Ok thanks, didnt realize that with the different corresponding function. My logic would be that y=2*(x+1/2) can be used to define every number in both sets (where y is 1-3 and x is 0-1). But there are numbers outside of the set 1-3, say 15. So if I made a different set, inclusive of 1-3 and 15, then there are more numbers in this new set.

I guess I understand that I'm wrong since mathematicians smarter than me have come up with theories/proofs to what you're saying, but I think there's logic in my argument.

How is that true though? For every number between 1 and 3, there is only one correlating number between 0 and 1 (1/x). But for every number between 0 and 1, there are two correlating numbers (x+1 and x+2)