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Math Help - Contradiction proofs

  1. #1
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    Contradiction proofs

    These are from lecture and I don't understand them thoroughly. Any tips that could help me to understand this better would be greatly appreciated. Here are the proofs.

    1) A positive integer is called prime if its only positive divisors are 1 and itself. Otherwise it is called composite.


    2) There are infinitely many primes.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by padsinseven View Post
    These are from lecture and I don't understand them thoroughly. Any tips that could help me to understand this better would be greatly appreciated. Here are the proofs.

    1) A positive integer is called prime if its only positive divisors are 1 and itself. Otherwise it is called composite.


    2) There are infinitely many primes.
    What don't you understand; the definition of a prime or that there are
    infinitly many of them, or the proof of the latter.

    RonL
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    proofs of these statements

    I got some messy notes from a classmate on these and I can't figure out the proofs of the statements. That was all that I wanted to see. Prove both statements. Thanks
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by padsinseven View Post
    I got some messy notes from a classmate on these and I can't figure out the proofs of the statements. That was all that I wanted to see. Prove both statements. Thanks
    The first statement is just a definition, there's nothing to prove.

    For the second, the most famous (and perhaps first) proof for the infinitude of primes was given by Euclid. It may be the proof you want.

    See here or here

    at the first link, other proofs besides Euclid's are shown.
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  5. #5
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    Quote Originally Posted by padsinseven View Post
    1) A positive integer is called prime if its only positive divisors are 1 and itself. Otherwise it is called composite.
    This is a side bar.
    I join many others who disagree with #1 as a definition of prime. I know that many use it.
    I even heard Keith Devlin it use on National Public Radio. However, that definition makes 1 a prime.
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  6. #6
    Senior Member DivideBy0's Avatar
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    What do you think is the best definition of a prime?
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    Quote Originally Posted by DivideBy0 View Post
    What do you think is the best definition of a prime?
    A positive integer with exactly two divisors is prime.
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  8. #8
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by Plato View Post
    A positive integer with exactly two divisors is prime.
    as far as i remember, the additional condition for a number to be prime is that it should be greater than 1. that what makes 1 not a prime..
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