Recent content by submartingale

What if we replace it by y=sup{M} if and only if given that y is an upper bound of M and x is any real number, y >x implies there exists m in M so that m >=x. Thanks

If you take y=x, then there exists m in M so that m>=x=y. But y is an upper bound of M, so y=x=m.

Hello everyone, is the following an equivalent definition of the supremum of a set M, M subset of R? y=sup{M} if and only if given that y is an upper bound of M and x is any real number, y >= x implies there exists m in M so that m >=x. pf: Let x_n be a sequence approaching y from...