# Is there a name/symbol for taking the bigger one from the two: a value and its reciprocal?

I have some algebraic function given in explicit form$-$let's take as an example $x^2-$that can attain values either $>1$ or $<1$ (let's exclude $=1$ here). I want to ascribe to a symbol $a$ the value of $x^2$ if $x^2>1$, and $1/x^2$ otherwise (so I want my $a>1$ always). So sometimes (i.e., for some values of $x$) $a=x^2$, but sometimes (for some other $x$'s) it will be $a=1/x^2$. Is there a name/symbol for such an operation?

It would seem I could do $a=\max\{x^2, 1/x^2\}$, but my real function is more complicated than $x^2$ so doing so explicitly will be messy. I could of course name the function, like $f(x)=x^2$ and then $a=\max\{f(x), 1/f(x)\}$, but this introduces a new symbol$-f(x)-$that I won't use anymore, as I'm only interested in $a$.

Question: Is there something$-$similar to $\max$, which takes the bigger of two (well, arbitrary many) values$-$that says "take the bigger from the two: value and its reciprocal"?

Note: Introducing some fancy notation, e.g. some weird brackets like $a=\uparrow x^2\uparrow$ is the same as simply introducing a function $f$.

• give a name to your complicated expression, e.g. call it $y$, and then write $$a:=\max(y,y^{-1})$$
• give a name to the function: $$f(x):=\max(x,x^{-1})$$ and then call it on you expression: $a=f(\text{complicated expression})$.