Natural number - Wikipedia, the free encyclopedia
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In mathematics, there are two conventions for the set of natural numbers : it is either the set of positive integers { 1, 2, 3, ... } according to the traditional definition or the set of non-ne...
en.wikipedia.org/wiki/Natural_number
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Set-theoretic definition of natural numbers - Wikipedia, the free encyclopedia
Several ways have been proposed to define the natural numbers using set theory. In standard (ZF) set theory the natural numbers are defined recursively by 0 = {} (the empty set) and n +1 = n ∪ { ...
en.wikipedia.org/wiki/Set-theoretic_definition_of_natur... en.wikipedia.org/wiki/Set-theoretic_definition_of_natural_numbers
natural number n. One of the set of positive whole numbers; a positive integer. ... The Peano axioms give a formal theory of the natural numbers. The axioms are:
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Given the Zermelo-Fraenkel axioms of set theory, one can prove that there exists an inductive set $X$ such that $\emptyset \in X$ . The natural numbers $\mathbb{N}$ are then defined to be the intersection of all subsets of $X$ which are inductive sets and contain the empty set as an element.
planetmath.org/encyclopedia/NaturalNumber.html planetmath.org/encyclopedia/NaturalNumber.html
The natural numbers are the counting numbers – the non-negative whole numbers. Some treatments of them, including mine, include zero as a natural, others do not. They are extensively studied.
www.chaos.org.uk/~eddy/math/found/natural.html www.chaos.org.uk/~eddy/math/found/natural.html
In mathematical equations, unknown or unspecified 'natural numbers' are represented by lowercase, italicized letters from the middle of the alphabet. The most common is 'n', followed by 'm', 'p', and 'q'. ... In mathematical equations, unknown or unspecified natural numbers are represented by lowercase,
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Natural Number Any of the standard counting numbers; a positive integer. ... Natural Selection The natural filtering process by which individuals with higher fitness are more likely to reproduce than individuals with lower fitness.
mitpress.mit.edu/books/FLAOH/cbnhtml/glossary-N.html
CiteSeerX - Document Details (Isaac Councill, Lee Giles): A prime concern in the design of any general purpose programming language should be the ease and safety of working with natural numbers, particularly in conjunction with discrete data structures. ... What About the Natural Numbers (1989) [3 citations — 2 self]
citeseer.ist.psu.edu/45669.html
Properties of the natural numbers related to divisibility, such as the distribution of prime numbers, are studied in number theory. Problems concerning counting, such as Ramsey theory, are studied in combinatorics.
www.bath.ac.uk/~cd243/natural.html www.bath.ac.uk/~cd243/natural.html
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