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Homework Help: Use induction in a non standard way

  1. Jul 17, 2013 #1
    So I have to do an induction but I am not quite sure how to set it up. I have already proven that at each step I have either my intended result or I can advance one more step. I have also proven that there are a finite number of steps.

    Intuitively I have essentially completed the proof. I just can't figure out how to present this in a way that is completely rigorous.

    I get the feeling that "Well there can only be finitely many steps so eventually it will happen" is not good enough.
  2. jcsd
  3. Jul 17, 2013 #2


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    I don't see how anyone can suggest anything when what you are trying to do is so vague.
  4. Jul 18, 2013 #3
    Well I feel a little bit guilty for even posting a homework question at all (It's cheeting). So I am not going to post specifics. I will clarify certain things if people have questions. I think that someone could figure this out with the information I have given. If not then I will just have to figure it out myself which is what I should be doing anyway.
  5. Jul 18, 2013 #4
    Sounds like a good "dot-dot-dot" proof, but maybe your professor doesn't like those. I.e. show the process of a couple steps, then "dot-dot-dot", then show the final step!
  6. Jul 18, 2013 #5


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    No, I was going to ask questions but this is so vague, it isn't in the ballpark of meaning anything.
  7. Jul 23, 2013 #6
    Yeah i wish I could dot dot dot this one but that's definitely not allowed. I reallized that I had messed up at an earlier part of this problem anyway. Thanks though.

    @verty While what I said was not 100% rigourus I could easily make it that way.

    For all natural numbers n, if x is not [itex]\geq[/itex] n, then x < n. Also there exists Y[itex]\in[/itex]N such that x [itex]\leq[/itex] Y.

    Prove that x exists and is a natural number.

    Edit: We must assume x is a natural number not prove it.
    Last edited: Jul 23, 2013
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