tetration ascii symbol convention

[bo198214]

I would suggest to unify our several different notations of tetration or hyperoperations, my proposal:

The usual tetration is denoted by ^^, i.e.

x ^^ 1 = x
x ^^ (n+1) = x ^ ( x^^n )

And the higher operations (as far as the index is involved in computations) are denoted by the original Ackermann function:

A₀(x,m) = x + m
A_n+1(x,1) = x
A_n+1(x,m+1) = A_n(x,A_n+1(x,m))

(where A_n(x,y) in pure ascii is then written as A(x,y,n), that was the way how Ackermann defined the function
in his original article http://www.springerlink.com/content/px2g58k5j3q45535/fulltext.pdf 1927 (where he called it phi))

Then especially is:

A₁(x,m) = x * m
A₂(x,m) = x ^ m = x^m
A₃(x,m) = x ^^ m
A₄(x,m) = x ^^^ m
A₅(x,m) = x ^^^^ m
....

[Keiji]

Hmm, I've always used # for tetration.

[bo198214]

Yes I know, some (including me) used # some used $ or even some used §.
But than we run quickly out of symbols for perhaps other operations.
And I think ^^ is quite mnemonic (easy to remember, and easy to derivate the meaning).

[houserichichi]

I'd second that. Arrow/chevron notation is much more common than the random symbols, but I'm not even participating in these discussions...I just felt like adding my two (purist) cents.

[Keiji]

Perhaps ^^ should only be used when the higher operations ^^^, ^^^^, etc, are being discussed as well. # is shorter and when only tetration is being discussed, it seems preferable. Nobody uses ** for exponentiation now, do they?

[bo198214]

A convention makes only sense if there is some commitment.
The advantage is that the notation hasnt to be introduced every time one is using it.

With the higher operations it is the same as with the higher dimensions. One rarely one speaks about 5 or 6 dimensions, rather either 4 or n. So most common use should be either ^^ or A(x,y,n). It would be useless to be used only in contexts with ^^^ or ^^^^.
The further advantage is that ^^ does not use up a new symbol but relies on the exponentiation symbol.

Ok, but Keiji anyway sticks so hard at his habits, that I am quite tired of making more convincing effort. I mean this is anyway no tetration board, so what do I care.

[Keiji]

Hmm, well conventions are more important in the wiki than here. But nobody's stopping you from using ^^ if you want to.

[bo198214]

*yawn*