Fair enough. I like discussing religion in circles like this one, because I'm convinced there is a lot of value to be found in religious traditions, but I find it hard to connect to the typical religious crowd.

Interesting example, because he could get in a spaceship at age 19, travel out and back at very high speeds, and arrive back at Earth 101 years later having aged just one year. He turned 20 and 120 at the same time.

I realize I've turned myself into a prime example of the pedantry you mentioned, but what I mean to say is that strict logic can be misleading if we don't have the whole picture, which we probably don't.

And not just that. I feel that many of the habits of thinking that lead to success in software engineering actually have pretty limited applicability, but too many software engineer internet commenters parochially assume those habits are superior and universally applicable. It's hard for me to articulate though, because I have those same habits and it's hard to see outside one's limitations.

While Z is not a subset of N, N maps 1-1, onto to Z (i.e., they have the same cardinality). That means every element of one set has a corresponding element in the other and vice versa.

Similarly, ismorphisms, homeomorphisms, diffeomorphisms are formalizations of the idea of "different but equivalent in the relevant structures".

I do not have a deeper point to make, but I think your intro argument is not as solid as you might imagine. Plus, things get weird when you go beyond discrete infinities and into the continuum and beyond.