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A set S is called 'denumerable' if there exists a bijection f : N → S. (a) Show that the set N>2 is denumerable because the function g: N → N>2, n + n+1 is a bijection. (b) Prove that set Z>-3 = {-3, –2, – 1,0, 1, 2, 3, 4, 5, . ..} is denumerable by building a bijec- tive function g: N → Z>-3.

A set S is called 'denumerable' if there exists a bijection f : N → S. (a) Show that the set N>2 is denumerable because the function g: N → N>2, n + n+1 is a bijection. (b) Prove that set Z>-3 = {-3, –2, – 1,0, 1, 2, 3, 4, 5, . ..} is denumerable by building a bijec- tive function g: N → Z>-3.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A set S is called 'denumerable' if there exists a bijection f : N → S. (a) Show that the set N>2 is denumerable because the function g: N → N>2, n > n + 1 is a bijection. (b) Prove that set Z>-3 = {-3, –2, –1,0, 1, 2,3, 4, 5, ...} is denumerable by building a bijec- tive function g: N → Z>-3•
Transcribed Image Text:A set S is called 'denumerable' if there exists a bijection f : N → S. (a) Show that the set N>2 is denumerable because the function g: N → N>2, n > n + 1 is a bijection. (b) Prove that set Z>-3 = {-3, –2, –1,0, 1, 2,3, 4, 5, ...} is denumerable by building a bijec- tive function g: N → Z>-3•
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