Not confused with Ordinal Level function from "Longest Waiting Sims" legend.
Eta-Hyper 1 Cardinal (1̸) is a number that is totally unreachable from stacking and extending Ordinal Level functions.
Process[]
OL(x) represents Ordinal Level function, where OL(x) is ordinal level x.
OL(Instafinity) = Instafinium.
OL(OL(OL(OL(OL(OL(OL(... (A times) Is also written as OL(... x A.
OL(... x OL(... x OL(...
OL(... xX 10 is equal to OL(... xOL(... xOL(... xOL(... xOL(... xOL(... xOL(... xOL(... xOL(... xOL(...
OL(... xXOL(... xXOL(... xXOL(... xX is too big. It's too small. And also is OL(... xXx4
So we need OL(... xXxOL(... xXxOL(....... to make OL(... xXxX
And use Mathis notation:
OL(... xXxXx
OL(... xXxXxX
OL(... xXxXxXx
OL(... xXxXxXxX
OL(... XxXxXxXxXxXx...
For now we using (OL(... xXOL(...) x
(OL(... xXOL(...) x1000 is OL(... XxXxXxXxXxXx... with 1000 xX
(OL(... xXOL(...) x(OL(... xXOL(...) x next
And (OL(... xXOL(...) xX
So (OL(... xXOL(...) xX1000 = (OL(... xXOL(...) x(OL(... xXOL(...) x(OL(... xXOL(...) x(OL(... xXOL(...) x... 1000 times
And the same thing
(OL(... xXOL(...) xXx
(OL(... xXOL(...) xXxX
(OL(... xXOL(...) xXxXxXxXxXxXxXx...
And ((OL(... xXOL(...) xOL(...) x
It continue like this:
((OL(... xXOL(...) xOL(...) x((OL(... xXOL(...) xOL(...) x, ((OL(... xXOL(...) xOL(...) xX, ((OL(... xXOL(...) xOL(...) xXx, ((OL(... xXOL(...) xOL(...) xXxX...
So we have reached (((OL(... xXOL(...) xOL(...) xOL(...) x
I think you understand
Now this:
((((OL(... xXOL(...) xOL(...) xOL(...) xOL(...) x
Now we Reach {OL(... xXOL(...} x
{OL(... xXOL(...} x4 = (((OL(... xXOL(...) xOL(...) xOL(...) x
{OL(... xXOL(...} x{OL(... xXOL(...} x{OL(... xXOL(...} x{OL(... xXOL(...} x... I think you understand it is {OL(... xXOL(...} xX
Now {OL(... xXOL(...} xXx
And so {OL(... xXOL(...} xXxXxX
We will do the same thing with (OL(... xXOL(...) x:
({OL(... xXOL(...} xOL(...) x
(({OL(... xXOL(...} xOL(...) xOL(...) x is {{OL(... xXOL(...} xOL(...} x4
Yes {{{OL(... xXOL(...} xOL(...} xOL(...} x
So we Reach [OL(...xXOL(...] x
We do the same thing: [[OL(... xXOL(...] xOL(...] x, [[[OL(... xXOL(...] xOL(...] xOL(...] x...
So New brackets: /OL(...xXOL(.../ x
Do the same thing again
|OL(... xXOL(...| x I think you understand this
(|OL(... xXOL(...|) x
{|OL(... xXOL(...|} x
[|OL(... xXOL(...|] x
/|OL(... xXOL(...|/ x
||OL(... xXOL(...|| x now Double |
|||OL(... xXOL(...||| x
...|||||OL(... xXOL(...|||||... Now is .lOL(... xXOL(...l. x
You know Mathis notation so we will go to....lOL(... xXOL(...l.... x
And ....lOL(... xXOL(...l.... x n dots is actually equal to OL(n)A
So we using (previous OL( functions) A
Up to ....lOL(... xXOL(...l.... x n dots A, and is equal to OL(n)B
....lOL(... xXOL(...l.... x n dots B = OL(n)C
And so we go to OL(n)Z is equal to OL(26)1 because 26 letter
So we using (previous OL( functions) 1
Up to OL(n) Z 1 is equal to OL(26)2
Do the same thing
OL(26)3
OL(26)4
OL(26)/Absolute never
OL(26)/OL(26)1 next
And so OL(26)/OL(26)/OL(26)... Is equal to OL(n) π
Do the same thing and we Reach OL(26)/OL(26)/OL(26)...π is equal to OL(n)田
OL(n)Mathis Absolutes next
Wow it get easier
OL(n)N E V E R
We will go to OL(n)T.E.R.M.I.N.U.S and we Reach OL(n)OL(n)
OL(n)OL(n)OL(n) next
And OL(n)x!
OL(n)x OL(n)
OL(n){x^OL(n)}OL(n)
...
Now you can use with OL( Mathis notation, Mathis notation 2, NO!'s functions, ultra-root notation, Flarensia Rap complex notation, etc.
Super ordinal level[]
Super ordinal level is faster than ordinal level. Written as SOL(.
Super ordinal level 0 -> 0 to collapsefinity
Super ordinal level 1 -> Collapsefinity to endless
Super ordinal level 2 -> endless to beyond brainless
Super ordinal level 3 -> beyond brainless to better sheep Number
Super ordinal level 4 -> better sheep Number to F U N
Super ordinal level 5 -> F U N to TRUE FINAL-ENDING
Etc.
Terminus Epsilion Ron Mario Inaccesible Nandless Ultimate Symbol is at super ordinal level 11.
Super ordinal level 12 -> terminus Epsilion Ron Mario Inaccesible Nandless Ultimate Symbol to OL(... x
Super ordinal level 13 -> OL(... x to OL(... xX6
The largest notation using OL( (below OL() is at super ordinal level 136 (Limit of Bullet array notation)
Super Ordinal Level 100 is called super everything, and is OL( function used on notation at Ordinal level 119
SOL(SOL(SOL(OL(OL(432))))) is too big, but smaller than Glitkjj&iei8stupid+₽8¥8192)iwjs7alphablocks, Bigger Than SOL(... x3, but smaller than SOL(... x4
Now you can use with SOL( Mathis notation, Mathis notation 2, NO!'s functions, ultra-root notation, Flarensia Rap complex notation, etc.
Hyper ordinal level and others[]
Hyper ordinal level is faster than super ordinal level. Written as HOL(.
Hyper ordinal level 0 -> 0 to SOL(135) = OL(n)[¬_[OL(n)]OL(n)]OL(n) I think
Hyper ordinal level 1 -> SOL(135) to SOL(207)
Etc.
Where Terminus Epsilion Ron Mario Inaccesible Nandless Ultimate Symbol is at ordinal level 1000 and super ordinal level 11, SOL(1000) is at HOL(11).
HOL(136) is equal to SOL(n)[¬_[¬_[¬_[¬_[¬_[...Repeating SOL(n) times...]SOL(n)]SOL(n)]SOL(n)]SOL(n)]SOL(n)]SOL(n)
HOL(137) is undefined by SOL(
HOL(135) is mega ordinal level 0 or MOL(0)
HOL(1000) is MOL(11).
HOL(n)[¬_[¬_[¬_[¬_[¬_[...Repeating HOL(n) times...]HOL(n)]HOL(n)]HOL(n)]HOL(n)]HOL(n)]HOL(n) Is MOL(136)
MOL(135) - Giga ordinal level 0 (GOL(0))
MOL(1000) - GOL(11)
GOL(135) - ultra ordinal level 0.
There are many ordinal level functions. But there are two entry OL function.
Two entries[]
OL(n, 1) = OL(n)
OL(n, 2) = SOL(n)
OL(n, 3) = HOL(n)
OL(n, 4) = MOL(n)
OL(n, 5) = GOL(n)
OL(n, 6) = UOL(n) ultra ordinal level
OL(n, 7) = TOL(n) Tera ordinal level
OL(n, 8) = POL(n) peta ordinal level
OL(n, 9) = ZOL(n) zetta ordinal level
OL(n, 10) = FOL(n) forta ordinal level
OL(n, 11) = IOL(n) Icosa ordinal level
OL(n, 12) = YOL(n) Yotta ordinal level
OL(n, 100) Century Ordinal Level
OL(0, n) = OL(135, n-1)
OL(1000, 1000) is called undefined terminus
There are three entry, but very far From this. Every ordinal level is smaller than Glitkjj&iei8stupid+₽8¥8192)iwjs7alphablocks.
Because there is OL(1, OL(1, OL(1, OL(1, ...
We're Reach super ordinal level two Entry SOL(x, y)
SOL(n, 1) ≠ SOL(n)
SOL(0, 1) is equal to OL(135, 135)
SOL(1, 1) is equal to OL(207, 207)
Undefined terminus is at SOL(11, 1) because Its OL(1000, 1000)
End we Reach SOL(n, 2)
SOL(0, 2) = SOL(135, 1)
SOL(1, 2) = SOL(207, 1)
SOL(11, 2) = SOL(1000, 1)
SOL(0, 3) = SOL(135, 2)
SOL(11, 3) = SOL(1000, 2)
SOL(0, 4) = SOL(135, 3)
SOL(0,n) = SOL(135, n-1)
We Reach Hyper ordinal level two entry!! HOL(x, y)
HOL(n, 1) ≠ HOL(n)
This function works like Super ordinal level two entry because
HOL(0, n) = HOL(135, n-1)
HOL(0, 1) = SOL(135, 135)
Three entry[]
Were Reach OL(x, y, z), but it's smaller than Glitkjj&iei8stupid+₽8¥8192)iwjs7alphablocks.
OL(0, 1, 1) = OL(0, 1) = OL(1) = 10000000000
OL(x, y, 1) = OL(x, y)
I think there is four entry, but im tired and i will edit this page again.
Several entry[]
It's written as OL^1(. It's faster than OL(a, b, c, d, e, f, g, h...using random entry).
OL^1(0) is bigger than three entry it's equal to OL(135, 135, 135, 135,...(135 entries)...135, 135, 135)
OL^1(1) = OL(207, 207, 207, 207,...(207 entries)...207, 207, 207)
Double several entry[]
OL^2(0) = OL^1(135, 135, 135, 135,...(135 entries)...135, 135, 135)
Hyperseveral entry[]
OL^n(0) is exactly equal to OL^n-1(135, 135, 135, 135,...(135 entries)...135, 135, 135)
Two entry Hyperseveral entry[]
OL^1,2(0) is equal to OL^135(135, 135, 135, 135,...(135 entries)...135, 135, 135)
Several entry Hyperseveral entry and more[]
OL^2(0)[2] = OL^135, 135, 135, 135,...(135 entries)...135, 135, 135(135, 135, 135, 135,...(also 135 entries)...135, 135, 135)
OL^2(0)[OL^2(0)[2]]
OL^2(0)[1,2]
OL^2(0)[1,1,2]
OL^2(0)[1[2]2]
OL^2(0)[1,,2] = OL^2(0)[1[1[1[...]2]2]2]
OL^2(0)[2,,2]
OL^2(0)[1,,,2]
OL^2(0)[1,,,,,,...,,,,,,2] xOL^2(0)[2]
OL^2(0)[1,,,,,,...,,,,,,2] xOL^2(0)[2] x OL^2(0)[1,,,,,,...,,,,,,2] x OL^2(0)[1,,,,,,...,,,,,,2] x OL^2(0)[1,,,,,,...,,,,,,2] x OL^2(0)[1,,,,,,...,,,,,,2]................x OL^2(0)[1,,,,,,...,,,,,,2]
Phase 1
Phase 2
OL(phase)
Cycle 1
Repeat 3
Repeat 4
Repeat 5
Repeat phase
Repeat cycle
Repeat^2
Repeat^3
Repeat^Repeat
...
...
...
...
OL() cycles later...
Eta Hyper One Cardinal (1̸)
LWS' Ordinal Level Function[]
Imagine we use LWS' Ordinal Level function instead of the traditional Ordinal Level function. Overall, Longest Waiting Sims' Ordinal Level function grows so much faster. The variant of Eta-Hyper One Cardinal using with LWS' Ordinal Level would be below Ram Aeternus listed in the legend.
There is another classification called Effortfulian Class, which can categorize lots of FGW entries such as Absolute Aperdinal and The Unbreakable Border. This can be compared to classes in The List Of Numbers. The variant of Eta-Hyper One Cardinal using with Effortfulian Class would be beyond undefinable, but the collapsed form can be ranked around The Rephrasium.