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Chromotron t1_iue4c7b wrote

Reply to comment by breckenridgeback in Eli5: Infinity ♾️ by [deleted]

> Consider a set S that is a subset of the reals,

That's where you went wrong: the set is simply not required to be contained in the reals. You can give any set X a total ordering such that the induced topology is discrete; similarly, we can give X a metric that makes it discrete, the discrete metric.

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breckenridgeback t1_iuenf2y wrote

Oh, I thought you were claiming an uncountable discrete subset of the reals (since your comparison was the rationals). Yes, obviously you can give any set the discrete topology (although the discussion of "between" suggests something more like an order metric?)

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