# Number System | Binary | Hexadecimal | Roman | Fractions

## 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.