The Real Number System

 

    Most of the time in a Mathematics class, Real numbers are always mentioned and we tend to think or rethink what are Real Numbers. In this blog, we will discuss what are real numbers.

The Set of Real Numbers

    The Set of Real Numbers is divided into different sets. It is designed for the use of each number set. All of the numbers/sets of numbers that will be discussed are under the Set of Real Numbers.

Irrational Numbers

    Irrational Numbers are numbers that are neither terminating nor repeating decimals. Some of the examples of Irrational numbers are trigonometric values, logarithmic values, square roots of positive non-perfect square numbers, the value of pi (π), and many more.

Rational Numbers

    Rational numbers are numbers that can be represented as a relation between two numbers such that the relation is in the form \[\frac{a}{b}\] where a and b are any integer but b is not 0.

Integers

    Since Integers are mentioned in the above paragraph, let us know what are integers. Integers are numbers that we use to count or to represent the number of objects discretely. Integers are divided into three sets, naming the following:

Positive Integers

    The Positive Integers are part of the Real Number System. These numbers are the ones that we commonly use, such as 1, 2, 3, and so on. We also call these numbers counting numbers.

Zero

    The number zero represents nothing. It is also part of the Real Number System. It is also neither positive nor negative. It is a neutral number.

Negative Integers

    The Negative Integers are related to the Positive Integers. The numbers that we use for counting but differ in signs. Negative integers (numbers) tend to have a negative sign (-) before the number. We can also say that negative numbers are the opposites of the Positive Integers.

Non-Integers

    The Non-integers are numbers that represent a comparison of quantities or showing a part of a whole. The numbers under the Non-Integers are fractions, terminating decimals, repeating decimals, percent, and ratio. 

What are the Real Numbers?

    From the line of Irrational Numbers up to the Non-integers, these are the numbers that belong to the Real number. Whenever the word "Real Number" is mentioned it can be a counting number, a negative number, a fraction, a decimal, a trigonometric value, a percent, and anything as long as it is a number under the above-mentioned subsets.