We Almost Made It Four Years Without Major Drama...
Better than I expected, to be honest. So, three weeks ago, User blog:SolverSeek666/some problem with my discord was posted, with SolverSeek asking about DM'ing googologists on Discord. P-bot would comment with the following: https://googology.fandom.com/wiki/User_blog:SolverSeek666/some_problem_with_my_discord?commentId=4400000000000046849. (For any comments using the username "Ytosk", that particular person has changed their username to Racheline and wishes to not be referred to by her former username. I made this mistake in a comment that will be linked later in the post, which is ignorant on my part. Rachel, if you're reading this, I apologize.) Well, Tsskyx happens to be active on this site as well, and he took offense to being accused…
ξ function
How powerful is this?
ξ(0)
ξ(0)+ξ(0)
ξ(1)
ξ(1)+ξ(0)
ξ(1)+ξ(1)
ξ(2)
ξ(ξ(1))
ξ(ξ(ξ(1)))
ξ(ξ(1,0))
ξ(ξ(1,0))+1
ξ(ξ(1,0))+ξ(1)
ξ(ξ(1,0))+ξ(ξ(1))
ξ(ξ(1,0))+ξ(ξ(1,0))=
ξ(ξ(1,0)+1)
ξ(ξ(1,0)+ξ(1))
ξ(ξ(1,0)+ξ(ξ(1)))
ξ(ξ(1,0)+ξ(ξ(1,0)))
ξ(ξ(1,0)+ξ(ξ(1,0)+ξ(ξ(1,0))))
ξ(ξ(1,0)+ξ(1,0))
ξ(ξ(1,0)+ξ(1,0)+ξ(1,0))
ξ(ξ(1,1))
ξ(ξ(1,ξ(1)))
ξ(ξ(1,ξ(ξ(1,0))))
ξ(ξ(1,ξ(ξ(1,ξ(ξ(1,0))))))
ξ(ξ(1,ξ(1,0)))
ξ(ξ(1,ξ(1,ξ(1,0))))
ξ(ξ(2,0))
ξ(ξ(2,0)+1)
ξ(ξ(2,0)+ξ(ξ(1,0)))
ξ(ξ(2,0)+ξ(ξ(2,0)))
ξ(ξ(2,0)+ξ(1,0))
ξ(ξ(2,0)+ξ(1,ξ(1,0)))
ξ(ξ(2,0)+ξ(1,ξ(2,0)))
ξ(ξ(2,0)+ξ(1,ξ(2,0)+ξ(1,ξ(2,0))))
ξ(ξ(2,0)+ξ(2,0))
ξ(ξ(2,1))
ξ(ξ(2,ξ(1,ξ(2,0))))
ξ(ξ(2,ξ(2,0)))
ξ(ξ(3,0))
ξ(ξ(4,0))
ξ(ξ(ξ(1),0))
ξ(ξ(ξ(ξ(1,0)),0))
ξ(ξ(ξ(ξ(ξ(ξ(1,0)),0)),0))
ξ(ξ(ξ(1,0),0))
ξ(ξ(ξ(ξ(1,0),0),0))
ξ(ξ(ξ(ξ(ξ(1,0),0),0),0))
ξ(ξ(ξ(1,0,0),0))
ξ(ξ(ξ(1,0,0),0)+ξ(1,0))
ξ…
Finity
'Finity'Bold text (∝) is a number which adds all positive finite integers that have been named or thought of discluding itself. If somebody says finity+1 they just made up a new finite number therefore finity+1 becomes smaller then finity So it is now an initial finity or potential finity
finity is larger than
- Nyarthototep
- Ultimate croutonillion
- Croutonillion
- Ultimate oblivion
- Large number garden number
An example of pbot calling me racist without evidence
I have been issued a warning for "labeling" pbot.
However, I have only been asking him about HIS labelings of other people, such as when he calls Rachel a plagiarizer, or an unknown member of the googology wiki a racist.
He never provided evidence for these labelings, only ever excuses, such as that he already provided them to someone else (unknown who) or that he cannot find a place to upload the evidence where it couldn't be deleted (many places exist, it shouldn't be taking this long, he just doesn't want to.)
In the following comment, he lumped me together with a bunch of other people and implied that these people are racists. Since he failed to specify which user, it is implied that he meant all of them are being racist, which, without e…
The N(n) function
N(n)= amount of possible circuits such that (number of inputs)+(number of Nand’s)+(Number of outputs)
Help with this notation please?
So I was making this notation, and ran into a bit of a roadblock. The bolded/underlined part is the part that needs work. Basically, how can I apply the ordinal to itself while maintaining maximum efficiency, sensibility, and simplicity? Thanks.
- Triangle Hexagon Ordinal Matrix Notation
- # can be any array or an empty array. Definitions with "1"s take priority. "ω" is not a variable.
- ◭a◮ = a↑↑...↑↑a with a ↑'s
- ◭a, 1◮ = ◭◭...◭◭a◮◮...◮◮ with ◭a◮ nestings
- ◭a, 1, 1, 1...(c 1's)◮ = ◭a, a, a...◭a, a, a......◭a, a, a...◭a, a, a...a◮◮...◮◮
- Steps: take off the last "1", replace every "1" with a, replace the last a with the whole array, nest it a times.
- Example: ◭3, 1, 1, 1◮
- Step 1: ◭3, 1, 1◮
- Step 2: ◭3, 3, 3◮
- Step 3: ◭3, 3, ◭3, 3, ◭3, 3, 3◮◮◮
◭a, 1, 1, 1...(c 1…
Hashtag Expansion System
We can define a Hashtag expansion as a set of steps which are:
- Firstly start with a expression, (eg: #(0)(1)(1)[3] )
- Then expand the last digit by the amount of times implied in the [n] brackets and square it. (our example is now #(0)(1)(0)(0)(0)[9] )
- Add the 0's into the [n] brackets and square it for each time a (0) is added in.
- Now Repeat steps 1, 2 and 3 untill you exhaust the last > 0 digit in which you expand into 0's.
(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)[4096]
...
x-oogols
Ok, so here is a concept I have decided to attempt as inspired by Tafgo's Monogols or Monogooogols, I will try attempt a googol or googol family for each prefix.
Monoogol = 101 = 10
[WIP]
When or how does a personal website become reliable?
I'm not saying this would happen to me, I'm pretty unreliable if you compare me to any other person in this wiki, but I was just curious.
What or how would a source (personal website) become reliable and not in need of the personal website tag? (what are the parameters for a website to achieve that?)
How much my M(k,s,l,d,m) funtion grows
Definition:
Let MC(k,s,l,d,m) be the smallest whole number bigger than the largest finite maximum of the total number of non-blank symbols written by a system of m deterministic Turing machines of the same style (alphabet size k, s non-halting states, d-dimensional hypercubic tape with d−1 non-infinite dimensions of length l, and at least one infinite dimension), where the transition function of each machine can be influenced by the entire set of transition functions of all other m−1 machines in the system, before all m machines eventually halt according to a defined joint halting condition. The tapes are initially all blank. If no such finite maximum exists (i.e., the number of non-blank symbols can grow indefinitely for some systems), the…
Monogoogols
Notice: All of these monogols are equal to 10
- Monogol - .
- Monogolplex -
- Monogolduplex -
- Monogoltriplex -
- Binogol -
I understand M-cardinal correctly?
ψ(Μ)=ψ(Ι)=ψ(Ω_Ω_…)
ψ(Ι(Μ)+1)=ψ(Ι+1)
ψ(Ι(Μ)+ψΙ(Ι(Μ)))=ψ(Ι+ψΙ(Ι))
ψ(Ι(Μ)*2)=ψ(Ι*2)
ψ(Ι(Μ)^2)=ψ(Ι^2)
ψ(Ι(Μ)^Ι(Μ))=ψ(Ι^I)
ψ(Ω_I(M)+1)=ψ(Ω_I+1)
ψ(Ω_Ω_I(M)+1)=ψ(Ω_Ω_I+1)
ψ(M+1)=ψ(Ι_2)
ψ(I(Μ+1)+ψΙ(Μ+1)(Ι(Μ+1)))=ψ(Ι_2+ψΙ_2(Ι_2))
ψ(Ι(M+1)^I(M+1))=ψ(Ι_2^I_2)
ψ(Ω_Ι(M+1)+1)=ψ(Ω_I_2+1)
ψ(Μ+2)=ψ(I_3)
ψ(Μ+3)=ψ(Ι_4)
ψ(Μ+ψΙ(Μ))=ψ(Ι_I(I))
ψ(Μ+ψΙ(Μ+ψΙ(Μ)))=ψ(Ι_ψΙ(Ι_ψΙ(Ι)))
ψ(Μ+ψΜ(Μ))=ψ(Ι_I)
ψ(Μ+ψΜ(Μ+ψM(Μ)))=ψ(Ι_I_I)
ψ(Μ*2)=ψ(Ι(2,0))
ψ(I(Μ*2)^I(M*2))=ψ(Ι(2,0)^I(2,0))
ψ(Ω_I(M*2)+1)=ψ(Ω_I(2,0)+1))
ψ(Ι_I(M*2)+1)=ψ(Ι_I(2,0)+1)
ψ(M*2+1)=ψ(Ι(2,1))
ψ(Μ*2+ψI(M*2))=ψ(Ι(2,ψΙ(2,0)))
ψ(M*2+ψΜ(Μ*2))=ψ(Ι(2,ψΙ(2,0)(I(2,0))))
ψ(Μ*2+ψΜ*2(M*2))=ψ(Ι(2,Ι(2,0))
ψ(Μ*3)=ψ(Ι(3,0))
ψ(Μ*4)=ψ(Ι(4,0))
ψ(Μ*ψΜ(Μ))=ψ(Ι(Ι,0))
ψ(Μ*ψΜ(Μ*ψΜ(Μ)))=ψ(Ι(Ι(Ι,0),0))
ψ(Μ^2)=ψ(Ι(1,0,0)
ψ(Μ^2*2)=ψ(I(2,0,0))
ψ(Μ^3)=ψ(I(1,0,0,0))
ψ(Μ^4)…
Bracketed Ordinal Notation (Definition + Analysis)
NOTE: THIS COULD BE ILL-DEFINED!
Let [] = 0, [[]] = 1, [[][]] = 2, et cetra... then lets define that [a] = which in our notation is [1, 1, 1 1].
[WIP]
Ampersand Array Notation, Part 3
Going beyond the "pipes" dimensions and going onto "brackets". The third part follows the brackets {}, and then super-brackets.
In this part we have changed something from previous.
& is still &
| is now {&}
|| is now {&&}
||| is now {&&&}
Time to move further.
- Part 1
- Part 2
- 1 Early Slash-Dimensions Level
- 1.1 Analysis
- 2 Early-Mid Slash-Dimensions Level
- 2.1 Analysis
- 3 Mid Slash-Dimensions Level
- 3.1 Analysis
- 4 Mid-Late Slash-Dimensions Level
- 5 Late Slash-Dimensions Level
- 6 Early Nested Dimensions Level
Dimensions range: {/} to {&/}
New rule: If you have || in the notation, change to {&}.
Extended version, if you have ||...|| (n), then change to {&&...&&} (n).
Separators involving pipes are removed in this part.
- Limit: f_{\omega^{\omega^{\omega+1}}}(a)
- a{/}a
- a{/}a&a
- a{/}a{&}a…
The Ordinal List - Part 1
- 1 0 to ω
- 1.1 OS #1
- 2 ω to ε0
- 2.1 OS #2 (ω to ω*2)
- 2.2 OS #3 (ω*2 to ω*3)
0
1 (multiplicative growth)
2 (exponential growth, eg: googol)
3 (tetrational growth, eg: giggol, grangol etc...)
4 (pentational growth, eg: gaggol, greagol etc...)
5 (hexational growth, eg: geegol, gigangol etc...)
6 (heptational growth, eg: gigol, gorgegol etc...)
7 (octational growth, eg: goggol, gulgol etc...)
8 (enneational growth, eg: gagol, gaspgol etc...)
9 (decational growth, eg: ogdagol, ginorgol etc...)
[WIP]
Ampersand Array Notation, Part 2
Here comes the Piped Parts, Note: | represents dimension, as / represents omega increment (in FGH).
Back to Part 1 For Earlier Parts
- 1 Dimensional Stage
- 1.1 Piped Substage
- 1.2 Piped Substage, Analysis
- 1.3 Multi-Piped Substage
- 1.4 Ampersanded Piped Substage
- 1.5 Slash-Ampersanded Piped Substage
- 1.6 Ampersanded Iterated Piped Substage
- 1.7 Slash-Ampersanded Iterated Piped Substage
- 2 Double Pipes Stage
- 3 Multiple Pipes Stage
- 4 Cubic arrays (||) stage
- A New Rule Would Be Considered, &//...// (b /'s)=|
- a|a
- a|a&a
- a|a&a&a
- a|a&a&a&a
- a|a&&a
- a|a&&a&a
- a|a&&a&&a
- a|a&&&a
- a|a&/a
- a|a&/a&/a
- a|a&/&a
- a|a&/&&a
- a|a&/&/a
- a|a&/&/&a
- a|a&//a
- a|a&//a&//a
- a|a&//&a
- a|a&//&&a
- a|a&//&/a
- a|a&//&//a
- a|a&///a
- a|a&///&a
- a|a&///&/a
- a|a&///&///a
- a|a&////a
- a|a&////&////a
- a|a&/////a
- Limit: f_{\omega^\omega}^2(a)
A New Rule: a|a&/…
Alpha Numbers for List of Googolisms
This is a list of List of Googolisms in ascending order with their associated Alpha Numbers.
Alpha Numbers are unique and accessible Real number inputs for the Alpha Function which generate large finite computable numbers.
- 1 Class 0 (0 - 6)
- 2 Class 1 (7 - 1,000,000)
- 3 Class 2 (1,000,000 - \(10^{1,000,000}\))
- 4 Uncomputable numbers
== (1) |- |the least transcendental integer | |}
Alpha Numbers are unique and accessible Real number inputs for the Alpha Function which generate large finite computable numbers.
They cannot be used to access Uncomputable numbers.
Garbles! (a very simple combinations/permutations game)
Hi! (I'm very new, so play nice)
A While ago I was on a TREE function kick after a numberphile video came out, and I worked out my own little number game involving Permutations, I ended up playing it until I "Solved" it, and was able to graph the game, I had a bunch of fun, and here's everything I did (also, there might be some math errors, and it might be really boring)
Garbles (Ging's Marbles, I'm amazing at naming things.) works with permutations.
You start with N unique marbles, e,g. N = 2. The goal is to make as many unique permutations of marbles as possible, these permutations can contain any number of marbles (like, for N=2, if we somehow had 4 marbles, 2 of each type, you could have a permutation with all 4 of those marbles in it, ju…
Lazy Array Notation
3RD VERSION
Lazy Array Notation or LAN is an array notation that got its name from lacking uniqueness and originality, hence the name "lazy."
⁅a⁆ = a
⁅a,b⁆ = a↑ba
⁅a,b,c⁆ = {⁅a,b⁆,⁅a,b⁆,...,⁅a,b⁆,⁅a,b⁆}, recursed c times using BEAF/BAN
For any entry beyond ⁅a,b,c⁆, it is equal to ⁅a,b,c,#⁆ = {⁅a,b,c,#⁆,⁅a,b,c,#⁆,...,⁅a,b,c,#⁆,⁅a,b,c,#⁆}, recursed according the last entry using BEAF/BAN, where # is any array.
This can be extended to Extended Lazy Array Notation.
⁅⁅a⁆⁆ = ⁅a,a,...,a,a⁆ with a entries
⁅⁅⁅a⁆⁆⁆ = ⁅⦉⁅⁅a⁆⁆,⁅⁅a⁆⁆,...,⁅⁅a⁆⁆,⁅⁅a⁆⁆⦊⁆ with ⁅⁅a⁆⁆ entries
- The "⦉ ⦊" symbols separates the brackets that are in the array or not in the array.
⁅⁅a,b⁆⁆ = ⁅⁅⁅...⁅⁅⁅a⁆⁆⁆...⁆⁆⁆ with b brackets
⁅⁅⁅a,b⁆⁆⁆ = ⁅⁅⁅...⁅⁅⁅a⁆⁆⁆...⁆⁆⁆ with ⁅⁅b⁆⁆ brackets
⁅⁅a,b,c⁆⁆ = ⁅⦉⁅⁅⁅..…
The growth rate of diagonalizing OCFs
This is visualization of the growth rate of OCF(Ordinal Collapsing Function) diagonalization.
Rules:
- Cd(x) can never be reached be from Cd(x-1) ,Ω ,the Ψ(x) OCF function and alephs.
- If x=-1 then Cd(x)=0
- If x=0 then Cd(x)=1
Analyzation:
Cd(1)= Inaccessible Cardinal
Cd(2)=Weakly Compact Cardinal
Find more on The Elkronic Numbers.
Busy Beaver on Ternary Cyclic Tags
What is Ternary?
Ternary is when 3 is used as a base, meaning that we can only count using 0,1,2.
Starting String
Let S be a ternary string of length k.
Rules
We define R as a set of rules to transform S using various methods. Rules in the form “a->b are called “doubles” where “a” is what we are transforming, and “b” is what we transform “a” into. “Singles” are rules in the form “c” that operate amongst the entire string S.
-If a->b where b=δ, this means “delete a”.
-every symbol 0,1,2 count as 1 symbol. The arrow “->” counts as 0 symbols.
-The single rule “$” means “copy the string and paste it to the end of itself”.
-The single rule “&” means “remove all trailing zeroes from the string”
-A ruleset can contain multiple of the same rule.
A combinatio…
Busy Beaver on Tree Enumerations
Introduction
A Dyck Word is a string of parentheses s.t:
- The amount of opening and closing parenthese are the same
- At no point in the string (when read left to right) does the number of closing parentheses exceed the number of opening parentheses, and vice versa
. . . . . . . . . . . . . . . . . . . . . . . . . .
Application to Googology
. . . . . . . . . . . . . . . . . . . . . . . . . .
Let D be a valid Dyck Word of length n. This is called our “starting word”.
Rules and Starting Word
Our starting word is what gets transformed through various rules.
We have a set of rules R which determine the transformations of parentheses.
Rule Format
The rules are in the form “a->b” (doubles) where a is what we transform, and b is what we transform “a” into, or “…
Busy Beaver using Dyck Words
Introduction
A Dyck Word is a string of parentheses s.t:
- The amount of opening and closing parenthese are the same
- At no point in the string (when read left to right) does the number of closing parentheses exceed the number of opening parentheses, and vice versa
. . . . . . . . . . . . . . . . . . . . . . . . . .
Application to Googology
. . . . . . . . . . . . . . . . . . . . . . . . . .
Let D be a valid Dyck Word of length n. This is called our “starting word”.
Rules and Starting Word
Our starting word is what gets transformed through various rules.
We have a set of rules R which determine the transformations of parentheses.
Rule Format
The rules are in the form “a->b” (doubles) where a is what we transform, and b is what we transform “a” into, or “…
not thatofalist
This is my very random and most likely pseudomathematical and semi-mathematical list of numbers, the parts in this will probably keep on increasing so just beware, there are atleast 2000+ numbers by like part 10 (estimated).
- Page 1: -ω to 0
- Page 2: 0 to 1
- Page 3: 1 to 10
- Page 4: 10 to 1010
- Page 5: 1010 to 101010
- Page 6: 101010 to 10101010
- Page 7: 10101010 to 10↑↑10
- Page 8: 10↑↑10 to 10↑1010
- Page 9: 10↑1010 to 10↑10↑101010
- Page 10: 10↑10↑101010 to {10, 10, 10, 10}
- Page 11: {10, 10, 10, 10} to {10, 10 [2] 2}
- Page 12: {10, 10 [2] 2} to {10, 10 [3] 2}
- Page 13: {10, 10 [3] 2} to {10, 10 [1, 2] 2}
- Page 14: {10, 10 [1, 2] 2} to {10, 10 [1 [2] 2] 2}
[WIP]
ExplodingE
Exploding E Notation is an array notation created by wikia user Uma19568324. It is very similar to both Hyper-E Notation and Linear Array Notation.
Rules:
E(n) = 10^n
E(n,1,1,1...,1) = E(n)
E(n,m) = E(E(n,m - 1),m - 1)
E(a,b,c,...,z) = E(A, A, A,...,z - 1) where each entry aside from the last is set to A, which is E(a, b, c,...,z - 1)
- Googol = E(100)
- Googolplex = E(100,2) = E(E(100)) = E(Googol)
- Googoltriplex = E(100,3) = E(E(100,2),2) = E(Googolplex,2) = E(E(Googolplex)) = E(Googolduplex)
- E(100,2,2) = E(E(100,2),E(100,2)) = E(Googolplex,Googolplex) > Googolplexidex
- E(100,2,1,2) = E(Googolplex,Googolplex,Googolplex)
- E(100,2,2,2) = E(E(100,2,2),E(100,2,2),E(100,2,2)) = E(E(Googolplex,Googolplex),E(Googolplex,Googolplex),E(Googolplex,Googolplex))
…
Planarian hydra (PMN 2.1)
Let \(V\) is the set of all vertex(ces) of a chart and \(E\) is the set of all edge(s)
Let us characterize the set \(\mathcal{L}\) as \(\mathcal{L} = \mathbb{N} \cup \{\omega, \mathord{+}\}\)
A chart \(\mathcal{G} = (V, E)\) is called way in case there exists an requesting \((v_1, v_2, \ldots, v_n)\) of its vertices such that:
\[
V = \{v_1, v_2, \ldots, v_n\}, \quad
E = \{\{v_i, v_{i+1}\} \mid 1 \leq i \leq n-1\},
\]
where \((v_i \neq v_j)\) for \((i \neq j)\).
A chart \(\mathcal{G} = (V, E)\) is called a limited on the off chance that \(V\) and \(E\) are limited sets
A established way could be a way \(\mathcal{G} = (V, E)\) and a uncommon vertex \(r \in V\) called the root is indicated.
A mapping \(\ell: V \to L\) is characterized that partners com…
Rooted Tree Function
Introduction/Background
We will represent finite labelled rooted trees T using parentheses as follows:
Let the root be labelled N. Then, N(A,B,…,k) means “children A,B,…,k connected to N.” We can branch out further as follows: N(A(X,X1),B,…,k) denotes “children A,B,…,k connected to N, with children from a labelled X and X1 respectively.” We can continue this process via nesting to create more complex trees. Examples include:
{1} A(B,C(D,E),F)
Explanation:
Root: A
Children of A: B,C(D,E),F
B: Leaf node
C: Internal node with two children D and E.
D and E: Leaf nodes
F: Leaf node
{2} R(A(B(C,D(E)),F),G(H,I(J(K),L)),M)
Explanation:
Root: R
Children of R: A,G,M
A has Children: B(C,D(E)) and F
B has Children: C and D(E)
C: Leaf node
D has Child: E
E: Leaf Node
F: …
Potentially Very Fast-Growing Function
Simplified Cyclic Tag (SCT)
**Queue and Alphabet**
We operate under the finite alphabet P={a,b}. Let Q be the queue (A.K.A initial sequence). This is a string in P of a finite length that will be transformed to another string.
**Ruleset**
Let R be a set of rules in the form a->b where a is what is being transformed, and b is what we transform the string to. If a->b where b=μ, delete symbol a.
**Rule Format**
Rules are followed from top to bottom, then looped back to the top.
**How to solve a queue**
We look to the leftmost symbol in our string and apply the given transformation in R.
**Termination Conditions**
Termination occurs when we reach the empty string ∅, or some string labelled S s.t ∄ any rule(s) in R to transform S any further.
**Ruleset Ex…
what is this in fast growing hierarchy?
so, i dont know how fast growing hierarchy works except for a couple parts of it, but there is no way i could find the closest approximation (or maybe the upper and lower bounds) of this number.
the number im talking about is the new biggest number ive ever created (as of 2025-05-07), really evil number.
i wanna know so i can put it on the approximations section, also so i know what class it is :D
really evil numberEvil Matrix Notation. ] \(\gets \)since evil matrix notation doesnt have a page yet, please refer to this image/document
also sorry for posting so many blogs, i just have a lot of questions i dont know the answers to :(
do i have to change the name of my notation?
i just found out that one of my notations, chained array notation (which doesn't have a page yet, but is on my website), is also the name of a notation from 2017. Do I still have to change the name of the notation, if I link my notation (and not the one from 2017) when I mention it? (of course, when I make the page for it, it will probably be called something like "Chained Array Notation (NathanTroyAdams154)")
i dwarfed CAN and CARN notation with my new notation
my last blog post talked about a notation and its extension i developed called CAN and CARN. these did go to some pretty big numbers, but i have developed a notation that is much stronger
it has two writing methods, but one is much smaller and organized than the other.
here is the image of the latex since i hate reformatting latex 😭 ]
Dimensional beaver
Busy beaver moves left or right it’s one dimensional call this DBB1(n)
DBB2(n) has new directions up and down
DBB3(n) has directions north and south, east and west
DBB4(n) has W direction and -W direction
DBBα(n) = DBBα[n](n) if a is a limit ordinal
- 1 undefined dimensional busy beavers
- 2 Related functions
- 2.1 Dimensional frantic frog function
- 2.2 dimensional Ne function
- 2.3 Higher dimensional Higher-order busy beaver functions
- DBB0(x)
- DBB-x(x)
is this a good notation
i was trying to develop a notation and i was wondering if i did good (i guess its more like a function but idk)
its called Chained Array Notation (CAN) and has an extension called Chained Array Recursion Notation.
\(\textbf{Chained Array Notation (CAN)}\)
\(a = b\to c\to \)
\( \left[ a,d \right] = b\to c\to d \)
\(\left[ a \right] = b\to c\to b \)
\(\left[ a,c,d \right] = b\to c\to c\to d \)
\([a,,d] = b\to c\to b\to d \)
\(
Pair sequence system is buchholz hydra with some modification
One chooses a leaf node \(a\) to chop off. On the other hand, hydra chooses a nonnegative integer \(n\) is growing in the equation \(n^{2^p}\) where \(p\) is the number of current step
If \(a\) has label 0 call the node's parent \(b\), and its grandparent \(c\) (if it exists). First we delete \(a\). If \(c\) exists, we make \(n\) copies of \(b\) and all its children and attach them to \(c\).
If \(a\) has label \(u + 1\), we go down the tree looking for a node \(b\) with label \(v \leq u\). Consider the subtree rooted at \(b\) — call it \(S\). Create a copy of \(S\), call it \(S'\). Within \(S'\), we relabel \(b\) with \(u\). Back in the original tree, replace \(a\) with \(S'\).
If this true, then why one have to proof the termination of pair …
Salad factorial
S*(X) = Supremefactorial^x(x) with x megafactorials behind it with X ultrafactorials behind it with X hyperfactorials behind it with X super factorials behind it with x exponential factorials applied to it with X bouncing factorials behind it with X Alternating factorials behind it with X mixed factorials behind it with X multi factorials behind it with x nested factorials behind it with x fibonirals of it applied to it with x Falling factorials applied to it with x tetrational factorials behind it with x Expostfacto function’s applied to it with x Compositorials applied to it with x Primorials behind it with x Pentatorials behind it with x Semiprimorials behind it with x sub factorials behind it with x Weak factorial functions applied …
made this way smaller than i meant it to be
the smallest number ever.
but its just a lot smaller than i thought itd be.
well thats all i had to share!! goodbye!! 🐜
FGH numbers
Numbers are sorted from smallest to largest. This'll be updated to fix formatting + adding new numbers
X pentated to 2
- 1^^^2=1
- 2^^^2=4
- 3^^^2=7625597484987
- 4^^^2=10^10^153.90699754796802834138179757972 (10^8.0723047260282253793826303970988e153)
- 5^^^2=10^10^10^2184.1257220888504206703564449008 (10^10^1,3357404838721369832785532676225e2184)
- 6^^^2=10^10^10^10^10^10^4,197758863027439715105490732277 (10^10^10^10^2,2679047111516980948175914734227e15767)
I'm not 100% sure if 6^^^2 is accurate but i know the other one are
does this look like a good sequence for a googolism im making for my friend or is it the worst garbage on this entire blue marble
latex trauma 🐜
im gonna upload it on my image gallery site because even after reading every article on this wiki i still dont know how to type in latex except with the \end{array}\right.\)
do you like my first googolisms or do they suck 🐜
Ampersand numbers
sorry for such a short blog post i just want opinions on anything i can improve on!! 🐜
Seek's Array Notation
my first ever array notation ever that is ever made in 2025 so good luck viewing my first ever array notation ever that is ever made in 2025 (wth am I saying lol)
also this is probably gonna be ill-defined, I'm not sure
btw here's my array notation contributed in google docs.
- 1 Genesis Array Notation
- 2 Second-Order Array Notation
- 3 Higher-Order Array Notation
- 4 Second Generation Array Notation
- 5 Higher Generation Array Notation
introducing the beginning of this array notation
Limit: , but not sure
introducing the semi-colon with subscript 2
Limit: Unknown
introducing the semi-colon with subscript
Limit: Unknown
introducing the colon, but not sure how it works
Limit: Unknown
Unknown
Limit: Unknown
that's all goodbye
Biggest number ever!!
(This is actually well-defined and probably pretty big, but I don't consider it very novel, so this blog post is mostly a joke.)
Assume \(V = \mathrm{HOD}\) and that \(\mathfrak{c}\) is a successor cardinal. Let \(\lambda\) be the unique cardinal with \(\mathfrak{c} = \lambda^+\). For \(f: \omega \to \omega\), define its iteration \(f^n(m)\) for \(n, m < \omega\) by \(f^0(m) = m\) and \(f^{n+1}(m) = f(f^n(m))\). If \(f, g: \omega \to \omega\), put \(f
Cardinal tetration
\(\aleph_0\)↑↑…\(\aleph_0\) with \(\aleph_0\) or \(\omega\) ↑’s = sup(\(\aleph_0\), \(\aleph_0\)\(\aleph_0\), \(\aleph_0\)↑↑\(\aleph_0\), \(\aleph_0\)↑↑↑\(\aleph_0\), \(\aleph_0\)↑↑↑↑\(\aleph_0\), \(\aleph_0\)↑↑↑↑↑\(\aleph_0\)….)
Sup stands for supremum see Infinitum and Supremum
Tetrational Numbers after \(\epsilon_0\) are \(\zeta_0\), \(\eta_0\), \(\varphi(3,0)\), \(\varphi(4,0)\), \(\varphi(5,0)\), etc
what is the growth rate of this matrix?
(0)=1
(0)(0)=2
(1)=ω
(1)(0)(0)(1)=ω*2
(1)(0)(0)(1)(0)(0)(1)=ω*3
(1)(0)(1)=ω^2
(1)(0)(1)(0)(0)(1)(0)(1)=ω^2*2
(1)(0)(1)(0)(1)=ω^3
(1)(1)=ω^ω
(1)(1)(0)(0)(1)(1)=(ω^ω)*2
(1)(1)(0)(1)=ω^ω+1
(1)(1)(0)(1)(0)(1)=ω^ω+2
(1)(1)(0)(1)(0)(1)(1)=ω^ω*2
(1)(1)(0)(1)(1)=ω^ω^2
(1)(1)(1)=ω^ω^ω
(1)(1)(1)(1)=ω^ω^ω^ω
(2)=ψ(Ω)
(2)(0)(0)(2)=ψ(Ω)+ψ(Ω)
(2)(0)(1)=ψ(Ω+1)
(2)(0)(1)(0)(1)=ψ(Ω+2)
(2)(0)(1)(0)(1)(1)=ψ(Ω+ω)
(2)(0)(1)(0)(1)(1)(1)=ψ(Ω+ω^ω)
(2)(0)(1)(0)(2)=ψ(Ω+ψ(Ω))
(2)(0)(1)(1)=ψ(Ω+ψ(Ω+1))
(2)(0)(1)(1)(1)=ψ(Ω+ψ(Ω+ψ(Ω+1)))
(2)(0)(2)=ψ(Ω*2)
(2)(0)(2)(0)(2)=ψ(Ω*3)
(2)(1)=ψ(Ω*ω)
(2)(1)(0)(2)=ψ(Ω*ω+1)
(2)(1)(0)(2)(0)(2)(1)=ψ(Ω*ω*2)
(2)(1)(0)(2)(1)=ψ(Ω*ω^2)
(2)(1)(1)=ψ(Ω*ω^ω)
(2)(1)(1)(2)=ψ(Ω*ψ(Ω))
(2)(1)(1)(2)(1)(1)(2)=ψ(Ω*ψ(Ω*ψ(Ω)))
(2)(1)(2)=ψ(Ω^2)
(2)(1)(2)(1)=ψ(Ω^2*ω)
(2)(1)(2)(1)(2)=ψ(Ω^3)
(2…
Fast Growing Hierarchy help
So I was analyzing this notation when I realized I wasn't exactly doing it right. What would be the right ones?
- [a] = a^aa
- [a, 1] = [[...+3w