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Basic Multi-Symbol Notation

Let start with a+b.

Then a++b = a+a+a+...+a+a+a with b a+a's

Finally, a+++...+++b = a+++...++a+++...++a+++...++ ... +++...++a+++...++a+++...++a+++...++ with b a+++...++a's

So a+++...+++b with n plus signs = a^(n-2)^b

Let define a*b = a+++...+++a with b plus signs

Then a*+b is repeated *, a*+++...+++b is repeated *+++...++, a**b = a*+++...+++a with b plus signs, etc.

Then a^b = a***...***a with b stars

Let + = [1], * = [2], and ^ = [3]

Here are basic rules of Basic Multi-Symbol Notation:

a[1]b = a+b

a#[n]b = a[n-1][n-1][n-1]...[n-1][n-1][n-1]a with b [n-1]'s where # is anything (can be nothing), and if it is a separator, it's level must be larger than n

a[n][m][m][m]...[m][m][m]b = a[n][m][m][m]...[m][m]a[n][m][m][m]...[m][m]a[n][m][m][m]...[m][m]a[n][m][m][m]...[m][m]...[n][m][m][m]...[m][m]a[n][m][m][m]...[m][m]a[n][m][m][m]...[m][m]a with b [n][m][m][m]...[m][m]'s

I think that's all.

FGH

a+b = f_1(b)

a++b = f_2(b)

a+++...+++b = f_n(b) where n is number of +'s

a*b = f_w(b)

a*+b = f_w+1(b)

a*++b = f_w+2(b)

a**b = f_w*2(b)

a^b = f_w^2(b)

a[n]b = f_w^n(b)

so basic symbol notation has a limit of f_w^w(n), or the limit of Aarex's Extended Up arrow notation (basic)

Nested Multi-Symbol Notation

-- UNDER CONSTRUCTION --

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