   Chapter 7.4, Problem 9ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# Show that the set of all nonnegative integers is countable by exhibiting a one-to-one correspondence between Z + and Z manex .

To determine

To prove:

The set of all nonnegative integers is countable by showing a one-to-one correspondence between Z+and Znonneg

Explanation

Given information:

f:ZnonnegZ+

Concept used:

A function is said to be one-to-one function if distinct elements in domain must be mapped with distinct elements in codomain.

A function is onto function if each element in codomain is mapped with at least one element in domain.

Proof:

Let f:ZnonnegZ+ as

f(x)=x+1

To show: f is one-to-one.

f(x)=f(y)x+1=y+1x=y

Therefore, f is one-to-one.

To show: f is onto

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