I believe there are differing ways to look at the concept of infinity. In one way, you can instantly say it exists when all one needs to do is keep adding one to the last number, thus theoretically, if one could live forever, one could count forever.
To counter that, one could also state that the universe will not last forever, thusly, you could not keep counting. Even a super computer would come up with an oddly huge number, before it’s inevitable destruction if from nothing else- from atomic decay.