Cowbacca wrote:siliconfury wrote:Cowbacca's on the right line with sets. When you have a set of numbers form 1 to infinity, you could have an infinite number of sets of those sets of numbers.

I did this in uni and we had to prove it (as in proper mathematical proof, not with words), and I vaguely remember something like this.

Thats pretty much spot on. This is one of the very first things we were taught at university level maths. If you're starting at 1 and moving to infinity, you can always call that set a subset of a larger set. In that case, the number of subsets are infinite. Therefore, the size of the largest set you have at any given time is larger than any of its subsets, and therefore is a larger infinity. You will, of course, never reach a finite set with finite subsets, so it just keeps going.

An even better one I prefer is to escape the conventional thinking that infinity goes "upwards". If I start with a set A = {n,1}, where A∈ℝ and try and list every subset imaginable, I'd soon begin to realise that it was impossible. Even though the numbers would

*tend*to zero, because the set of Real numbers contain all rational and irrational numbers, my decimal figures would just keep getting longer and longer.