Hmm I’ve consulted a mathematician that I know, and they say that cardinality isn’t really the same as “size”, but comparing the two infinite sets of the same cardinality is basically meaningless because infinity is not a “number”, even though one set is provably “bigger” than the other set
Yeah, if you use an arbitrary standardized measuring stick, the problem goes away, as it is no longer infinite.
Still a fun thought experiment to demonstrate how unintuitive infinities are!
Anyway, major kudos to you for engaging with this thread in good faith! That is so rare these days, I barely venture to comment anymore. Respect.
… and thank you for the opportunity to share a weird math fact!
Hmm I’ve consulted a mathematician that I know, and they say that cardinality isn’t really the same as “size”, but comparing the two infinite sets of the same cardinality is basically meaningless because infinity is not a “number”, even though one set is provably “bigger” than the other set