of points of S. 6.30 Show that a set consisting of a finite number of points in E is bounded. Gnita numher of snherical neighhorhoods in E is bounde

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Q: [3.12] Let S be a nonempty convex set in R", and let f. R" → R be defined as follows:

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Q: . Let A CQ satisfying the following conditions: (a) A + Ø and A # Q. (b) If p E A and q E Q with q <…

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Q: Prove that if ø is convex, then a-[$(x + Az) – Þ(x)] is nondecreasing for å > 0.

A: As  φ is convex we conclude that its second derivative :  φ'' is always positive ∴  φ''(x) &gt; 0…

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Q: of E. 4. Let E CR be a bounded set. Prove sup E e Ë.

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Q: 9. Which is true for a nonempty subset S of R? * If S is nonempty and sup S exists, then S is…

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Q: Show that the following pairs of sets S and T are equinumerous by finding a specific bijection…

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