A nonempty set T1 is finite if and only if there is a bijection from T1->T2?

[phillyolly]

Homework Statement

Prove that a nonempty set T1 is finite if and only if there is a bijection from T1 onto a finite set T2.

The Attempt at a Solution

There are at least two different solutions to this problem that I found online:

http://answers.yahoo.com/question/index?qid=20090319202703AACrlT8

http://www.cramster.com//answers-sep-10/advanced-math/bijection-finite-set-prove-nonempty-set-t1-finite_921466.aspx

Is there any other solution? For a dummy like me these solutions are hard enough to understand them completely. If you can help me get the idea, I will really appreciate it.

 

[micromass]

Hi Phillyolly!

What is your definition of finite?

 

[phillyolly]

Hi Micromass! :-)

Definition of finite:

A set S is said to be finite if it has n elements for some n in N or is empty.

 

[gb7nash]

Well...

<-

Assume there exists a bijection from T1 to T2. Since there exists a bijection from T1 to T2, this means that |T1| = |T2|. Since T2 is finite...

->

T1 is finite. Define T2 to be T1, so...

 

[micromass]

Well, first you'll need to know what it means that "a set has n elements"...