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- '''Is zero a natural number?''' <br> Whether [[zero (mathematics)|0]] is a natural number or not is not a mathematical question16 KB (2,562 words) - 00:45, 13 October 2009
- 61 bytes (5 words) - 07:48, 11 November 2009
- 12 bytes (1 word) - 01:39, 11 November 2007
- 91 bytes (9 words) - 16:26, 17 June 2009
- 670 bytes (84 words) - 17:24, 27 August 2009
- 291 bytes (36 words) - 08:06, 19 August 2009
- 395 bytes (45 words) - 07:44, 11 November 2009
Page text matches
- 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 by1 KB (167 words) - 15:43, 1 November 2010
- Greater in size (number of elements, length, area, etc.) than any natural number117 bytes (16 words) - 00:12, 26 October 2009
- The number of its elements is a natural number (0,1,2,3,...)97 bytes (12 words) - 18:46, 6 July 2009
- The number of its elements is larger than any natural number. (See: [[Finite set]].)121 bytes (17 words) - 19:09, 6 July 2009
- Atomic quantum number labeling atomic shells; usually denoted by the non-zero natural number ''n''.136 bytes (17 words) - 08:10, 18 September 2009
- Bounded (or limited) in size (length, area, etc., or number of elements) by a natural number129 bytes (19 words) - 23:57, 25 October 2009
- The largest positive natural number which divides evenly all numbers given.112 bytes (14 words) - 18:35, 26 June 2009
- A set of [[axiom]]s that completely describes the [[natural number]]s.106 bytes (15 words) - 05:59, 1 November 2010
- 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 number2 KB (326 words) - 18:28, 17 July 2009
- {{r|Natural number}}1 KB (169 words) - 19:54, 11 January 2010
- ...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 in1 KB (199 words) - 10:50, 18 June 2009
- {{r|Natural number}}203 bytes (25 words) - 18:31, 26 October 2008
- {{r|Natural number}}307 bytes (44 words) - 16:27, 26 July 2008
- {{r|natural number}}189 bytes (21 words) - 16:20, 17 June 2009
- [[if and only if]] for every [[real number]] ε > 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
- ...'''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
- ...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 pro275 bytes (38 words) - 10:24, 7 June 2008
- * In [[set theory]], ''standard model'' of the [[natural number]]s usually refers to the set <math>\mathbb N</math> constructed inductively1 KB (212 words) - 21:14, 9 September 2020
- In other words, if — from a given set with ''n'' elements (''n'' a natural number) —1 KB (222 words) - 16:36, 4 January 2013
- {{r|Natural number}}1 KB (169 words) - 16:45, 27 April 2010
- ...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
- ...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
- {{r|Natural number}}2 KB (247 words) - 17:28, 11 January 2010
- {{r|Natural number}}969 bytes (124 words) - 18:42, 11 January 2010
- {{r|Natural number}}626 bytes (79 words) - 16:01, 11 January 2010
- {{r|Natural number}}165 bytes (18 words) - 19:20, 12 November 2009
- {{r|Natural number}}618 bytes (80 words) - 16:24, 11 January 2010
- 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
- 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 n2 KB (406 words) - 20:45, 8 February 2010
- {{r|Natural number}}2 KB (262 words) - 19:07, 11 January 2010
- is the traditional notation for the [[cardinality]] of the set of [[natural number]]s.1 KB (214 words) - 13:35, 6 July 2009
- {{r|Natural number}}113 bytes (13 words) - 06:03, 1 November 2010
- Let ''f'' be a function on the [[natural number]]s. We say that the ''average order'' of ''f'' is ''g'' if2 KB (254 words) - 08:27, 19 December 2011
- ...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 the3 KB (496 words) - 22:16, 7 February 2010
- {{r|Natural number}}421 bytes (51 words) - 18:51, 10 January 2010
- {{r|Natural number}}267 bytes (32 words) - 19:16, 17 June 2009
- Let ''f'' be a function on the [[natural number]]s. We say that the ''normal order'' of ''f'' is ''g'' if for every &epsil2 KB (276 words) - 16:53, 6 December 2008
- ...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 \le1 KB (211 words) - 17:02, 7 February 2009
- Let (''a''<sub>''n''</sub>) be a [[sequence]] indexed by the [[natural number]]s. The ''ordinary generating function'' may be defined purely formally as1 KB (148 words) - 13:24, 19 December 2009
- {{r|Natural number}}535 bytes (68 words) - 18:22, 11 January 2010
- {{r|Natural number}}667 bytes (90 words) - 16:09, 11 January 2010
- {{r|Natural number}}709 bytes (94 words) - 18:27, 11 January 2010
- The '''integers''' ([[Latin]] word ''integer'' means "untouched") are the [[natural number]]s ([[1 (number)|1]], [[2 (number)|2]], [[3 (number)|3]], …), 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
- '''Is zero a natural number?''' <br> Whether [[zero (mathematics)|0]] is a natural number or not is not a mathematical question16 KB (2,562 words) - 00:45, 13 October 2009
- ...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>\scriptsty4 KB (576 words) - 12:00, 1 January 2013
- ...tural numbers<ref>[http://en.citizendium.org/wiki/Natural_number Notation] Natural number</ref>3 KB (474 words) - 15:58, 19 March 2022
- if its elements can be "numbered" using the [[natural number|natural numbers]].10 KB (1,462 words) - 17:25, 25 August 2013
- if its elements can be "numbered" using the [[natural number|natural numbers]].10 KB (1,462 words) - 17:24, 25 August 2013
- If the natural number <math>\scriptstyle p\ </math> is a [[prime number]] then it holds that4 KB (776 words) - 20:44, 20 February 2010
- The [[natural number]]s with the usual order form a directed set, and so a [[sequence]] is a spe1,002 bytes (167 words) - 17:12, 7 February 2009