As far as I know, there is no proof that infinity does not exist, however I suspect it is true. There is no infinity, only very big numbers.

Experience tells us that everything that we once thought infinite has been shown to be finite. For example time and space, like the universe, are finite *.

Reason also tells us that infinity doesn't exist. Infinity is a concept that the human mind cannot rationalize and comprehend. It is an abhorrent thought.

* But, you might say, if the universe expands forever outwards, which is certainly a possibility, won't time go on infinitely? No, as the universe expands, its entities and energy will be spread out. The entropy of the universe will increase, it will in effect flatten, and it will begin losing dimensions.

If infinity does not exist, it means there are no true singularities.