I mean that it is sort of a rhetorical sleight of hand to say that real numbers 'exist'. Integers for instance exist, in that they count things and label the ca

I mean that it is sort of a rhetorical sleight of hand to say that real numbers 'exist'. Integers for instance exist, in that they count things and label the cardinalities of sets. And rational numbers exist because they label the ratios of cardinalities. Negatives are the difference. Etc. But for any particular real it is much more tenuous. You can't produce any physical system that demonstrates almost all real numbers in any way. Some of them obey equations so you can talk about 'the solution to this equation', which is real enough. But most of them are inaccessible, even in principle, and I think the only reason people default to thinking they have the same existence as like, integers, is because we're taught them early enough that we don't question it.