A Notation Question (raising the highest value in pow-tower to a different power)

[jaydfox]

Any thoughts on the expression of the function in this thread?  What is the standard operator for hyper-4 in this forum? I am used to using the up-arrow notation, is that received okay here?

I don't think there's a standard notation.  We try to be flexible, as long as it's clear what you mean.  When in doubt, define your notation before you use it, or after the first use, and then just be consistent.

As far as notations we use here, I've seen the use of the double caret, such as 4^^3, which would be 4^(4^4), assuming that the single caret is exponentiation.  This is essentially the same as up-arrow notation you mentioned (Knuth arrow notation?).

I myself am partial to the left-sided superscript:

\( {}^{3}{4} = 4^{4^{4}} \)

I can't remember if there's a better way to write a left-sided superscript in TeX.  I haven't been on the forum much for the past 4-5 years.  Maybe one of the other regular forum members will remember.

The downside of the left-sided superscript is that it doesn't have a clear extension to pentation.  With the up-arrow notation, pentation would be a triple up arrow.  So when you're getting into a deep discussion about iteration theory, up-arrow notation is probably more appropriate.  If you're getting into a deep discussion about tetration specifically, then the left-sided superscript is a little more compact.  But it's all a question of preference.