If S is a non-empty set of real numbers which is bounded above, then a real number s is the supremum of S if and only if the following two conditions hold : (i) x 0, 3 some x e S such that x > s - E.

If S is a non-empty set of real numbers which is bounded<br>above, then a real number s is the supremum of S if and only if the following<br>two conditions hold :<br>(i) x<s V xeS.<br>(ii) Given.any ɛ> 0, 3 some x e S such that x > s - E.<br>

Extracted text: If S is a non-empty set of real numbers which is bounded above, then a real number s is the supremum of S if and only if the following two conditions hold : (i) x
~~0, 3 some x e S such that x > s - E.~~

Jun 05, 2022

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If S is a non-empty set of real numbers which is bounded above, then a real number s is the supremum of S if and only if the following two conditions hold : (i) x 0, 3 some x e S such that x > s - E.

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