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Tips for proofs

  1. Jul 19, 2013 #1


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    does anyone have any tips on learning how to do proofs. completing a proof isn't something im good at, at all. I know how to get answers and I can do the math but explaining it to someone step by step, using the right communication. Seems like a foreign language to me. any tips on learning what ways to approach a proof?
  2. jcsd
  3. Jul 19, 2013 #2


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    There are several factors. One is considering possibilities. A proof must be general so it must work for all possibilities not just some. You need to know several general approaches like contradiction, contrapositive, induction, direct and so forth. Several things you will want to do is read some common proofs like there are infinite primes and sqrt(2) is irrational and try to understand why the proof works and how someone would come up with it. Practice proving simple things like e^x is not a polynomial and the square of an even number is even.
  4. Jul 19, 2013 #3


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    the square of an even number is even.
    the way I would prove that.
    because an even number times an even number equals an even number.
    sounds terrible I know..
  5. Jul 19, 2013 #4


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    Any even number n can be written in the form n = 2k, for some integer k. (An odd number can be written in the form 2m + 1.)

    What do you get when you square 2k? Can you convince yourself that the result is also even?

    There are a couple of books that might be helpful to you: The Nuts and Bolts of Proofs, and How to Read and Write Proofs. You should be able to do a web search on those titles and come up with the authors and other info.
  6. Jul 19, 2013 #5
    I read them both :smile:
  7. Jul 20, 2013 #6


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    Eddybob123: Did they work? Are you now comfortable with writing proofs? And can you understand other proofs that you read?
  8. Jul 21, 2013 #7
    That's not a proof at all, it's an assertion.

    If you set out to prove that the square of an even number is an even number, you start from what an even number is, and what a square is, and show that it is even.

    You can't assume that an even number times an even number is an even number, because you are assuming what you are trying to prove in the guise of a slightly more general statement.
  9. Jul 22, 2013 #8


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    you're right. that is where my language barrier suffers.
  10. Jul 22, 2013 #9


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    One of the things one needs to learn about matheatics is that mathmatical definitions are "working definitions". That is, you can use the precise words of the definitions in problems or proofs.

    If I were asked to prove that "the product of two even numbers is an even number", the first thing I would think about is the definition of "even number".

    So- do you know what an even number is? What is the definition of an even number?

    (Saying that "2, 4, 6 are even numbers" or "even numbers are numbers like 2, 4, 6" are NOT definitions.)
  11. Jul 22, 2013 #10


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    would you care to define an even number for me?
  12. Jul 22, 2013 #11


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    It is a number which can be factored as ##2n##, where ##n## is an integer.
  13. Jul 22, 2013 #12
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