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

  • Thread starter phillyolly
  • Start date
  • #1
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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-se...-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.
 
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Answers and Replies

  • #2
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Hi Phillyolly! :smile:

What is your definition of finite?
 
  • #3
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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.
 
  • #4
gb7nash
Homework Helper
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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...
 
  • #5
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Well, first you'll need to know what it means that "a set has n elements"...
 

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