You can't divide something by infinity. It is not a number. 2infinity is just infinity. No number is greater than infinity. It just means continues forever. Either it does or it doesn't. There's no in-between, no greater than, no comparing two of them, there is nothing to compare. I get the sets concept and what you are demonstrating. But the mistake made is in the definition of the sets. It's as if you are assuming they are finite when you compare them.