Show that a set S is infinite if and only if there is a

Chapter 1, Problem 80E

(choose chapter or problem)

Get Unlimited Answers
QUESTION:

Problem 80E

Show that a set S is infinite if and only if there is a proper subset A of S such that there is a one-to-one correspondence between A and S.

Questions & Answers

QUESTION:

Problem 80E

Show that a set S is infinite if and only if there is a proper subset A of S such that there is a one-to-one correspondence between A and S.

ANSWER:

Problem 80E

Show that a set S is infinite if and only if there is a proper subset A of S such that there is a one-to-one correspondence between A and S.

                                                               Step by Step Solution

Step 1 of 4

Consider the two non-empty sets as A and B.

Consider the function f that ranges from A to B such that each element of B is assigned to every element of B.

This is given as,

Add to cart


Study Tools You Might Need

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back