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Now I'm going to extend Psi's Letter Notation to Îµ_0. The concept is a bit complicated (and unique), so please get ready.
This concept is for expressing fractional values used in the notation.
First, consider a pair of an ordinal at integer points, but it's no problem because all these FS are used in the hierarchy.
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This is a (WIP) continuous version of the Psi Levels Scale. Let n be the number(level), x be the fractional part of n and y be the fractional part of 10n. e.g. if n=3.1415..., x=0.1415... and y=0.415...
Also, I use Ïˆ(n) for the number corresponding to Psi Level n.
Suggestion 1. (Psi's Letter Notation)
10â†‘â†‘x=10^x (0
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ERROR: THIS IS A MESS.
It is an extension of chained arrow notation. Actually, arrows are not used. They all turned into arrays.
, where there are 16 layers.
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This notation is supposed to express Linear Omega Level intuitively, so don't expect it to go any higher.
a[c]b is supposed to be is an array.
a[#,1]b=a[#]b
a[#,n,m]b=a[#,a[#,n]b,m1]b
3>3>64>2=3[27,63]3=3[1,64]4
Graham's number=3[4,64]3
3>3>65>2=3[27,64]3
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As you know, zootzoot is googol!1, zootzootplex is googolplex!1, and zootzootduplex is googolduplex!1. Then, we can see the rule:
Rule: ZootzootÎ± is googolÎ±!1 using hyperfactorial array notation, where Î± is any string while googolÎ± is welldefined.
The zootzootzootplex looks like the exception, but since googolzootplex is not defined, the rule is not applied to this.
Here are some numbers:
 zootzooti=(102^51)!1, derived from googoli.
 zootzootij=(104^52)!1, derived from googolij.
 zootzootiji=(106^53)!1, derived from googoliji.
 zootzootiv=(108^54)!1, derived from googoliv.
 zootzootv=(110^55)!1, derived from googolv.
 zootzootex=(120^60)!1, derived from googolex.
 zootzootbang=((10^100)!)!1, derived from googolbang.
 zootzootding=(10^500)!1, derived from goâ€¦