[Swizec]

> Does it makes sense in the real world to assert the existence of an infinite set, and have different sizes of infinities as a consequence?

Yes it does. But I might be biased because I'm a programmer and one of my jobs is adding constraints to unsolvable problems so they become solvable in the infinite set my clients actually care about.

It's surprising how easy it is for somebody to specify a problem that is unsolvable, only for it to become solvable once you ask them what they really want.