The rules of transfinite arithmetic take over. Infinity times 2 There are many other infinite sets whose sizes are interesting and surprising to compare. This means that they are the same size. There are as many even numbers as there are counting numbers. Infinity times two is infinity.
Infinity divided by two is infinity.
These are all the fractions whose numerator is one. There are an infinite number of those. We could make infinitely many such lists, each one with infinitely many rational numbers on it. Certainly that must be more than infinity. We can't just say that it seems like there are more rational numbers than counting numbers, we have to prove that there are.