Table of Contents
Introduction to Real Numbers
In mathematics, a real number is a number that represents a quantity along a line. The real numbers include the natural numbers, integers, rational numbers, and irrational numbers. Real numbers are often represented by a point on a number line. The number line can be thought of as a continuum of points, with each point representing a real number.
Real Numbers
A real number is a number that represents a point on a number line. Real numbers include rational and irrational numbers. Rational numbers are numbers that can be expressed as a ratio of two integers, while irrational numbers are numbers that cannot be expressed as a rational number.
Euclid’s Division Lemma
The Euclid’s Division Lemma is a mathematical theorem that helps in the division of one number by another. The theorem states that if a number is divided by another number, the remainder will be the same as the division of the second number by the first number.
Fundamental Theorem of Arithmetic
The Fundamental Theorem of Arithmetic states that every number can be written as a product of prime numbers.
Irrational Numbers
Irrational numbers are real numbers that cannot be expressed as a rational number. The decimal expansion of an irrational number never ends and never repeats. The most famous irrational number is pi, which is the ratio of a circle’s circumference to its diameter.
Rational Numbers
- Rational numbers are numbers that can be expressed as the quotient of two integers, a numerator and a denominator. In other words, rational numbers are numbers that can be written in the form p/q, where p and q are both integers and q is not equal to 0.
- The set of all rational numbers is denoted by Q.
- Some examples of rational numbers include 1/2, 3/4, and -7/8.
