"Infinite set" actually has a formal definition and such sets do exist. The set of all the natural numbers exists, and therefore, the size of the set also exists. That size happens to be a non-finite number called Aleph-Null. Your argument is wrong. And it does behave like a number because you can do basic arithmetic with it.

"Infinite set" actually has a formal definition and such sets do exist. The set of all the natural numbers exists, and therefore, the size of the set also exists. That size happens to be a non-finite number called Aleph-Null. Your argument is wrong. And it does behave like a number because you can do basic arithmetic with it.