TITLE: Symbol for "the greater of the two values"
QUESTION [11 upvotes]: I'm looking for an operator that returns the greater of two values.
Here's an example. If $a=5$, $b=6$ and $???$ is the operator, I'd like to have $x$ equal $b$ when I do $x=a???b$, since $b$ is the larger of the two values.

REPLY [3 votes]: For $S=\{a_1,\cdots,a_n\}$, define $*$ inductively by operator $*:\mathbb{R}^n\to\mathbb{R}$ as $*(a_1,a_2)=\dfrac{|a_2-a_1|+a_2+a_1}{2}$ if $n=2$ and $*:\mathbb{R}^{n+1}\to\mathbb{R}$ as $*(a_1,...,a_n,a_{n+1})=*(*(a_1,\cdots,a_n),a_{n+1})$. Thus $*(a_1,\cdots,a_n)=\max S$ for any set $S=\{a_1,\cdots,a_n\}$.