$11.$ I try to define a function f : P$($Z$)\backslash \{\}$ N by$,$ for A $$ Z$,$ A $6=$

f $($A$)=$

$$

$$

$$

min$($A$)$ if A $$ N

max$($A$)$ if A $$N

$0$ else

$.$

Here $$N denotes the set of negative integers $\{1,2,3,...\}.$ Does this function make

sense? Why or why not?