Number

Concept of a mathematical object used to count, measure, and label

Number

A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, and so forth. Numbers can be represented in various forms, such as numerals, and can be used in arithmetic operations like addition, subtraction, multiplication, and division.

A representation of different sets of numbers.

History

The concept of number has evolved over time. Early humans used simple tally marks to keep track of quantities. The development of numeral systems allowed for more complex calculations and record-keeping. Ancient civilizations such as the Babylonians, Egyptians, and Romans developed their own numeral systems.

Khmer numerals from the Sambor inscriptions.

Types of Numbers

Numbers can be classified into different types based on their properties and the operations that can be performed on them.

Natural Numbers

Natural numbers are the set of positive integers starting from 1. They are used for counting and ordering.

Integers

Integers include all whole numbers, both positive and negative, as well as zero. They are used in situations where both positive and negative values are needed.

Rational Numbers

Rational numbers are numbers that can be expressed as the quotient of two integers, where the denominator is not zero. They include fractions and whole numbers.

Real Numbers

Real numbers include all the numbers on the number line, encompassing both rational and irrational numbers. They are used to measure continuous quantities.

Complex Numbers

Complex numbers consist of a real part and an imaginary part. They are used in advanced mathematics and engineering to solve equations that have no real solutions.

A diagram illustrating the natural numbers.

Numeral Systems

Numeral systems are ways of representing numbers. The most common system in use today is the decimal system, which is based on the number 10. Other systems include the binary system, used in computing, and the Roman numeral system, used in ancient Rome.

Arithmetic Operations

Numbers are used in various arithmetic operations:

• Addition - Combining two numbers to get a sum.
• Subtraction - Finding the difference between two numbers.
• Multiplication - Repeated addition of a number.
• Division - Splitting a number into equal parts.

Related Pages

• Mathematics
• Numeral system
• Arithmetic
• Algebra