prove inf(S) = -sup(-S) given that S={-s, s∈S}. :confused:
D david New member Joined Oct 9, 2011 Messages 30 Sep 13, 2012 #1 prove inf(S) = -sup(-S) given that S={-s, s∈S}.
D daon2 Senior Member Joined Aug 17, 2011 Messages 1,003 Sep 13, 2012 #2 I'll get you started. Let I be the infemum of S. Then I <= s for all s in S. Also, if J <= s for all s in S, then J <= I. But this implies -I >= -s for all s in S, i.e. -I is an upper bound for -S. Continue.
I'll get you started. Let I be the infemum of S. Then I <= s for all s in S. Also, if J <= s for all s in S, then J <= I. But this implies -I >= -s for all s in S, i.e. -I is an upper bound for -S. Continue.
