To elaborate on what Liz said, the way you compare sizes of infinite sets is by constructing functions between them. If you can place the items in the two sets in a one-to-one correspondence, the sets are the same size. If you try doing that between set A and set B, but there are elements in set A with no corresponding element in set B, then set A is bigger.
Cantor’s diagonalization argument proves that there are more reals than integers. I found some explanations that aren’t too jargony here. It’s a great introduction to reasoning about infinities. If you’re interested in the topic in general, I highly recommend Everything and More by David Foster Wallace, regardless of your level of math knowledge.
To elaborate on what Liz said, the way you compare sizes of infinite sets is by constructing functions between them. If you can place the items in the two sets in a one-to-one correspondence, the sets are the same size. If you try doing that between set A and set B, but there are elements in set A with no corresponding element in set B, then set A is bigger.
Cantor’s diagonalization argument proves that there are more reals than integers. I found some explanations that aren’t too jargony here. It’s a great introduction to reasoning about infinities. If you’re interested in the topic in general, I highly recommend Everything and More by David Foster Wallace, regardless of your level of math knowledge.