Basic question on math notation of max and min

Question

When we write $\text{max}\left \{x,y \right \}$ and $\text{min}\left \{x,y \right \}$ then what do we actually mean? Does it mean the maximum and minimum of both the things that are inside $\left \{ \right \}$. Say $\epsilon = \text{max}\left \{1,3 \right \}$ then what does it exactly mean in a numeric sense? If $x = 1$ and $y = 3$, then is $\epsilon = \text{max}\left \{1,3 \right \}$ the biggest number formed from $x$ and $y$?

Answer 1

For real $a$ and $b$ (and in general for any $a$ and $b$ belonging to some order), $\max\{a, b\} = a$ if $a \geq b$; otherwise, $\max\{a, b\} = b$.

Answer 2

Yes, $\max(1,3)$ means the biggest number from both and $\min(1,3)$ means the smallest number.