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

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)

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.

Not between floating point numbers.