Symbol for "the greater of the two values"

You can always write $x=\max\{a,b\}$; this is common. A less common notation is $x=a\lor b$; although it is used, it is uncommon enough that I would definitely define it before using it. Note too that the more common notation easily generalizes to the maximum of any finite set of numbers: if $A=\{a_k:k=1,\ldots,n\}$, for instance, you can write $x=\max A$, $x=\max\{a_1,\ldots,a_n\}$, or $x=\max\{a_k:k=1,\ldots,n\}$.

The matching usages for the smaller of two numbers are $\min\{a,b\}$ and $a\land b$.

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 $S=\{a_1,\cdots,a_n\}$.