Results 1 to 2 of 2

Math Help - Proposition induction

  1. #1
    Newbie
    Joined
    Sep 2008
    Posts
    17

    Proposition induction

    Let P(n) be a proposition about integers n such that p(1) is true and such that P(j) is true for all positive integers j < k, trhen P(k) is true. Prove that P(n) is true for all positive integers n.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,326
    Thanks
    1241
    Quote Originally Posted by helpinmath View Post
    Let P(n) be a proposition about integers n such that p(1) is true and such that P(j) is true for all positive integers j < k, trhen P(k) is true. Prove that P(n) is true for all positive integers n.
    That's a proof by induction.

    Basically, you show it's true for the base step. You've said it is...

    i.e. P(1) is true.

    Then you assume it's true for an arbitrary value, in this case j...

    i.e. P(j) is true.

    By showing the next value is also true, you have completed the proof. This is called the inductive step.

    Since you said that k = j+1 and P(k) is true, the inductive step is complete and thus the proof is complete.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Fibonacci Proposition
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: February 25th 2011, 04:11 PM
  2. Proposition Help!?
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: November 29th 2009, 03:16 PM
  3. What is the use of the salinon proposition
    Posted in the Geometry Forum
    Replies: 1
    Last Post: November 20th 2009, 05:43 PM
  4. Mathematical induction: Proof of proposition
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: October 16th 2009, 06:35 PM
  5. Proof of Proposition
    Posted in the Discrete Math Forum
    Replies: 6
    Last Post: August 15th 2007, 10:40 AM

Search Tags


/mathhelpforum @mathhelpforum