[jimhefferon]

This post is not about real numbers, though. It's about floating point numbers.

[ot]

Even if we were talking about real numbers (which we're not), it would still be true that (0, 1) and (1, +inf) have the same cardinality :)

As touched on in the post, 1/x is an explicit bijection (but any set of real numbers that contains an interval has the same cardinality)

[mbauman]

But perhaps that's the interesting point — 1/x is *cannot be* an exact bijection for floating point numbers, because there's not a one-to-one mapping between the two sets.