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

## 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:

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.

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Hi Phillyolly!

What is your definition of finite?

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
Homework Helper
Well...

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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...

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

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