(i) Show that |(0, 1)] = [R], where (0, 1) = {x ≤ R : 0 < x < 1}. (ii) Show that [(0, ∞)] = [R], where (0, ∞) = {x € R: x>0}. You don't need to prove that the functions you define are bijections.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.1: Polynomial Functions Of Degree Greater Than
Problem 36E
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4. (i) Show that |(0, 1)| = |R|, where (0, 1) = {x R: 0 < x < 1}.
(ii) Show that (0, ∞)] = [R], where (0, ∞) = {x € R: x>0}.
You don't need to prove that the functions you define are bijections.
Transcribed Image Text:4. (i) Show that |(0, 1)| = |R|, where (0, 1) = {x R: 0 < x < 1}. (ii) Show that (0, ∞)] = [R], where (0, ∞) = {x € R: x>0}. You don't need to prove that the functions you define are bijections.
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