Which of the following statements is not correct A Mathemati

Which of the following statements is not correct? A. Mathematical induction involves first proving a statement S1 and then proving a second statement, that Sk implies Sk + 1. B. Mathematical induction is a method of proof. C. A necessary skill to master before attempting a proof by mathematical induction is the ability to write three forms of a statement, S1, Sk, and Sk + 1. D. Mathematical induction proves facts about all positive real numbers.

Solution

Mathematical induction is a way of proving a statement by initially proving it for a base case for a natural number k (which are not the same as positive real numbers) and then proving it for an inductive case where the next higher natural number \'k+1\' is taken. It is assumed that if the proof is valid for one natural number then it must also be true and valid for higher natural numbers. And thus one can generalize the situation for all natural numbers.

therefore, \'Mathematical induction proves facts about all positive real numbers\' is an incorrect statement.