As long as you're careful, you can treat infinity as a number. It lacks some nice properties but can allow you to clean up a lot of statements. For instance if you want to define a measure on some sigma algebra, it's useful to be able to let some sets have infinite measure. Analogously, you may have a function that has an integral, but one which does not converge.

Anyway, numbers aren't real. They're all "concepts", so, as long as our statements are consistent, we can do what we want!

what is an example of a mathematician using infinity as a number?