epsilon delta proofs notation question

Question

If I want to say let $\delta$ be less than $\epsilon/6$ or $1$, whichever is smaller do I denote it as

$\delta< \min\{\epsilon/6,1\}$ or $\delta< \min(\epsilon/6,1)$??

Answer 1

You normally write $\delta < \min \{ \epsilon/6 , 1 \}$ which makes it immediately clear what you mean.

I've never seen anyone using $\delta < \min(\epsilon /6 ,1 )$ for expressing this, because $\{ \}$ normally denotes a set and $()$ denotes a touple (ordered). In the case of $\min$ it does not make sence to use an ordered structure as argument anyways.

Answer 2

It is usually like this: $$\delta\ <\ \min(\varepsilon/6,\,1)\,.$$ If you want, $\min$ is a function in two (or more) variables -- we can also call it an operation.
On the other hand, the notation $\min S$ is also valid where $S$ denotes a set (of any ordered things).