What is the slowest growing function ever? How do you represent it? With slow-growing hierarchy.
Category: The googology series
In this category, we will be exploring different hyper-operations, like ↑ (Knuth’s arrow notation), TREE functions, SSCG, and many, many more. If your brain becomes a black hole on the journey, don’t blame me!
I don’t think you have any idea how fast I am
I'm fast as fΓ0(n) boi What on Earth is fΓ0(n)? Remember the last post, Fast as (insert word here) boi, where I talked about the fast-growing hierarchy? These are just extensions on it. Let's take a step down. Do you remember ω? The ordinal that used the diagonal of the hierarchy table? (I'll be completely … Continue reading I don’t think you have any idea how fast I am
Fast as (insert word here) boi
You guessed it: fast-growing hierarchy! On Wikipedia and the Googology Wikia, it's complicated and long and boring and zzZZZZZZ... so I'll try my best to simplify it. Define a function, f0(n) = n + 1. It doesn't grow so fast, does it? For fa(n), that is fa-1n(n), where that denotes doing the previous function n … Continue reading Fast as (insert word here) boi
Fish number 3.
We're doing this again! I'm skipping Fish Number 2 because I'm really confused by it. I'll do it next time. Remember Fish Number 1? With the S and SS map? We have to define a new map. The s(n) MAP! This is mainly just copied from the Googology Wikia. Define s(n) map as: s(1)f := … Continue reading Fish number 3.
Who loves fish? If you do, YOU'LL LOVE THIS! jk but this number is still huge, but smaller than Rayo's number.
Don’t ask this particular beaver to do your work for you.
Busy beavers and Turing machines and big numbers and ... what.
One amazing step for man…
This is a really big step. RAYO'S NUMBER. It's defined as Rayo(10^100). For all I know, it might end with 7. What is Rayo(n)? So you see, there used to be this battle at MIT named THE BIG NUMBER DUEL The duel was not a fighting duel. No! This duel was to see which person … Continue reading One amazing step for man…
Funny incoming. And also, xkcd is here. And no, I don't know if that number is involved in this. Remember Graham's number? Let's call it G. I'll have to define something. Ackermann's function. If you know this, then great! If not, then here it is. Wilhelm Ackermann created a function named after himself. The function … Continue reading xkcd
Seriously, what is this?
SSCG(3)? WTF? So, you remember TREE(3)? It's WAY, WAY BIGGER than that. Now, to understand this, we need to know FRIEDMAN'S SSCG FUNCTION. Information provided by Wikipedia and Googology Wikia. A simple subcubic graph. If your first reaction was "What?" then you're probably not alone. A simple subcubic graph is a finite "simple graph" with … Continue reading Seriously, what is this?
The largest number yet… a tree.
Honestly, three trees are way larger than graham's number. All the information provided is from Numberphile, again. TREE(3). Remember Graham's Number? Well, this TREE(3) is so large, Graham's Number will look tiny. Miniscule. It all starts from a game that looks fun. You know trees? No, not nature. Mathematical trees. Kinda. Let's play a game. … Continue reading The largest number yet… a tree.