Results 1 to 2 of 2

Math Help - setup an induction

  1. #1
    Junior Member
    Joined
    Oct 2008
    Posts
    56

    setup an induction

    Hi,

    Could someone help me with setting up a problem . So i want to prove something by induction on k = 0,1,2,3,4...n, clearly k \in Z+

    I have two functions: g(x) and f(x) and i have observed that

     g(0) = y
     f(0) = g(0) = y
     f(1) = g(f(0))+g(g(f(0)))
     f(2) = g(f(1))+g(g(f(1)))
     ...
    so it looks like :
     f(k) = g(f(k-1))+g(g(f(k-1))) and if i check that for all k up to 100 i get correct numbers.

    And as I said i would like to prove this (  f(k) = g(f(k-1))+g(g(f(k-1)))) by induction on k So my question is what is my base case and what my induction hypothesis? To me it looks like my base case is :

     g(0) = y
     f(0) = g(0) = y

    and my induction H:

     f(k) = g(f(k-1))+g(g(f(k-1)))

    but what confuses me is if if i plug in 0 for k here i get :

     f(0) = g(f(0))+g(g(f(0)))
     f(0) = g(y)+g(g(y))

    which is not y which means that either i have wrong idea about my base case (although i always recieve f(0) = g(0)) or my induction hypothesis is wrong (but for all k > 0 i always get the right numbers if i apply  f(k) = g(f(k-1))+g(g(f(k-1))) ). I don't know how to connect these two together.

    One more information . This ofcourse works if y = 0 but y = 1,2,3..n so  y\in N and  g(y)> y

    Thank you

    baxy
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Mar 2013
    From
    Nederland
    Posts
    4

    Re: setup an induction

    Hi,

    You made a small error in plugging in 0 for k.

    If you were to plug in 0, you would get
    f(0) = g(f(-1)) + g(g(f(-1)))
    Now, f probably is not defined on -1, so what you are trying to prove is this:


    1. For n=0, f(0) = g(0) = y.
    2. For n=1, 2, 3, ..., f(k) = g(f(k-1)) + g(g(f(k-1))).

    The second part can be proved by induction, proving the following two subparts seperately:
    2a. f(1) = g(f(0)) + g(g(f(0))
    2b. If f(k) = g(f(k-1))) + g(g(f(k-1))) (induction hypothesis), then  f(k+1) = g(f(k))) + g(g(f(k)))

    Hope this helps
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Reimann Sum Setup
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 30th 2012, 09:17 AM
  2. GLMM setup
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: May 14th 2012, 05:44 AM
  3. Setup help
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: July 15th 2009, 10:20 PM
  4. Problem that I don't know how to setup
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 11th 2008, 06:05 AM
  5. [T-89 Ti]Help! How to setup 5th square of 25?
    Posted in the Calculators Forum
    Replies: 3
    Last Post: April 5th 2008, 08:41 AM

Search Tags


/mathhelpforum @mathhelpforum