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Homework Help: Direct proofs help

  1. Jun 12, 2012 #1
    1. The problem statement, all variables and given/known data

    Let nεZ,Prove that 1-n^2>0, then 3n-2 is an even integer.

    2. Relevant equations

    3. The attempt at a solution

    I proved it like this. I think its right but im not able to word it correctly.

    Since 1-n^2>0 therefore n=0. Then 3n-6=3(0)-6=-6. Since 0 is an integer, 3n-6 is even.

    How can I learn to word this correctly because im having some trouble with it?
  2. jcsd
  3. Jun 12, 2012 #2
    Try posting in the number theory forum, this isn't really calculus.
  4. Jun 12, 2012 #3
    this is intro to proofs actually. Im trying to self study.
  5. Jun 12, 2012 #4
  6. Jun 12, 2012 #5
    I wouldn't worry too much about proper wording as long as you get the concept. n has to equal zero and -6 is an even integer...sounds proved to me. :)

    Although, you probably shouldn't take my advice. I'm shunned by many in academia due to my deep detestation of pretentiousness. ;)
  7. Jun 12, 2012 #6


    Staff: Mentor

    The above is confusing. A better statement would be
    Let n ##\in## Z. If 1 - n2 > 0, then show that 3n - 2 is an even integer.
    Note that you have a typo in your work. You're supposed to prove that 3n - 2 is an even integer.

    I would say it like this:
    Since 1 - n2 > 0 and n ##\in## Z, then n = 0.
    So 3n - 2 = - 2, which is an even integer.

    Therefore, for any integer n, if 1 - n2 > 0, then 3n - 2 is an even integer.

    It should NOT be posted in the number theory section. That section and the other sections under Mathematics are not for homework and homework-type problems

    No, here is probably fine, although the Precalc Mathematics section would also be a good choice.
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