Define g : (-1,1) → R by g(x) = 1- x2 Identify a bijection h : (0, 1) → (-1,1); you don't have to show that this is a bijection. Then show that |(0,1)| = |IR| by identifying explicitly a bijection from (0, 1) to R. Explicit: stated in terms of a formula (not necessarily simplified)

Define g : (-1,1) → R by g(x) = 1- x2 Identify a bijection h : (0, 1) → (-1,1); you don't have to show that this is a bijection. Then show that |(0,1)| = |IR| by identifying explicitly a bijection from (0, 1) to R. Explicit: stated in terms of a formula (not necessarily simplified)

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.2: Integral Domains And Fields

Problem 16E: Prove that if a subring R of an integral domain D contains the unity element of D, then R is an...

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Define g:(-1,1) + R by g(x) = 1 - 22 Identify a bijection h : (0,1)+(-1,1); you don't have to show that this is a bijection. Then show that |(0,1)] = |R| by identifying explicitly a bijection from (0, 1) to R. Explicit: stated in terms of a formula (not necessarily simplified)

Define g : (-1,1) → R by g(x) =
1- x2
Identify a bijection h : (0, 1) → (–1, 1); you don't have to show that this is a bijection. Then show that
|(0,1)| = |IR| by identifying explicitly a bijection from (0, 1) to R.
Explicit: stated in terms of a formula (not necessarily simplified)

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