Real numbers are a fundamental concept in mathematics and form a broad and essential set of numbers used to represent quantities on the number line.
The set of real numbers includes all rational and irrational numbers and is denoted by the symbol “R.” Real numbers encompass a wide range of values, including integers, fractions, decimals, and numbers that cannot be expressed as fractions, such as √2 and π.
Here are some key types of real numbers: Integers: Integers are whole numbers, both positive and negative, and zero. They are expressed without any fractional or decimal parts.
Examples include -3, -2, -1, 0, 1, 2, 3, and so on.
Rational Numbers: Rational numbers are numbers that can be expressed as a fraction of two integers (a/b), where “a” is the numerator and “b” is the non-zero denominator.
All integers are rational numbers, as they can be written with a denominator of 1. Additionally, fractions and terminating or repeating decimals are also rational numbers.
Examples include 1/2, -3/4, 0.25, 0.333…, etc.
Irrational Numbers: Irrational numbers are numbers that cannot be expressed as fractions and have non-terminating, non-repeating decimal expansions.
Examples of irrational numbers include √2, √3, π (pi), e, etc. Irrational numbers are infinite and non-repeating and cannot be written exactly as fractions.
Real Numbers: The set of real numbers includes both rational and irrational numbers. This means that any number that can be represented on the number line is a real number.
The set of real numbers is continuous and extends infinitely in both positive and negative directions. Whole numbers : are a set of numbers that includes all the natural numbers (positive integers) along with zero.
Whole numbers are denoted by the letter “W” or “ℤ⁺” and are represented as follows: W = {0, 1, 2, 3, 4, 5, 6, …} The set of whole numbers consists of the counting numbers (1, 2, 3, 4, 5, …), and zero is included as well. Whole numbers are non-negative and do not include any fractions, decimals, or negative numbers.