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What’s the distinction between finiteness and hyper-finiteness?

I ask because of the following: For all X, if X is a set then X is finite if and only if there exist no X1 and X2 such that X1 is a subset of X, X1 is not identical to X, and X2 is a bijection between X and X1.

If we use the transfer principle we then get the following: For all X, if X is a set then X is hyper-finite if and only if there exist no X1 and X2 such that X1 is an internal subset of X, X1 is not identical to X, and X2 is an internal bijection between X and X1.

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  • This is a question about non-standard analysis. It doesn't belong here. Commented 5 hours ago

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