Real numbers are defined as the set of what?

Real numbers are defined as the set of what?

• A. The set of rational numbers.
• B. The set of irrational numbers.
• C. The set of rational and irrational numbers (all numbers).
• D. Only integers.

Answer: (C)

Real numbers cover every point on the number line, including both rational and irrational numbers. Rational numbers are numbers that can be written as a fraction of integers, which includes integers themselves since any integer can be expressed as n/1. Irrational numbers cannot be written as a fraction of integers, and their decimal representations go on forever without repeating. Because the real numbers include both types, they constitute all numbers, not just one type or a smaller subset. The other options describe only part of the real numbers or a smaller group (like integers, which are just a subset of rationals), so they don’t capture everything.

Real numbers cover every point on the number line, including both rational and irrational numbers. Rational numbers are numbers that can be written as a fraction of integers, which includes integers themselves since any integer can be expressed as n/1. Irrational numbers cannot be written as a fraction of integers, and their decimal representations go on forever without repeating. Because the real numbers include both types, they constitute all numbers, not just one type or a smaller subset. The other options describe only part of the real numbers or a smaller group (like integers, which are just a subset of rationals), so they don’t capture everything.