01/22/2008, 05:02 AM

Actually, I briefly talked about this with the computer arithmetic section, and near the end about the "no overflows" part. But yes, this is one of the more prominent applications of tetration, for which I reference Holmes' work (PDF) in my paper.

And when it comes to notation, "p (*) [b # n]" can also be written "(b^)^n(p)" in ASCII, or as usual. If the parentheses are what is inspiring you to need a new notation, then the simplest solution would be to just drop them as: . Although your notation looks very much like traditional scientific notation, this may not be a good thing, as it is confusing and easy to mistake for scientific notation. I think iterated exponential notation should be unambiguous, and consistent. The "p (*) [b # n]" notation is neither. As for computer notation, just like many programming languages have "#E#" notation for scientific notation (assuming base 10), there could some benefit to having a similar convention for iterated exponentials, where either "p T n" (T for tetration, although I've also seen this used for scientific notation when the base is 10, T for ten) or "p S n" (S for "super") could be used to separate the mantissa (p) and height (n). But unless someone writes a programming language with these operators, I don't think anyone is going to use them.

Andrew Robbins

And when it comes to notation, "p (*) [b # n]" can also be written "(b^)^n(p)" in ASCII, or as usual. If the parentheses are what is inspiring you to need a new notation, then the simplest solution would be to just drop them as: . Although your notation looks very much like traditional scientific notation, this may not be a good thing, as it is confusing and easy to mistake for scientific notation. I think iterated exponential notation should be unambiguous, and consistent. The "p (*) [b # n]" notation is neither. As for computer notation, just like many programming languages have "#E#" notation for scientific notation (assuming base 10), there could some benefit to having a similar convention for iterated exponentials, where either "p T n" (T for tetration, although I've also seen this used for scientific notation when the base is 10, T for ten) or "p S n" (S for "super") could be used to separate the mantissa (p) and height (n). But unless someone writes a programming language with these operators, I don't think anyone is going to use them.

Andrew Robbins