Infinity is not a "really really big number". It is not "the biggest number that exists". It's not the number you get when you divide by zero. There is no such thing as a finite infinity.
It's not equal to the volume of the universe, the density of a black hole, or the the IQ of God. Infinity isn't any of these things because it's not a number or quantity of any kind. Infinity is a concept.
Technically speaking, infinity is a transfinite number. (In this context, you're better off saying "omega-null".) Whatever concrete, finite number you pull out of your head, infinity is bigger. You can approach it (using a limit), but you won't ever reach it.
If you could treat infinity like a number, then you'd have to confront the fact that two times infinity is infinity, ten plus infinity is infinity, and infinity divided by 1048576 is infinity. Combining this with the factually incorrect idea that 1/0 = infinity, you could easily prove that all numbers are equal to each other and mathematics as a discipline is a bunch of self-contradictory nonsense.
This is in spite of the fact that your personal computer is still chugging along just fine in merry ignorance of your superior wisdom.