Results 1 to 3 of 3

Math Help - Odometer Principle

  1. #1
    Senior Member Sampras's Avatar
    Joined
    May 2009
    Posts
    301

    Odometer Principle

    Prove that the Odometer Principle with base  b gives the representation  x_{n-1} \ldots x_{1}x_{0} for the natural number  N = x_{n-1}b^{n-1} + \cdots + x_{1}b + x_0 .


    Odometer Principle to find the successor of a natural number to base  b : Start by considering the rightmost digit.


    • If the digit we are considering is not  b-1 , then replace it with the next digit in order, and terminate the algorithm.


    • If we are considering a blank space (to the left of all digits) then write in it the digit  1 , and terminate the algorithm.


    • If neither of the above holds then we are considering the digit  b-1 . Replace it with the digit  0 , move one place to the left, and return to the first bullet point.


    Proof. We use induction on  n . For  n=0 ,  N = x_0 = x_0 . Now suppose that for  n=k ,  N = x_{k-1}b^{k-1} + \cdots + x_{1}b + x_0 = x_{k-1} \ldots x_{1}x_{0} . So now we look at  x_0 (the rightmost digit) and apply the Odometer Principle?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Apr 2009
    From
    Atlanta, GA
    Posts
    408

    Clarity?

    I am having trouble understanding the problem. What exactly is your question?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member Sampras's Avatar
    Joined
    May 2009
    Posts
    301
    Quote Originally Posted by Media_Man View Post
    I am having trouble understanding the problem. What exactly is your question?
    The first sentence.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Well ordering principle and the maximum principle
    Posted in the Advanced Algebra Forum
    Replies: 6
    Last Post: August 3rd 2010, 08:31 AM
  2. first principle
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: January 23rd 2010, 04:17 AM
  3. first principle help!!
    Posted in the Algebra Forum
    Replies: 1
    Last Post: January 18th 2010, 12:13 PM
  4. Odometer Palindromes....
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: December 8th 2009, 03:06 PM
  5. Momentum Principle and Energy Principle Problem
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: October 4th 2009, 01:42 AM

Search Tags


/mathhelpforum @mathhelpforum