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[H] Let 0 be the set of odd integers and consider the function T: Z → 0 defined by r(n) = 2n – 3. Show that r is onto, by (1) finding an element, say x of Z that gets sent to an arbitrary element y in 0 (make sure you show that your element does in fact get sent to y) and then (2) prove that r is in fact an element of Z.

[H] Let 0 be the set of odd integers and consider the function T: Z → 0 defined by r(n) = 2n – 3. Show that r is onto, by (1) finding an element, say x of Z that gets sent to an arbitrary element y in 0 (make sure you show that your element does in fact get sent to y) and then (2) prove that r is in fact an element of Z.

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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Let \( O \) be the set of odd integers and consider the function \( \Gamma : \mathbb{Z} \to O \) defined by \(\Gamma(n) = 2n - 3\). Show that \( \Gamma \) is onto, by (1) finding an element, say \( x \) of \(\mathbb{Z}\) that gets sent to an arbitrary element \( y \) in \( O \) (make sure you show that your element does in fact get sent to \( y \)) and then (2) prove that \( x \) is in fact an element of \(\mathbb{Z}\).
Transcribed Image Text:Let \( O \) be the set of odd integers and consider the function \( \Gamma : \mathbb{Z} \to O \) defined by \(\Gamma(n) = 2n - 3\). Show that \( \Gamma \) is onto, by (1) finding an element, say \( x \) of \(\mathbb{Z}\) that gets sent to an arbitrary element \( y \) in \( O \) (make sure you show that your element does in fact get sent to \( y \)) and then (2) prove that \( x \) is in fact an element of \(\mathbb{Z}\).
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