Of course, you could argue that a bijection class of sets is there to formalize the notion of a quantity that generalizes to infinite sets.
Indeed, 2 sets like (1,2,3) and (A,B,C) have the same cardinality, which is 3, and cardinality is IMO the generalization of quantities to infinite sets like the real numbers. Indeed, 2 sets have the same cardinality if and only if they have a bijection.
That said, cardinality is a very coarse-grained way to look at quantities, as the Turing Machine computable sets and all arithmetical sets, which include Turing uncomputable sets, are both countable:
Of course, you could argue that a bijection class of sets is there to formalize the notion of a quantity that generalizes to infinite sets.
Indeed, 2 sets like (1,2,3) and (A,B,C) have the same cardinality, which is 3, and cardinality is IMO the generalization of quantities to infinite sets like the real numbers. Indeed, 2 sets have the same cardinality if and only if they have a bijection.
That said, cardinality is a very coarse-grained way to look at quantities, as the Turing Machine computable sets and all arithmetical sets, which include Turing uncomputable sets, are both countable:
https://en.m.wikipedia.org/wiki/Cardinal_number