## The Ultimate Infinity

Infinity is big. There are infinitely many integers. But there is another infinity that’s so large, it is greater than the first infinity. Let’s call this infinity:2. There is an even greater infinity that can’t be matched up to infinity:2. It’s infinity:3. Infinity:3 is larger than the set of *numbers*. There are more…um…things in infinity:3 than there are numbers in the whole of existence.

So you can keep doing this until you get to infinity:infinity. But then you can do it all again so you have infinity:infinity:infinity. You can keep cycling until you have infinity:infinity….infinity:infinity, with an infinite number of infinities. But the number of infinities in the chain is only infinity:1. What if there are infinity:infinity infinities in the chain, or infinity:infinity….infinity:infinity infinities in the chain? And how many infinities are there in THAT chain? So you end up getting a number that is so incredibly big, it’s not even infinity. It’s a whole entire realm of number that cannot be defined in any way by anything, ever. I will call this number thing “infinitismo”. Nothing is bigger than infinitismo.

What do you think of this concept? Do you understand it?

It is really cool. š

Where’s a crazy smiley when you need one?

Edit 8/2/09: This concept already exists, and it is known as “omega”.

http://en.wikipedia.org/wiki/Continuum_hypothesis

Apparently, there is no infinity bigger than 2^infinity. That’s weird.