Implementation of mathematics in set theory: Difference between revisions

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We now have two different implementations of the natural numbers in [[NFU]] (though
they are the same in [[ZFC]]): finite ordinals and finite cardinals. Each of these
supports the T operation in [[NFU]]. It is easy to prove that <math>T(n)</math> is
a natural number in [[NFU]] + Infinity + Choice (and so <math>|N|</math> and the first
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restricted to N or to P(N), R (the set of reals) or indeed any set ever considered in classical
mathematics outside of set theory.
 
There are no analogous phenomena in [[ZFC]]. See the main [[New Foundations]] article for
stronger axioms that can be adjoined to [[NFU]] to enforce "standard" behavior of familiar
mathematical objects.