The real question is, is infinity really the largest number.
For example if we call infinity - omega, then omega + 1 is bigger than omega, but still infinitely large.
If we keep going we can get omega + omega = 2omega.
Continuing we get to omega^omega, but then omega^omega+1>omega^omega.
If we keep going, we can get omega^omega^omega... - omega times. Then if we take that number +1, we get something bigger still, and start all over again.
Meaning there are infinitely many, infinitely large numbers. By this definition omega-omega=0 (I think).