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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
- 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
- 61 bytes (5 words) - 07:48, 11 November 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
- ...the equation ''x'' + 1 = 0 has no solutions if ''x'' is supposed to be a [[natural number]], but it does have a solution6 KB (951 words) - 05:01, 8 December 2009
- {{r|Natural number}}3 KB (353 words) - 03:48, 24 September 2013
- 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 than6 KB (884 words) - 18:03, 8 September 2020
- ...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
- # 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
- // 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 n3 KB (416 words) - 07:55, 10 September 2020
- 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
- ...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 t7 KB (1,066 words) - 05:40, 6 March 2024
- ...<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
- sometimes also called '''highest common factor''') of two or more [[natural number]]s5 KB (797 words) - 04:57, 21 April 2010
- ...how that the relation of divisibility is a [[partial order]] in the set of natural number <math>\mathbb{N},</math> and also in <math>\mathbb{Z}_+</math>35 KB (5,836 words) - 08:40, 15 March 2021
- 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 than8 KB (1,204 words) - 18:09, 8 September 2020
- 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 app11 KB (1,680 words) - 18:00, 8 September 2020
- ...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 t14 KB (2,281 words) - 12:20, 13 September 2013
- ...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
- ...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
- 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 especia11 KB (1,589 words) - 08:58, 9 September 2020
- 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 t18 KB (2,917 words) - 10:27, 30 August 2014
- * Let ''M'' be the [[natural number]]s (including zero) with addition as the operation. The corresponding conv2 KB (338 words) - 17:41, 23 December 2008
- ...;∧ ''n'' >2 ⇔ ''n'' = 3 when ''n'' is a [[natural number]]. ... ∨ ''n'' ≤ 2 ⇔ ''n'' ≠ 3 when ''n'' is a [[natural number]].9 KB (1,308 words) - 13:37, 16 July 2011
- ; If n is a natural number, we define the factorial of n as:9 KB (1,405 words) - 08:29, 2 March 2024
- 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 a10 KB (1,611 words) - 22:55, 20 February 2010
- ...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 negativ8 KB (1,266 words) - 03:23, 27 April 2010
- ...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 [[car19 KB (2,948 words) - 10:07, 28 February 2024
- 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
- ...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 st15 KB (2,506 words) - 05:16, 11 May 2011
- : ''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
- :''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
- 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
- ...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 on21 KB (3,089 words) - 10:08, 28 February 2024
- ...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]]. Mo4 KB (745 words) - 23:17, 25 October 2013
- ...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 a15 KB (2,340 words) - 08:27, 9 September 2020
- ...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
- is used for the ''q''-analogue of a natural number ''n''.7 KB (1,134 words) - 16:18, 22 January 2010
- ...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 "multiplica8 KB (1,339 words) - 13:11, 8 August 2021
- ...]] 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, whic8 KB (1,209 words) - 08:09, 28 September 2013
- ...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
- 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 num30 KB (4,289 words) - 16:03, 20 January 2023
- ...''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''', b7 KB (1,151 words) - 14:44, 26 December 2013
- 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 in34 KB (5,174 words) - 21:32, 25 October 2013
- ...</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
- where ''ℓ'' is a [[natural number]].34 KB (5,282 words) - 14:21, 1 January 2011