inf of a finite set I often see the notation
$$\inf \{x_1,..,.x_n\}$$
or 
$$\inf\{s,t\}$$
Is this considered appropriate notation or is it considered better to use $\min$ in these cases?
 A: Using $\mathrm{inf}$ is not incorrect, but may cause a moments pause when someone reads it.  Using $\mathrm{min}$ will not cause this pause.  Your goal should always be to communicate as effectively as possible so go with $\mathrm{min}$ unless you have a specific and compelling reason not to.
A: It depends on the order you have on the set. Even with finite sets, an infimum can differ from a minimum. The infimum is the greatest lower bound while the minimum is an infimum belonging to the original set.
Take the set $\{0,1,2\}$ with the partial order $\prec$ defined by : $0\prec 1$ and $0\prec 2$. Then
$$ \inf \{1,2\} = 0 $$
but $\min\{1,2\}$ does not even exist.
A: Whichever you use it is okay, but there is a difference.
For min the result must be an element of the set while for inf that doesn't have to be the case.
$\inf \{ i\mid i = 1/2 ^ n\} = 0$ 
while $0$ is not part of the set
$\min \{ i\mid i = 1/2 ^ n\}$ is undefined because what is the lowest value in the set? 
A: um.there is no distinction between them,but I prefer min.
