" is, of course, possible. (We say "natural number", "rational number" not "naturality" or "rationality", and it should not be
    5 KB (698 words) - 15:37, 2 October 2013
  • DCTII
    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
    6 KB (884 words) - 18:03, 8 September 2020
  • Cardinal number
    ...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).
    11 KB (1,808 words) - 17:50, 26 June 2009
  • Number
    # 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]].
    11 KB (1,701 words) - 20:07, 1 July 2021
  • Zcosft2.cin
    // 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
    3 KB (416 words) - 07:55, 10 September 2020
  • Multinomial coefficient
    Let ''k''<sub>1</sub>, ''k''<sub>2</sub>, ..., ''k''<sub>m</sub> be [[natural number]]s giving a [[Partition (mathematics)|partition]] of ''n'':
    2 KB (365 words) - 06:50, 22 January 2009
  • Atomic number
    ...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
    7 KB (1,066 words) - 05:40, 6 March 2024
  • Polynomial/Advanced
    ...<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>
    10 KB (1,741 words) - 10:04, 3 January 2009
  • Greatest common divisor
    sometimes also called '''highest common factor''') of two or more [[natural number]]s
    5 KB (797 words) - 04:57, 21 April 2010
  • Talk:Atomic number
    ...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
    4 KB (656 words) - 13:00, 7 July 2008
  • Number theory/Signed Articles/Elementary diophantine approximations
    ...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>
    35 KB (5,836 words) - 08:40, 15 March 2021
  • DCTIII
    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
    8 KB (1,204 words) - 18:09, 8 September 2020
  • DCTI
    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
    11 KB (1,680 words) - 18:00, 8 September 2020
  • Prime number/Citable Version
    ...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
    14 KB (2,281 words) - 12:20, 13 September 2013
  • Non-Borel set/Advanced
    ...ably many sets of the form treated in G ("7" being replaced with arbitrary natural number). Still a Borel set!
    2 KB (402 words) - 20:47, 30 June 2009
  • Polynomial ring
    ...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]]''
    4 KB (604 words) - 23:54, 20 February 2010
  • Fourier operator
    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
    11 KB (1,589 words) - 08:58, 9 September 2020
  • Prime number
    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
    18 KB (2,917 words) - 10:27, 30 August 2014
  • User:Peter Schmitt
    [[Natural number]]
    3 KB (321 words) - 04:32, 22 November 2023
  • Convolution (mathematics)
    * Let ''M'' be the [[natural number]]s (including zero) with addition as the operation. The corresponding conv
    2 KB (338 words) - 17:41, 23 December 2008
  • Logic symbols
    ...;∧&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]].
    9 KB (1,308 words) - 13:37, 16 July 2011
  • Lisp
    ; If n is a natural number, we define the factorial of n as:
    9 KB (1,405 words) - 08:29, 2 March 2024
  • User:Drew R. Smith/MOSArchive
    :: 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
    6 KB (959 words) - 03:47, 22 November 2023
  • Paradoxes and fuzzy logic
    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
    10 KB (1,611 words) - 22:55, 20 February 2010
  • Talk:Logarithm
    == Extension of logarithms to non-natural number exponents ==
    16 KB (2,648 words) - 22:41, 3 January 2009
  • Simon Stevin
    ...egrees. He considered all kinds of [[real number]]s on an equal footing—[[natural number]]s, roots (the majority of which are [[irrational number]]s), and negativ
    8 KB (1,266 words) - 03:23, 27 April 2010
  • Real number
    ...are [[uncountable]]; that is, there are strictly more real numbers than [[natural number]]s, even though both sets are [[infinite set|infinite]]. In fact, the [[car
    19 KB (2,948 words) - 10:07, 28 February 2024
  • Fast Fourier transform
    where <math>N</math> is natural number; usually, <math>N=2^q</math> for some natural <math>q</math>;<br>
    9 KB (1,368 words) - 11:59, 8 September 2020
  • Vector space
    ...t style = "vertical-align: 17%"><math>\mathbb{R}^n</math></font> for any [[natural number]] ''n''; or the [[complex number|complex plane]] or powers of it, <font st
    15 KB (2,506 words) - 05:16, 11 May 2011
  • Slater orbital
    : ''n'' is a [[natural number]] that plays the role of [[principal quantum number]], ''n'' = 1,2,...,
    5 KB (822 words) - 17:36, 14 November 2007
  • Set (mathematics)
    :''A'' = {x | 1 < x < 10, x is a natural number} ...as follows: A is the set of all x, where x is between 1 and 10, and x is a natural number. A could also be written as:
    17 KB (2,828 words) - 10:37, 24 July 2011
  • Logistic sequence
    for some [[natural number|natural]] <math>n</math> such that <math>|f^{-n}(z)|\ll 1</math>.
    9 KB (1,388 words) - 11:08, 20 November 2011
  • Fraction (mathematics)
    ...of a [[numerator]] (an [[integer]] — the part) and a [[denominator]] (a [[natural number]] — the whole). For instance, the fraction <math> \scriptstyle \frac{3}{5 ...Equivalent fractions|equivalent fraction]] with an integer numerator and a natural number denominator. A fraction with equal numerator and denominator is equal to on
    21 KB (3,089 words) - 10:08, 28 February 2024
  • Cantor's diagonal argument
    ...venient proof that the set <math>2^{\mathbb{N}}</math> of subsets of the [[natural number]]s (also known as its [[power set]]) is not [[countable set|countable]]. Mo
    4 KB (745 words) - 23:17, 25 October 2013
  • Iteration of function
    ...e cases, when number <math>n</math> of iterations can be simplified to a [[natural number]], expressed with integer constant. Attempts to call [[Nest]] to evaluate a
    15 KB (2,340 words) - 08:27, 9 September 2020
  • Hydrogen-like atom
    ...and the magnetic quantum number ''m''. These three quantum numbers are [[natural number]]s, their definitions and ranges are:
    19 KB (2,981 words) - 18:31, 3 November 2021
  • Geometric series
    is used for the ''q''-analogue of a natural number ''n''.
    7 KB (1,134 words) - 16:18, 22 January 2010
  • Power function
    ...ven if some of these operations are not yet defined, <math>z^n</math> for natural number <math>n</math> can be considered as just iteration of function "multiplica
    8 KB (1,339 words) - 13:11, 8 August 2021
  • Talk:Prime number/Archive 2
    ...ves, and zero, this is incorrect. ''Whole number'' should be replaced by ''natural number'' or by ''positive whole number.'' ...and especially the first sentence, accessible for everybody. "Integer" or "natural number" might be a problem. However, we also want to be correct. I think that "pos
    29 KB (4,820 words) - 02:18, 2 April 2008
  • Benjamin Peirce
    ...]] elements that have the property that ''a''<sup>''n''</sup> = 0 for some natural number ''n''. Most of these properties are now very well-known for matrices, whic
    8 KB (1,209 words) - 08:09, 28 September 2013
  • Particle in a box
    ...st also be greater than zero, so <math>n</math> is restricted to being a [[natural number]], <math>1,2,3,...</math>.
    16 KB (2,810 words) - 11:31, 5 April 2011
  • User talk:Daniel Mietchen/Archive 5
    == Natural number/Related Articles == Daniel, you and Howard have edited [[Natural number/Related Articles]].
    21 KB (3,302 words) - 17:26, 4 December 2009
  • Mathematics
    The study of quantity starts with [[number]]s, first the familiar [[natural number]]s and [[whole number]]s and arithmetical operations on them, which are cha | [[Natural number]]s|| [[Whole number]]s|| [[Integer]]s || [[Rational number]]s || [[Real num
    30 KB (4,289 words) - 16:03, 20 January 2023
  • Category theory
    ...''typed'' functions. For example if we consider the function that takes a natural number and doubles it, we may regard this as a function from '''N''' to '''N''', b
    7 KB (1,151 words) - 14:44, 26 December 2013
  • User:Subpagination Bot/Task 1/Log 4
    ...], [[Natural breed]], [[Natural family planning]], [[Natural language]], [[Natural number]], [[Naval Supply Depot Oakland]], [[Naval Vessel Register]], [[Navy Grog]]
    23 KB (2,434 words) - 12:48, 15 March 2024
  • CZ:Mathematics Workgroup
    [[natural number]],
    24 KB (3,085 words) - 08:58, 23 March 2021
  • Theory (mathematics)
    Definition: a prime number is a natural number having exactly two divisors. (These are 1 and the number itself, of course. ...formal theory stipulates a new primitive notion "prime" and a new axiom: a natural number is prime if and only if it has exactly two divisors. This axiom is used in
    34 KB (5,174 words) - 21:32, 25 October 2013
  • Euclidean space
    ...</math></font> is a [[space]] of dimension ''n'', where ''n'' is a finite natural number not equal to zero.
    9 KB (1,403 words) - 02:22, 14 October 2013
  • User:Anthony Argyriou/WPbasicarticles2
    ### [[Natural number]]
    23 KB (2,294 words) - 08:39, 22 April 2024
  • User talk:Howard C. Berkowitz/Archive 3
    == Natural number/Related Articles == Howard, you and Daniel have edited [[Natural number/Related Articles]].
    60 KB (9,868 words) - 10:32, 23 March 2024
  • User:Anthony Argyriou/WPbasicarticles1
    ## [[Natural number|Natural number]]
    33 KB (3,868 words) - 09:02, 4 May 2024
  • Spherical harmonics
    where ''ℓ'' is a [[natural number]].
    34 KB (5,282 words) - 14:21, 1 January 2011
  • User talk:Thomas Simmons
    | double-struck capital N (for [[natural number]]s set)
    56 KB (8,699 words) - 19:01, 15 July 2011
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