Both parts please 5. (P19, Page 12) Define S = {x € R | x² < x}. Do the following.Use properties of real numbers to prove that 1 is an upper bound for S.(a)[Properties needed: (i) If a ± 0, a² > 0. (ii) If a > 0, then a- > 0. (iii) If a < b and 0 < c, then ac < bc.](b)Use the Method of Proof by Contradication to prove that sup S = 1.

(a) x2<xx2-x<0x(x-1)<0Either x<0, x-1>0 ....(i)or x>0, x-1<0 ....(ii)if x≠0…

5. (P19, Page 12) Define S = {r € R | ² < x}. Do the following. (a) Use properties of real numbers to prove that 1 is an upper bound for S. [Properties needed: (i) If a ± 0, a² > 0. (ii) If a > 0, then a¯1> 0. (iii) If a < b and 0 < c, then ac < bc.]

5. (P19, Page 12) Define S = {r € R | ² < x}. Do the following. (a) Use properties of real numbers to prove that 1 is an upper bound for S. [Properties needed: (i) If a ± 0, a² > 0. (ii) If a > 0, then a¯1> 0. (iii) If a < b and 0 < c, then ac < bc.]

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section: Chapter Questions

Problem 63RE

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Question

Both parts please

5. (P19, Page 12) Define S = {x € R | x² < x}. Do the following.
Use properties of real numbers to prove that 1 is an upper bound for S.
(a)
[Properties needed: (i) If a ± 0, a² > 0. (ii) If a > 0, then a- > 0. (iii) If a < b and 0 < c, then ac < bc.]
(b)
Use the Method of Proof by Contradication to prove that sup S = 1.

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