The question is about mathematical induction and which type of numbers it applies to.

1. Problem Description

The question is about mathematical induction and which type of numbers it applies to.

2. Solution Steps

Mathematical induction is a method of proving that a statement is true for all natural numbers (positive integers). The basic steps are:

1. Base case: Prove the statement is true for the first natural number (usually $n=1$).

2. Inductive hypothesis: Assume the statement is true for some arbitrary natural number $k$.

3. Inductive step: Prove that if the statement is true for $k$, then it must also be true for $k+1$.

If these three steps are completed, then the statement is true for all natural numbers.

Natural numbers are typically defined as positive integers including

1. The set of natural numbers is denoted by $N = \{1, 2, 3, ...\}$. Real numbers include all rational and irrational numbers. Rational numbers can be expressed as a fraction $p/q$ where $p$ and $q$ are integers and $q \ne 0$. Irrational numbers cannot be expressed in this form (e.g., $\sqrt{2}$, $\pi$). Complex numbers are of the form $a + bi$ where $a$ and $b$ are real numbers and $i$ is the imaginary unit ($i^2 = -1$).

Since mathematical induction is directly used for proving statements involving natural numbers, the most appropriate answer is "Natural number."

3. Final Answer

d. Natural number