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- Natural numbers, also called counting numbers, are the numbers used for counting things. Natural numbers are always whole numbers (integers) and exclude zero, so one is the smallest natural number12. Other definitions include zero, so that the non-negative integers {0, 1, 2, 3,...} are also called natural numbers2. A natural number can be defined as an equivalence class of finite sets under the equivalence relation of equinumerosity3.Learn more:✕This summary was generated using AI based on multiple online sources. To view the original source information, use the "Learn more" links.Natural numbers, also called counting numbers, are the numbers used for counting things. Natural numbers are the numbers small children learn about when they first start to count. Natural numbers are always whole numbers (integers) and exclude zero, so one is the smallest natural number.simple.wikipedia.org/wiki/Natural_numberNatural numbers (): The counting numbers {1, 2, 3,...} are commonly called natural numbers; however, other definitions include 0, so that the non-negative integers {0, 1, 2, 3,...} are also called natural numbers. Natural numbers including 0 are also sometimes called whole numbers.en.wikipedia.org/wiki/List_of_types_of_numbersGottlob Frege and Bertrand Russell each proposed defining a natural number n as the collection of all sets with n elements. More formally, a natural number is an equivalence class of finite sets under the equivalence relation of equinumerosity.en.wikipedia.org/wiki/Set-theoretic_definition_of_na…
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In mathematics, the natural numbers are the numbers 0, 1, 2, 3, etc., possibly excluding 0. Some define the natural numbers as the non-negative integers 0, 1, 2, 3, ..., while others define them as the positive integers 1, 2, 3, .... Some authors acknowledge both definitions whenever convenient. Some texts … See more
Ancient roots
The most primitive method of representing a natural number is to use one's fingers, as in finger counting. Putting down a tally mark for each object is another primitive method. Later, a … See moreThere are two standard methods for formally defining natural numbers. The first one, named for Giuseppe Peano, consists of an autonomous See more
• "Natural number", Encyclopedia of Mathematics, EMS Press, 2001 [1994]
• "Axioms and construction of natural numbers". apronus.com. See moreThis section uses the convention $${\displaystyle \mathbb {N} =\mathbb {N} _{0}=\mathbb {N} ^{*}\cup \{0\}}$$.
Addition
Given the set See moreTwo important generalizations of natural numbers arise from the two uses of counting and ordering: cardinal numbers and See more
• Bluman, Allan (2010). Pre-Algebra DeMYSTiFieD (Second ed.). McGraw-Hill Professional. ISBN 978-0-07-174251-1 – via Google Books. See more
Wikipedia text under CC-BY-SA license WebMay 23, 2023 · Learn what natural numbers are, how they differ from whole numbers and integers, and what mathematical properties they have. See examples of natural numbers and non-natural numbers, and …
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