you can show two sets have the same number of elements without having an intrinsic notion of "number" - find a bijection between them, mapping every member of set A to set B and vice versa, and you know you have two identically-sized sets without doing any counting.
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you can show two sets have the same number of elements without having an intrinsic notion of "number" - find a bijection between them, mapping every member of set A to set B and vice versa, and you know you have two identically-sized sets without doing any counting.
And for completeness’s sake, this is how the concept of "having the same size" can be, and indeed is, extended to infinite sets.