Which of the following is NOT a characteristic of real numbers?

• A. They can be positive or negative
• B. They can be irrational
• C. They cannot be represented on a number line
• D. They include whole numbers

Answer: (C)

Real numbers encompass a wide range of values that can be represented on the number line, which includes both rational and irrational numbers. The real number system consists of positive numbers, negative numbers, whole numbers, integers, and fractions. They can be categorized into several subsets and can indeed be plotted along a one-dimensional continuum known as the number line.

The statement that real numbers cannot be represented on a number line is inaccurate. Every point on the number line corresponds to a real number, whether it is rational (such as 1/2 or -3) or irrational (like π or √2). This characteristic is fundamental to real numbers. Thus, it's clear that the correct answer is that they cannot be represented on a number line, as that contradicts the defining traits of real numbers.