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 ??