Real numbers
Real numbers are a mathematical concept that includes all rational and irrational numbers
Real numbers are a mathematical concept that includes all rational and irrational numbers. They are called “real” because they can be represented on a number line, and they exist in physical reality.
Rational numbers can be expressed as fractions, where the numerator and denominator are both integers, and the denominator is not zero. For example, the numbers 1/2, -3/4, and 6 can all be represented as rational numbers. Rational numbers can be positive, negative, or zero.
On the other hand, irrational numbers cannot be expressed as fractions and have non-terminating or non-repeating decimal representations. Some examples of irrational numbers include π (pi), √2 (the square root of 2), and e (Euler’s number). Irrational numbers are also real numbers because they can be located on the number line, although their decimal representations are infinite and non-repeating.
Real numbers can be compared with each other using different mathematical operations such as addition, subtraction, multiplication, and division. They can also be represented as points on a number line, where positive numbers are greater than zero and negative numbers are less than zero. This allows for the visual representation of real numbers and their relationships to each other.
Overall, real numbers encompass all possible values that can be represented in our number system, including both rational and irrational numbers. They form the foundation of mathematical operations and have various applications in different branches of mathematics, physics, engineering, and other scientific fields.
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