It’s interesting that you choose dividing by zero as your comparison to infinity, because there are infinite possible solutions to x/0.

I think if you ask a mathematician what x/0 is, they’ll say “undefined” or “that’s not a valid question”. But if you ask how many natural numbers there are they’ll say “infinity” (or ℵ-zero). But we could have defined x/0 as “foo” to see what resulted, like sqrt(-1) is *i*. But I think not much results and so people don’t bother, and maybe we shouldn’t have bothered with infinity either.

(I don’t think the same about infinitesimals though! Analysis is a valid field of study!)

how often was zero (or nothingness) included in the paradoxes in the book?

There’s one of the silly 1==2 tricks where a divide-by-zero is obfuscated. There’s a number that involve infinite series, or infinite processes. The chapters on formal systems, voting, physics, etc don’t involve such things though, so I wouldn’t say that they’re all based on it.

The book “solves” the paradox by stating that, yes, you can add an infinite number of guests to Hilbert’s hotel, even when it was full to begin with. Again, it’s only stating

surprisingresults and if Hilbert considered it sufficiently surprising to articulate then I’m not going to argue!It’s not that infinity doesn’t work, it’s that it struck me that it’s barren of interesting structure. Yes, infinity + infinity is still infinity. And there’s an unlimited number of infinities that are sufficiently ill-behaved that they don’t even form a set. It seems like a concept that has very little to offer.