Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Mathematical proof

  1. Jun 29, 2008 #1
    1. The problem statement, all variables and given/known data
    The thing is that there is a question which needs me to prove something. I have done it already but the thing that troubles me is that it wants me to prove this:

    [tex]a_{1}+a_{2}+a_{3}+.................a_{K}>K[/tex]
    [tex]a_{i}[/tex] is a positive integer.
    I know this is always true. but how should I prove it mathematically?
     
    Last edited: Jun 29, 2008
  2. jcsd
  3. Jun 29, 2008 #2

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    I see two ways to proceed:

    (1) Attempt to precisely elaborate why you know it's true. Then translate those precise reasons into logical implications

    (2) Try to prove it for special cases of your own choosing. Then, see if you can generalize your proof to the general case.
     
  4. Jul 2, 2008 #3
    that's not true always .

    example :

    take [tex] a_i=1[/tex] , for all [tex]i[/tex].

    So , we get [tex]\overbrace{1+1+\cdots+1}^K =K \not > K [/tex]
     
  5. Jul 3, 2008 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    I presume you mean [itex]a_1+ a_2+ \cdot\cdot\cdot+ a_K\ge K[/itex] where the an are positive integers.

    Looks like a good candidate for "proof by induction".
     
  6. Jul 3, 2008 #5
    why proof by induction? The way I was thinking of it is like this:
    Rewriting each [tex]a_i[/tex] as [tex]1+c_i[/tex], we have
    [tex](1+c_1)+(1+c_2)+\cdots+(1+c_K)=K+c_1+c_2+\cdots+c_K=K+C \geq K[/tex]​
     
  7. Jul 4, 2008 #6
    This seems self-evident? The lowest positive integer is 1. If you have n numbers, all being positive, the sum cannot be smaller than n.

    k
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Mathematical proof
  1. Mathematical Proof? (Replies: 10)

  2. Mathematical Proof (Replies: 6)

  3. Mathematical Proofs (Replies: 3)

  4. Mathematical Proofs (Replies: 5)

  5. Mathematical Proofs (Replies: 15)

Loading...