   Chapter 7.4, Problem 32ES ### 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 Z × Z , the Cartesian product of the set of integers with itself, is countably infinite.

To determine

To prove:

×, the cartesian product of the set of integers with itself, is countably infinite.

Explanation

Given information:

f is well defined and one-to-one function.

Concept used:

Bijection is countably infinite.

Calculation:

The object is to prove that ×, the cartesian product of the set of integers with itself, is countably infinite.

Let A be the set of positive integers.

Put the elements of × in one to one correspondence with A.

Let A={(Ik,Jk)/Ik,Jk,k=1,2,....}.

To show that A is countably infinite.

Let f:×

It is enough to show that there is a bijection from × to the set of integer .

For, let f:× be defined by f(Ik,Jk)=k

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