Question

Suppose that A is a non-empty bounded set of real numbers that has no
largest member and that a is in A. Explain why the sets A and A \{a} have
exactly the same upper bounds.

Answer 1

i think you can work directly from the definition of upper bound
b is an upper bound of A if for every a in A a<= b
since a is not b, then for all
if x in A\{a} x <= b and there is no smaller one