We are only taking sizes here not “is it a group” etc. So let’s play that old 21s drinking game, but infinitely instead of 1 to 21, and rename 1 to 1, 2 to 4,

We are only taking sizes here not “is it a group” etc. So let’s play that old 21s drinking game, but infinitely instead of 1 to 21, and rename 1 to 1, 2 to 4, 3 to 9 and so on, up to x for any x. Same set, different lingo. That you can’t map back 5 is irrelevant although kind of leaves a bad taste.