The problem asks us to identify which of the given options is not a part of the principle of mathematical induction. The options are: a. Random selection of number b. Inductive step proof c. Basis step, Hypothesis step and inductive step proof d. Hypothesis step e. Basis step

1. Problem Description

The problem asks us to identify which of the given options is not a part of the principle of mathematical induction. The options are:

a. Random selection of number

b. Inductive step proof

c. Basis step, Hypothesis step and inductive step proof

d. Hypothesis step

e. Basis step

2. Solution Steps

Mathematical induction is a method of proving that a statement is true for all natural numbers. It consists of the following steps:

1. Basis Step: Prove that the statement is true for the initial value, usually $n = 0$ or $n = 1$.

2. Inductive Hypothesis: Assume that the statement is true for some arbitrary integer $k \ge 0$ (or $k \ge 1$).

3. Inductive Step: Prove that if the statement is true for $n=k$, then it must also be true for $n=k+1$. This step typically involves using the inductive hypothesis to show that the statement holds for $n=k+1$.

The options include basis step, inductive step proof, and hypothesis step. A random selection of a number is not part of mathematical induction.

3. Final Answer

a. Random selection of number