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i+2+3+ ·+n = zn(n+1) 5. Let S be a nonempty subset of R that is bounded above, with upper bound b. Prove that b = sup(S) if the following condition holds : for every e > 0 there is IE S such that b –...

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5i+2+3+ ·+n = zn(n+1) 5. Let S be a nonempty subset of R that is bounded above, with upper bound b. Prove that b = sup(S) if the following condition holds : for every e > 0 there is IE S such that b – e < x < b. To prove this, assume that there is some real number c with the property that c2 x for every r E S and that c < b. Show that this assumption leads to a contradiction, and explain why the contradicted assumption proves that b= sup(S).
Extracted text: i+2+3+ ·+n = zn(n+1) 5. Let S be a nonempty subset of R that is bounded above, with upper bound b. Prove that b = sup(S) if the following condition holds : for every e > 0 there is IE S such that b – e < x < b. To prove this, assume that there is some real number c with the property that c2 x for every r E S and that c < b. Show that this assumption leads to a contradiction, and explain why the contradicted assumption proves that b= sup(S).
Answered 103 days After Jun 09, 2022

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Ajay answered on Sep 21 2022
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