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 set R, of real numbers and Z the set of integers. Both sets are infinite, however R has a higher level of infinity than Z, obviously. So can a bijection exist between one such infinite set and its infinite subset?