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 \}

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