Let $A$ be any non-empty subset of $\mathbb{R}$. Then $s = \sup A$ iff $s$ has the following properties:
$s \geq a$ for every $a \in A$,
if $t < s$, then there exists an $a \in A$ such that $a > t$.
Prove it? having problem in proving 2.
Let $A$ be any non-empty subset of $\mathbb{R}$. Then $s = \sup A$ iff $s$ has the following properties:
$s \geq a$ for every $a \in A$,
if $t < s$, then there exists an $a \in A$ such that $a > t$.
Prove it? having problem in proving 2.
, then there exists an $a\in A$ such that $a>t$" (without the Latexed symbols) which doesn't appear in the actual post.– 2012-10-01