Results 1 to 3 of 3

Math Help - Induction question

  1. #1
    Newbie
    Joined
    Feb 2009
    Posts
    15

    Induction question

    If you have an equation like
    n<2^n for n>=0

    do you just work one side of the equation at a time like

    n<2^(n+1) ....

    or do you do both sides like

    n+1<2^(n+1) ......

    Thanks for the help.
    Last edited by smellatron; May 2nd 2009 at 04:25 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by smellatron View Post
    If you have an equation like
    n<2^n for n<=0

    do you just work one side of the equation at a time like

    n<2^(n+1) ....

    or do you do both sides like

    n+1<2^(n+1) ......

    Thanks for the help.
    are you sure this is for n <= 0? that would mean we are doing induction for negative integers, not completely strange, but very uncommon. also, it is trivial to use induction for such a claim, since 2^n is always positive, while n is nonpositive for n<=0. clearly it will always be the case 2^n > n under such conditions.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member TheAbstractionist's Avatar
    Joined
    Apr 2009
    Posts
    328
    Thanks
    1
    Quote Originally Posted by smellatron View Post
    If you have an equation like
    n<2^n for n>=0

    do you just work one side of the equation at a time like

    n<2^(n+1) ....

    or do you do both sides like

    n+1<2^(n+1) ......

    Thanks for the help.
    Hi smellatron.

    In an induction proof, the statement n<2^n is what you assume as your inductive hypothesis and the statement n+1<2^{n+1} is what you then try to prove. There is no value in considering n<2^{n+1}.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. a question about induction
    Posted in the Algebra Forum
    Replies: 3
    Last Post: January 18th 2009, 04:25 AM
  2. induction question..
    Posted in the Calculus Forum
    Replies: 5
    Last Post: January 6th 2009, 06:23 AM
  3. Question on induction
    Posted in the Discrete Math Forum
    Replies: 8
    Last Post: July 18th 2008, 08:49 PM
  4. Induction question
    Posted in the Algebra Forum
    Replies: 2
    Last Post: March 3rd 2008, 08:54 AM
  5. Induction question..
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: December 2nd 2007, 05:00 PM

Search Tags


/mathhelpforum @mathhelpforum