Rural Dictionary

fast food adultery

When you and your spouse say you are going to eat healthy together and then one of you eats fastfood in secret

It was only 2 weeks into the new year and I committed fast food adultery behind my wives back.

by Glenydotcom2 January 8, 2018

fast food hottie

The thin, flawless, outright sexy girls you see in fast food commercials on television.

Did you see that hot babe on that tv commercial? She looks nothing like the mutant swine you actually see eating at fast food establishments on a regular basis.

*Sigh* I know! Fast food hotties.

by still-single October 17, 2011

Think fast chucklenuts!

Get ready cause if you hear someone scream this you are about to get flash banged by really anyone. Most commonly the Scout from TF2.

"Think fast chucklenuts!"

by Freaky_Fesh May 31, 2023

The fast growing hierarchy (shortened to FGH) is a method of defining large numbers. It takes in two inputs.

We define f(0,n) = n+1. For example: f(0,3) = 4. Next step is iteration. f(1,n) is f(0,f(0...f(0,n)...)) where f(0,...) is iterated n times. For example, f(1,2) = f(0,f(0,2)) = 4. Same rules for f(m,n).

Now let's define what ordinals are. Very simplified, they're a kind of infinity.
Consider this: |||....|

This has infinite sticks, but there's a 1st stick, 2nd stick... the last stick is the ωth stick. You can have ω+1, ω+2, ω+3 etc too. For our purposes, a limit ordinal is an ordinal that has no finite part at the end (so ω+3 is not a limit ordinal but ω×3 is.).

So how can we use this within FGH? We need to define a fundamental sequence (FS). An FS is the steps we take to reach a new limit ordinal. So the FS for ω is 0,1,2... and for ω×2 it's ω,ω+1,ω+2...
We can write this as: ωn = n, ω×2n = ω+n, ω^2n = ω×n and so on. There are more ordinals, but it'll do for our purposes.

This is not the only system for an FS. There's more, but I cannot fit it in an entry.

Now consider an ordinal α. Now FGH can be defined concretely:
for f(α,n):
if α is 0, it is n+1.
if α is not a limit ordinal, it is f(α-1,f(α-1...f(α-1,n)...)) where f(α-1,...) is iterated n times.
if α is a limit ordinal, it is f(αn,n).

Let's do an example: f(ω,3) = f(3,3) = f(2,f(2,f(2,3))). I know that f(2,n) = n×2^n, so it's 1.804356 × 10^15151336, which is HUGE! Imagine how large f(ω,10) is.