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In internal set theory, why is it that if there is a bijection between $x$ standard and $n\in\mathbb{N}$, then $n$ is necessarily standard ?

fyusuf-a
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  • Could you please expand on the terms used? Every standard set containing only standard points is (standard) finite. Is that your questions? Or is the question why a finite set with a non-standard number of elements can not be standard? – Lutz Lehmann Jun 01 '14 at 14:48

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In priciple you are asking wyh $\{1,2,3,...,\mu\}$ can only be a standard set if $\mu$ is standard?

By set operations, if $\{1,2,3,...,\mu\}$ is standard then also $\{mu+1,\mu+2,...\}$ must be standard. Since the minimum of a set of natural integers is a standard operation, then $\mu+1$ and thus $\mu$ must be standard.

Lutz Lehmann
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