MathJax - 2022-09-28

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Martin Sleziak

4:57 AM

There was a post with this title: Is $e^e^...^n$ ever an integer?

I wanted to fix the exponent in some way that looks reasonable.

\ddots isn't what I want: Is $e^{{e^{\ddots}}^n}$ ever an integer?

Is there the version of \ddots which goes in the other direction and works in MathJax?

Q: How to type three points diagonally?

In an equation, I want to display three points like "...", but instead of horizontally, they should be diagonally. I'm sure there must be a command to do that, but a google search did not really help. Any idea?

I have tried this: Is $e^{{e^{\ \dots\ }}^n}$ ever an integer?

That's a bit similar to the notation used in the tag-info for tetration: $^na=\underbrace{a^{a^{\ \dots\ ^{a}}}}_n$. math.stackexchange.com/tags/tetration/info math.stackexchange.com/posts/49909/revisions

Wikipedia uses: $${^{n}a} = \underbrace{a^{a^{\cdot^{\cdot^{a}}}}}_n$$

So the corresponding expression here would be: $e^{e^{\cdot^{\cdot^{n}}}}$

Q: Is $e^{{e^{\ \dots\ }}^n}$ ever an integer?

Let $n$ be a positive integer. It is clear that $e^n$ is not integer because $e$ is transcendental (not algebraic). Now for each positive integer $k$ let $F^k(n)$ denote the $k$-fold composition of $F(n)=e^n$. Is $F^k(n)$ ever an integer? I am also (primarily) interested in this question for comp...

nt.number-theory irrational-numbers

I am not sure what is a good way to write the title in MathJax. Wikipedia article about tetration uses something like: $e^{e^{\cdot^{\cdot^{n}}}}$ which gives $e^{e^{\cdot^{\cdot^{n}}}}$. I have asked in the MathJax chatroom for advice. Feel free to revert to the original title, if you prefer that one. — Martin Sleziak 1 min ago

12 hours later…