So, what if we just re-named numbers, and just gave them a different label.
Instead of 1, we call it 1 squared, which is 1.
Instead of 2, we call it 2 squared, which is 4.
Instead of 3, we call it 3 squared, which is 9.
Here is where the problem (question number one) exists.
We've skipped over a lot of numbers so far.. 2, 3, 5, 6, 7, 8.. but these sets STILL have the same number of members.