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- |<center>'''Natural numbers example''' Numbers less than [[0]] (such as [[−1]]) are not natural numbers. ...7 KB (924 words) - 01:12, 17 January 2017
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- ...atical truth. It can be used to prove that something is true for all the [[natural numbers]] (all the positive whole numbers). The idea is that * Assume that the statement is true for any natural number <math>n</math>. (This is called the ''induction step''.) ...3 KB (574 words) - 14:25, 26 October 2015
- ...tten as <math>(\mathbb{N} , +)</math>. The name of the magma would be "The natural numbers under addition". ...1 KB (250 words) - 05:20, 8 November 2014
- .... Subtraction of two numbers can produce a negative number, which is not a natural number, but it is an integer. ...atical object by including new elements. The integers are a closure of the natural numbers by including negative numbers. The [[real numbers]] are a closure o ...2 KB (271 words) - 03:33, 15 January 2015
- ...table, and so is a set with one hundred things in it. A set with all the [[natural number]]s (counting numbers) in it is countable too. It's [[infinite]] but ...m countable if we can find a way to list them all without missing any. The natural numbers have been nicknamed "the counting numbers" since they are what we u ...2 KB (379 words) - 14:57, 30 April 2017
- |<center>'''Natural numbers example''' Numbers less than [[0]] (such as [[−1]]) are not natural numbers. ...7 KB (924 words) - 01:12, 17 January 2017
- ...is a quantifier. Therefore, the sentence "every natural number has another natural number larger than it" is a quantified expression. Quantifiers and quantifi Quantifiers are also used in natural languages. Examples of quantifiers in English are ''for all'', ''for some'' ...8 KB (1,219 words) - 06:11, 20 June 2016
- ...al differential equations. According to above the applications, we had had natural question of how to characterize of the space by space of classical function ...en set in ℝ''<sup>n</sup>'' and 1 ≤ ''p'' ≤ +∞. The [[natural number]] ''m'' is called the order of the Sobolev space ''W<sup>k,p</sup>'' ...2 KB (249 words) - 16:54, 23 January 2015
- ..., [[etc]]. They are often written using [[Knuth's up-arrow notation]]. [[Natural number]] level hyperoperations can be defined [[recursive]]ly as a [[piecew ...610 bytes (75 words) - 16:07, 12 March 2013
- ...] and not from any human construct. Planck units are only one system of [[natural units]] among other systems. They are considered unique, because these unit Natural units help physicists to reframe questions. [[Frank Wilczek]] puts this su ...4 KB (570 words) - 21:33, 20 October 2014
- ...assigns to each symbol and formula of some [[formal language]] a unique [[natural number]] called a '''Gödel number (GN)'''. The concept was first used by [[ ...igned to each [[symbol]] of a [[mathematical notation]], and a stream of [[natural number]]s can then represent some form or function. A [[numbering (computab ...5 KB (850 words) - 23:57, 1 January 2015
- The cardinality of a finite set is a [[natural number]]. The smallest cardinality is 0. The [[empty set]] has cardinality ...issing any. Examples include the [[rational number]]s, [[integer]]s, and [[natural number]]s. Such sets have a cardinality that we call <math>\aleph_0</math> ...2 KB (375 words) - 06:00, 4 July 2015
- A '''triangular number''' is a number that is the sum of all of the [[natural number]]s up to a certain number. For example, 10 is a triangular number be ...641 bytes (69 words) - 16:41, 27 September 2015
- '''Wilson's theorem''' is a theorem of [[number theory]]. Let ''n'' be any [[natural number]]. Wilson's theorem says that ''n'' is a [[prime number]] if and onl ...476 bytes (82 words) - 14:59, 16 August 2013
- ...hm|natural logarithm]]. It is given by the limiting difference between the natural logarithm and the harmonic series <ref name="gm">{{cite web|title=The Euler ...3 KB (394 words) - 20:03, 16 July 2017
- The example below uses two of the simplest infinite sets, that of [[natural number]]s, and that of positive [[fraction (mathematics)|fractions]]. The i ...is a [[Bijective function|bijection]] which associates each element of the natural numbers, to one element of the fractions: ...12 KB (1,234 words) - 02:16, 5 September 2016
- ...e cardinality. For countable sets (sets with the same cardinality as the [[natural number]]s) this cardinality is [[aleph-null|<math>\aleph_0</math>]]. ...contains the natural numbers as a subset, but is no bigger than the set of natural numbers since the rationals are countable: there is a bijection from the na ...5 KB (910 words) - 20:39, 8 September 2016
- ...ardinality of the [[real number]]s is larger than the cardinality of the [[natural number]]s. ...1 KB (154 words) - 17:56, 8 October 2014
- |'''Natural variables''' ...sake of completeness, the set of all <math>N_i</math> are also included as natural variables, although they are sometimes ignored. ...3 KB (426 words) - 10:54, 19 June 2013
- '''Kin selection''' or '''kin altruism''' is a form of [[natural selection]]. Some [[animal]]s [[cooperation|cooperate]] with [[kinship|rela ...by [[R.A. Fisher]] in 1930,<ref>{{cite book |title=The genetical theory of natural selection |last=Fisher |first=R.A. |authorlink= |coauthors= |year=1930 |pub ...4 KB (585 words) - 23:42, 9 March 2015
- *{46,189,1264} is its own subset, and it's a proper subset of the set of [[natural number]]s. ...980 bytes (159 words) - 10:02, 8 June 2017