> I personally have my doubts that real numbers exist in any meaningful sense
I think we're in agreement here in principle. (Since we're on the topic, I'd like to add that naming this suspicious set "real" numbers is a tad bit ironic)
That said, I don't like the idea of having a group of people "owning" words as if they had a monopoly over them. The statement "the cardinality of integers is the same as real numbers" can be understood to mean "real numbers should actually be computable numbers".
I didn't bother to look up what Hotz wrote on twitter that triggered this discussion, I was just providing context that the issue of cardinality isn't as settled as some might think. It's probably not fruitful to argue whether a statement from hearsay uses words accurately or not though.
I think we're in agreement here in principle. (Since we're on the topic, I'd like to add that naming this suspicious set "real" numbers is a tad bit ironic)
That said, I don't like the idea of having a group of people "owning" words as if they had a monopoly over them. The statement "the cardinality of integers is the same as real numbers" can be understood to mean "real numbers should actually be computable numbers".
I didn't bother to look up what Hotz wrote on twitter that triggered this discussion, I was just providing context that the issue of cardinality isn't as settled as some might think. It's probably not fruitful to argue whether a statement from hearsay uses words accurately or not though.