Depends on which infinities. For example, the amount of even numbers and the amount of even+odd numbers are both infinity (aleph null). so the set of all even numbers is the same size as the set of all even and odd numbers. However the set of all numbers between 0 and 1 is infinitely larger than either of those (aleph one).
½ * Infinity != infinity?
Depends on which infinities. For example, the amount of even numbers and the amount of even+odd numbers are both infinity (aleph null). so the set of all even numbers is the same size as the set of all even and odd numbers. However the set of all numbers between 0 and 1 is infinitely larger than either of those (aleph one).
And then there are those giant insects that never forget: the aleph ants.