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    angora's Avatar
    angora Posts: 1, Reputation: 1
    New Member
     
    #1

    Aug 3, 2005, 08:07 AM
    Proof by induction
    How can I prove the following?
    for any integer n>=1,
    {celling of [lg(n+1)]} = (floor of lg n) + 1
    thanks for the help
    reinsuranc's Avatar
    reinsuranc Posts: 92, Reputation: 6
    Junior Member
     
    #2

    Sep 4, 2005, 10:52 AM
    Hi. I understand induction, but I am confused.

    Is lg supposed to be logarithm?

    What is celling? Is this supposed to be ceiling?

    What do ceiling and floor have to do with logarithms?

    Maybe you can restate this problem.
    CroCivic91's Avatar
    CroCivic91 Posts: 729, Reputation: 23
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    #3

    Sep 4, 2005, 01:46 PM
    "lg x" is short for "logarithm of x with the base 2".

    "Celling" should indeed be "ceiling". "Ceiling" is a function that takes a real number and returns an integer, in the following rule:

    ceiling( x ) = min{ n : n >= x & n is an integer }
    For example, ceiling( pi ) = 4, ceiling( -pi ) = -3

    "Floor" is a function defined as:

    floor( x ) = max{ n : n <= x & n is an integer }
    For example, floor( pi ) = 3, floor( -pi ) = -4

    Of course, floor( 3 ) = 3, and ceiling( 3 ) = 3.

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