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Math Help - Countability - Finite Set

  1. #1
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    Countability - Finite Set

    There is a statement in my book -

    "a proper subset of a finite set and the finite set itself - can't have same cardinality"

    Just wanted to check with you guys - To prove this we have to use Pigeon-Hole Principle. Correct? There is no way out without assuming that.

    A yes/no would be good enough. (I know how to do the proof with Pigeon-Hole Principle)
    Thanks
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  2. #2
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    Quote Originally Posted by aman_cc View Post
    There is a statement in my book -

    "a proper subset of a finite set and the finite set itself - can't have same cardinality"

    Just wanted to check with you guys - To prove this we have to use Pigeon-Hole Principle. Correct? There is no way out without assuming that.

    A yes/no would be good enough. (I know how to do the proof with Pigeon-Hole Principle)
    Thanks

    Yes, though right now out of the blue I can't be 100% sure whether this is the UNIQUE way to prove it.

    Tonio
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  3. #3
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    Quote Originally Posted by tonio View Post
    Yes, though right now out of the blue I can't be 100% sure whether this is the UNIQUE way to prove it.

    Tonio
    Thanks Tonio. It would definitely be interesting, though, to know if there are other ways to do it.
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