   Chapter 7.4, Problem 26ES ### 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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# Prove that any infinite set contain a countable infinite subset.

To determine

To prove:

Any infinite set contains a countably infinite subset.

Explanation

Given information:

any infinite set

Proof:

Let A be an infinite set. Since the set is infinite, the set cannot be empty.

A0

Since A is not empty, there exists some element a1A.

As A is infinite, the set will remain infinite when a1 is removed from the set and thus the remaining set A{a1} will still contain some element a2A{a1}.

As A{a1} is infinite, the set will remain infinite when a2 is removed from the set and thus the remaining set A{a1,a2} will still contain some element a3A{a1,a2}

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