What is the number after infinity?

Infinity is as big as you can get, so there is no number after it.

There is also a "negative infinity" going the other way, so the total number of integers could be considered as two infinity (2 x ∞), or two ∞ plus 1 if you include zero. But usually infinity is defined to include the entire set of integers.

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Except that infinity plus infinity, or even infinity times infinity is still infinity. However, infinity to the power of infinity is a higher level of infinity (Aleph1 rather than Aleph0). And if that does not do your head in, there is a lot more to the mathematics of infinities.