What is a Real Number?

Real numbers are traditionally defined as the set of all rational and irrational numbers, which are commonly represented using the real number line. This article will discuss what real numbers are, and how they are used in mathematics and engineering.

The Definition of a Real Number

Real numbers can be divided into two distinct categories: rational numbers, and irrational numbers. Rational numbers are defined as numbers that can be expressed in the form of fractions, and include all integers, negative numbers, zero and the fractional equivalents of all these numbers. Irrational numbers are numbers that cannot be expressed as a fraction and include numbers such as pi and the square root of two. When combined, these two categories of numbers are referred to as real numbers.

Applications of Real Numbers

Real numbers have a wide range of applications in both mathematics and engineering. In mathematics, real numbers are often used to represent the magnitude of a quantity; for example, the length of a line or the area of a circle can be expressed in terms of a real number. In engineering, real numbers are often used to represent physical values such as voltage, temperature or sound pressure.

Summary

Real numbers are a category of numbers that combines both rational numbers and irrational numbers. This category of numbers is widely used in both mathematics and engineering, and is often used to express the magnitude of a physical quantity. In mathematics, real numbers are used to represent the length of a line or the area of a circle while in engineering they are often used to represent physical values such as voltage, temperature or sound pressure.