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1. (a) Consider the set S = {n(-1)" : n e N}. Verify the existence or otherwise of Min(S) and Max(S). 2n (b) Let B = : ne { 3n + 1° "€N. 1 i. Prove that inf B 2 2 ii. Show sup B 3 (c) If x, y E R such that r > 0 and y > 0. Using the fact that , V x ER, x2 > 0, prove each of the following. i. Vry < 1 (x + y) . ii. xy < (2² + y²) .

1. (a) Consider the set S = {n(-1)" : n e N}. Verify the existence or otherwise of Min(S) and Max(S). 2n (b) Let B = : ne { 3n + 1° "€N. 1 i. Prove that inf B 2 2 ii. Show sup B 3 (c) If x, y E R such that r > 0 and y > 0. Using the fact that , V x ER, x2 > 0, prove each of the following. i. Vry < 1 (x + y) . ii. xy < (2² + y²) .

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 32EQ
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1. (a) Consider the set S = {n(-1)" : n e N}. Verify the existence or otherwise of Min(S) and Max(S). 2n (b) Let B = : neN Зп + 1 1 i. Prove that inf B 2 ii. Show sup B 3 (c) If x, y E R such that x > 0 and y > 0. Using the fact that , Vx E R, x² > 0, prove each of the following. 1 (x + y). i. 2 ii. xy < (x2 + y²). iN
Transcribed Image Text:1. (a) Consider the set S = {n(-1)" : n e N}. Verify the existence or otherwise of Min(S) and Max(S). 2n (b) Let B = : neN Зп + 1 1 i. Prove that inf B 2 ii. Show sup B 3 (c) If x, y E R such that x > 0 and y > 0. Using the fact that , Vx E R, x² > 0, prove each of the following. 1 (x + y). i. 2 ii. xy < (x2 + y²). iN
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