## Types of Numbers

**Natural numbers**

**(ℕ)**

*The counting numbers {1, 2, 3, …}, are called natural numbers. They include all the counting numbers i.e. from 1 to infinity.*

### Whole numbers (w)

*They are the natural numbers including zero. Not all whole numbers are natural numbers, but all natural numbers are whole numbers.*

### Integers (Z)

*Positive and negative counting numbers, as well as zero.*

### Rational numbers (Q)

*Numbers that can be expressed as a fraction of an integer and a non-zero integer.*

### Real numbers (ℝ)

*All numbers that can be expressed as the limit of a sequence of rational numbers. Every real number corresponds to a point on the number line.*

### Irrational numbers

*A real number that is not rational is called irrational.*

### Complex Numbers (C)

*Includes real numbers and imaginary numbers, such as the square root of negative one.*

### Hypercomplex numbers (C)

*Includes various number-system extensions: quaternions, octonions, tessarines, coquaternions, and biquaternions.*

## Number representations

Decimal

The standard Hindu–Arabic numeral system using base ten.

Binary

The base-two numeral system used by computers.

Roman

The numeral system of ancient Rome, still occasionally used today.

Fractions

A representation of a non-integer as a ratio of two integers. These include improper fractions as well as mixed numbers.

Scientific Notation

A method for writing very small and very large numbers using powers of 10. When used in science, such a number also conveys the precision of measurement using significant figures.

Knuth’s up-arrow notation and Conway chained arrow notation

Notations that allow the concise representation of extremely large integers such as Graham’s number.