Given that alpha is an upper bound of a given set S of real numbers, prove that the following two conditions are equivalent:(adsbygoogle = window.adsbygoogle || []).push({});

a) We have alpha=sup(S)

b) We have alpha belongs to S closure

I'm trying to prove this using two steps.

Step one being: assume a is true, then prove b is true.

Step two being: assume b is true, then prove a is true.

Could anyone help me with step two?

Assuming alpha belongs to S closure.....

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# Prove alpha=sup(S) is equivalent to alpha belongs to S closure

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