> If sizes were sensible then… Sorry, but they simply don’t meet your (non-standard) definition of sensible. Both of the sets you mentioned can be interpreted

> If sizes were sensible then… Sorry, but they simply don’t meet your (non-standard) definition of sensible. Both of the sets you mentioned can be interpreted as the set of even integers. This set is in bijection with itself (trivially), and thus is not considered to be strictly smaller than itself.