# How to express the min operator as a binary operator

I'd like to use the $\min$ operator as a binary operator that returns the lowest of two given numbers. I'm not sure if this is the correct use of it, or if I should use something else.

$\text{Given four integers, }A,B,C, \text{ and }D \text{, take the lesser of the values between } A \text{ and } B \text{ and add it to the lesser value between }C \text{ and }D.$

I would perhaps express it like this:

$\min(A,B) + \min(C,D)$

But perhaps this is also correct:

$(A \min B) + (C \min D)$

And I think I've also seen something like this:

$(A, B)_{\min} + (C, D)_{\min}$

Is there some convention on this? Also, is this the correct operator to use, or is there a more expressive form?

• $\text{min}(A, B) + \text{min}(C, D)$ is fine and moderately standard. – Qiaochu Yuan Jul 30 '15 at 22:46

## 1 Answer

I'm not sure there's a hard-and-fast convention, but I've commonly seen

$\min\{A,B\}$ and $\max\{A,B\}$

which also gives flexibility for sets, as well as

$A \downarrow B$ and $A \uparrow B$

for when an operation was needed.