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Natural numbers: Difference between revisions
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(Created page with "The '''natural numbers''', or '''counting numbers''', are a system of numbers which includes the positive integers \( 1, 2, 3, \dots \), and under some definitions also includes zero. If zero is to be considered a natural number, which is usually the case in set theory, the natural numbers are precisely the finite ordinals. ==Encodings== The natural numbers are fundamental objects in mathematics, and thus different areas of math have different conventions of e...") |
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===Zermelo ordinals===
[[:wikipedia:Ernst Zermelo|Ernst Zermelo]] provided an alternative construction of the natural numbers, encoding \( 0 = \varnothing \) and \( n + 1 = \{ n \} \) for \( n \ge 0 \). Unlike the Von Neumann ordinals, Zermelo's encoding can only be used to represent finite ordinals.
===Frege and Russell===
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