Results 1 to 4 of 4

Math Help - induction

  1. #1
    Member
    Joined
    May 2008
    Posts
    94

    induction

    Hi there,

    I have a question...

    When to take n = 0 (base case) and when to take n = 1 (base case) for proving statement P(n) by induction?

    I've seen two-three examples some take n = 1 and some take n = 0.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor kalagota's Avatar
    Joined
    Oct 2007
    From
    Taguig City, Philippines
    Posts
    1,026
    some hints:

    they often say: prove by induction that this statement is true for all n\geq a..

    that a becomes your base case..

    more often than not, they say that the statement is true for all natural numbers, thus n=1 is your base.. (but others say it should be n=0.. however, by convention 0 is not a natural number)


    EDIT: it just depends on what principle you use.. try reading Principle of Mathematical Induction
    Last edited by kalagota; June 17th 2008 at 06:16 AM. Reason: some infos are added..
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor Reckoner's Avatar
    Joined
    May 2008
    From
    Baltimore, MD (USA)
    Posts
    1,024
    Thanks
    75
    Awards
    1

    Question

    Quote Originally Posted by kalagota View Post
    but others say it should be n=0.. however, by convention 0 is not a natural number
    What convention? I've heard many definitions that both include and exclude 0, and I am not aware of any general agreement.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor kalagota's Avatar
    Joined
    Oct 2007
    From
    Taguig City, Philippines
    Posts
    1,026
    Well, at least in our country (in particular in our university), most professors who had graduate studies in other countries, tell us zero is not included.

    and it must be consistent to the fact that if zero is included (in the set N), then the set of whole numbers must be equal to the set of natural numbers. But, are they? And if they are, what is the sense of calling one on another name?

    oh well, i maybe too young to debate on it. just ask your own professors about your local "convention".
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Strong induction vs. structural induction?
    Posted in the Discrete Math Forum
    Replies: 13
    Last Post: April 21st 2011, 12:36 AM
  2. Replies: 10
    Last Post: June 29th 2010, 12:10 PM
  3. induction help
    Posted in the Discrete Math Forum
    Replies: 7
    Last Post: April 19th 2010, 05:39 AM
  4. Mathemtical Induction Proof (Stuck on induction)
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: March 8th 2009, 09:33 PM
  5. Induction!
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: March 7th 2008, 04:10 PM

Search Tags


/mathhelpforum @mathhelpforum