Yeah no, nothing is bigger than infinity. That's why it's called infinity, end of story. You can add all you want, but infinity will always be infinity because it is infinite.
1to the power of 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 To the power of 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 0000000¹⁰⁰⁰⁰⁰×10¹⁰⁰⁰⁰ = N
No, I'm afraid. You can prove that TREE(4), for example, is larger than TREE(3). With TREE(4), we can make all the trees possible with TREE(3) and then, even if we've used up all other colours, we could make at least TREE(3) more trees out of just the fourth colour by just building a very tall tower of dots and then going down by one. Thus, TREE(x) > 2(TREE(x-1)).
@2:42 - [BIG BRAIN MOMENT] Actually, Rayo's Number is being defined as being the largest number that is smaller than Alpeh Nol. If there was a number in between Rayo's Number and Alpeh Nol, that number would be Rayo's Number.
Actually, unless I'm mistaken, Rayo's number is defined as the smallest positive integer bigger than any finite positive integer named by an expression in the language of first-order set theory.
The thing that always sticks in my throat with these numbers is that for Graham's Number we can see how it's constructed and why it's so large, but Tree(3) et al are described as "omg like, SOOOOO big... you can't even..." without any attempt to ever SHOW with even a hand-waving attempt at the operations used to BEGIN the climb to it.
I think infinity should behave like tetris game. After some point, it will turn negative, then down to zero again. And this point could have been called absolute point since 1/0 equals this point. If we think about the number line is on a sphere, that would make more sense.
I think I get it so the first color can only have one vertex the second color can have two vertices and that's why you only get three out of three two. Because I was wondering why can't you just take two green dots and stick a line between them.
