Any help with this proof would be appreciated:

If x1 and x2 are least upper bounds for A, then x1 = x2

least upper bound of A is denoted by sup(A)

Thanks!

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- Mar 30th 2011, 01:16 AMjstarks44444Least Upper Bound proof
Any help with this proof would be appreciated:

If x1 and x2 are least upper bounds for A, then x1 = x2

least upper bound of A is denoted by sup(A)

Thanks! - Mar 30th 2011, 01:43 AMemakarov
The

*least*upper bound means "less than or equal to any upper bound." Thus, x1 <= x2 and x2 <= x1. Also, <= is antisymmetric.