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cyclopentane's definitions

Cardinal

Obscure slang for a man's penis.
Don't put your cardinal around that hoe.
by cyclopentane October 30, 2022
mugGet the Cardinalmug.

The Alpine Kiss

Doing a line of cocaine with your special other from opposite ends, then kissing when your noses touch.
I met my love by doing The Alpine Kiss
by cyclopentane July 11, 2022
mugGet the The Alpine Kissmug.

sin

why does everyone hate sinusoids so much?
anyways, sin(x) is the height of a point on the unit sphere which is x radians away from 0 radians
sin pi over two is equal to one.
by cyclopentane June 27, 2023
mugGet the sinmug.

Georg Cantor

Alpha male gigachad who invented set theory, was called a liar through his whole life, discovered an even stronger notion of infinity, went insane, died, and then everyone realised how true everything he said was.
Georg Cantor is a set theorist, usually considered the first one.
by cyclopentane June 8, 2023
mugGet the Georg Cantormug.

Fast Growing Hierarchy

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.
Graham's Number is approximately equal to f(ω+1,3) within the Fast Growing Hierarchy.
by cyclopentane December 1, 2022
mugGet the Fast Growing Hierarchymug.

Finnish Memes

Finnish Memes (often abbreviated FMs) are in an alternate reality bubble within our own world, they appear to be what people would find funny in a world similiar, but different from ours.
Finnish memes are crazy, and you can never understand them since they're in, well... finnish.
by cyclopentane August 4, 2022
mugGet the Finnish Memesmug.

extraserial

(n.) Content related to a piece of media that isn't a direct part of it. Think mini-episodes, standalone animations, offshoot series, etc.
This show's pretty good, but steer clear of the post-credits, the extraserial stuff is pretty mid.
by cyclopentane December 3, 2024
mugGet the extraserialmug.

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