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Homework Help: Induction principle homework

  1. Jul 16, 2010 #1
    S={t[tex]\in[/tex]Z+ | (3t-200)/2 [tex]\in[/tex]Z+}

    how to i find the element of S, provided some of this theorem:

    1. every nonempty set of non negetive integer contains a least element: that is, some integer a in S such that a=<b for all b's belongingmto S

    2. if a and b any positive integer, then there exist a positive integer n such that na<b

    3. induction principle

    from theorem 1. how do i find the least integer??
    Last edited: Jul 16, 2010
  2. jcsd
  3. Jul 17, 2010 #2


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    Staff Emeritus
    Science Advisor
    Gold Member

    Re: integers

    Your goal is just to find the least element of S? I wouldn't use any of those. Look at the function that describes S... it's increasing with t, so you just want to make it as small as possible
  4. Jul 18, 2010 #3
    Re: integers

    can clarify a bit more,
    i don't know how to make it small as possible
  5. Jul 19, 2010 #4
    Re: integers

    help T_T, someone,.. clarify for me. owho
  6. Jul 19, 2010 #5


    Staff: Mentor

    Re: integers

    Graph y = (3/2)t - 100 for t > 0. The graph is a portion of a straight line.
  7. Jul 19, 2010 #6
    Re: integers

    ok, i thought of that, hmm, i'll try to convey my inept attempt

    the smallest possible are (3/2)t>100 for y to be positive
    t must be even for (3/2)t to me integer,


    so, S={2n+68 l n[tex]\in[/tex]Z}

    correct me please

    so, i don't need use those above definition(except for induction)
  8. Jul 19, 2010 #7


    Staff: Mentor

    Re: integers

    For what t is (3/2)t - 100 > 0?
    For what t in Z+ is the inequality above satisified?
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