A real number is a basic mathematical concept that represents a value that can be expressed on a number line. It comprises rational numbers, which can be expressed as fractions, and irrational numbers, which cannot be expressed as fractions and have infinite non-repeating decimal representations.
Real numbers are a fundamental part of the real number system, which also includes integers and natural numbers. Unlike integers, which include both positive and negative whole numbers, real numbers encompass all possible values on the number line, including both positive and negative fractions, as well as zero.
Real numbers possess certain properties, such as closure under addition, subtraction, multiplication, and division. This means that when two real numbers are combined using these operations, the result will always be another real number. Additionally, real numbers exhibit the properties of commutativity, associativity, and distributivity in these operations.
Moreover, real numbers can be compared using the concepts of greater than (>), less than (<), greater than or equal to (≥), and less than or equal to (≤). These relationships form the basis for mathematical calculations, equations, and inequalities involving real numbers.
In summary, real numbers are a comprehensive set of values that can be represented on a number line, encompassing rational and irrational numbers. They possess various properties and can be combined and compared using mathematical operations and relationships. Real numbers are foundational to many mathematical concepts and are widely used in various fields, from physics and engineering to finance and statistics.
