Equivalence classes of sets under directions is the standard way of defining “size” (cardinality), so unless you are talking about some more specific idea this is not just something in some circles of math.
There are also ordinals, which are ordered sets under order isomorphism. You use cardinals when you only care about size (meaning each element doesn’t have an individual identity), and ordinals when you also care about order (so each apple still doesn’t have an individual identity, but the way they are lined up on the plate matters)
Honestly neither are useful to most mathematicians, beyond distinguishing countably infinite from uncountably infinite.
Equivalence classes of sets under directions is the standard way of defining “size” (cardinality), so unless you are talking about some more specific idea this is not just something in some circles of math.
There are also ordinals, which are ordered sets under order isomorphism. You use cardinals when you only care about size (meaning each element doesn’t have an individual identity), and ordinals when you also care about order (so each apple still doesn’t have an individual identity, but the way they are lined up on the plate matters)
Honestly neither are useful to most mathematicians, beyond distinguishing countably infinite from uncountably infinite.