Arg_max and Arg_min

$arg \; \underset{x\epsilon S }{max} f(x)$

x in the set S , such that x can give the max f(x).

$arg \; \underset{x\epsilon S }{max} f(x) = \left \{x\epsilon S :f(x) = \underset{x\epsilon S }{max} f(y) \right \}$

similar idea for min f(x)

$arg \; \underset{x\epsilon S }{min} f(x) = \left \{x\epsilon S :f(x) = \underset{x\epsilon S }{min} f(y) \right \}$