by **Moosey** » June 11th, 2019, 1:42 pm

I have a huge finite number for you:

ω-1. It’s even bigger than Sam’s number.

Strictly speaking, ω is the magnitude of the set of all finite natural numbers, and the magnitude of a finite set of natural numbers starting from zero is its last number +1. Obviously, the main problem with this is that you can’t say this about an infinite set of finite numbers. Also, subtraction is rather Ill-defined with infinite ordinals, since there isn’t any last number before a limit ordinal, and you can think of subtraction as the iteration of the predecessor function, P(n), which is n-1. n-1 is just the last number before n (when we’re dealing with integers), so:

You cannot subtract 1 from a limit ordinal, and ω is a limit ordinal. ω-1 is, quite literally, the last finite number. And there’s no such thing.

If you’re a Googologist you probably got that this was a joke by the time you read the words Sam’s number.

My rules:

They can be found

hereAlso,

the tree gameBill Watterson once wrote: "How do soldiers killing each other solve the world's problems?"