Okay this is just a musing I'm having and it might be already talked about or proven or whatever.

If G is an infinite set and H is an infinite subset of G, can a bijection occur between G and H?

In this case G does not equal H.

For example the setR,of real numbers andZthe set of integers. Both sets are infinite, howeverRhas a higher level of infinity thanZ, obviously. So can a bijection exist between one such infinite set and its infinite subset?