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Real Analysis Question (Suprema, Infima and $\mathbb R$)

Question:

Suppose $U$ is a non-empty subset of $\mathbb R$, bounded above, with supremum $s$. If $a$ is any number satisfying $a < s$, explain why there is some $u\in U$ with $a < u$.

Please can someone help with this question?

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    Perhaps if you write out the definition of "supremum" all will become clear.2012-02-21

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