How many numbers are in Pi?

It's irrational.

You can not multiply infinity. Infinity is not a number.

Suppose you have an infinite hallway with an infinite amount of numbered rooms. They're all full. If an infinite tour bus with an infinite amount of tourists arrives, and they all want a room, you can accomodate them the following way: you ask the current guests to move to the room number that is double their current room number. Since there are infinite even numbers, you will now have cleared an infinity of rooms for your new guests.

I hope I don't have to argue that infinity + 3 is still infinity.

But you did not, because if you have infinity rooms, you will continue filling them up with infinity guests. You will never fill up every fill up every room.

If you have an countably infinite amount of rooms, and a countably infinite amount of guests, the correspondence is 1:1; thus, the rooms will be filled up. By countably infinite, I mean a set with which one can define a one-to-one function from the counting numbers to the set. The definition of infinity is "unending"; saying that "you will never fill up every room" is saying " either infinity > infinity, or infinity ends somewhere."