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Whats the different?

  1. Jun 29, 2009 #1
    1. The problem statement, all variables and given/known data
    this is the 2 statement bout mathematica induction from different book ..fist is from spivak book : (1) P(1) is true
    (2) whenever P(k) is true ,P(k+1) is true
    and 2nd from courant book :
    (1) if the assertion Ar is known to be true ,then the truth of assertion Ar+1 will follow
    (2) the first statment A1 is known to be true ..

    2. Relevant equations

    3. The attempt at a solution

    what i think is the statment from spivak is more easy to digest and more reasonable in process , you must make sure that "one" is true first .. but courant say in diferrent way ..i dont know ..its look same in mathematica reasoning ??
  2. jcsd
  3. Jun 29, 2009 #2


    Staff: Mentor

    They both say the same thing, although the steps are in the opposite order. In Spivak, P(1), P(2), ..., P(k), P(k + 1), ... represent a sequence of statements. In Courant, the sequence of statements is written as A1, A2, ..., Ar, Ar + 1, ...

    BTW, it's called mathematical induction. Mathematica is a computer program.
  4. Jul 13, 2009 #3


    User Avatar
    Science Advisor

    I have always thought of "induction" as "knocking over dominos. If you know
    1) you can knock over the first domino and
    2) any one domino will knock over the next one

    then you know that all dominos will fall.

    But the answer to your question is exactly what Mark44 said originally: there is no difference except that they have stated the two conditions in reversed order.
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