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RhubarbJayde (talk | contribs) (Created page with "1 is the next natural number after 0. In the system of Von Neumann ordinals and Zermelo's formalization of the natural numbers, it is represented by the set \(0+1 = \{\{\}\}\), while in the logical formalization of natural numbers it is identified with the proper class of singletons. Also, as a Church numeral, it is identified with the lambda calculus expression \(\lambda f. \lambda x. f(x)\). 1 is the least Additive...") |
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1 is the least [[Additive principal ordinals|additive principal ordinal]], being equal to \(\omega^0\), and as such is the least ordinal with a nonempty [[Cantor normal form|CNF]] representation. |
1 is the least [[Additive principal ordinals|additive principal ordinal]], being equal to \(\omega^0\), and as such is the least ordinal with a nonempty [[Cantor normal form|CNF]] representation. |
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It is equal to the identity in the monoid of [[natural numbers]] under multiplication. |
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Latest revision as of 14:00, 31 August 2023
1 is the next natural number after 0. In the system of Von Neumann ordinals and Zermelo's formalization of the natural numbers, it is represented by the set \(0+1 = \{\{\}\}\), while in the logical formalization of natural numbers it is identified with the proper class of singletons. Also, as a Church numeral, it is identified with the lambda calculus expression \(\lambda f. \lambda x. f(x)\).
1 is the least additive principal ordinal, being equal to \(\omega^0\), and as such is the least ordinal with a nonempty CNF representation.
It is equal to the identity in the monoid of natural numbers under multiplication.