List - Types of Numbers

Main types
Natural numbers	The counting numbers {1, 2, 3, ...}, sometimes including zero.
Integers	Positive and negative counting numbers, as well as zero.
Rational numbers	Numbers that can be expressed as a fraction of two integers.
Real numbers	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 or transcendental.
Complex numbers	Includes real numbers and imaginary numbers, such as the square root of negative one.
Number representations
Decimal	The standard Hindu–Arabic numeral system using base ten.
Binary	The base-two numeral system used by computers. See positional notation for information on other bases.
Roman numerals	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 ten. 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.
Signed numbers
Positive numbers	Real numbers that are greater than zero.
Negative numbers	Real numbers that are less than zero.
Because zero itself has no sign, neither the positive numbers nor the negative numbers include zero. When zero is a possibility, the following terms are often used:
Non-negative numbers	Real numbers that are greater than or equal to zero. Thus a non-negative number is either zero or positive.
Non-positive numbers	Real numbers that are less than or equal to zero. Thus a non-positive number is either zero or negative.
Types of integers
Even and odd numbers	A number is even if it is a multiple of two, and is odd otherwise.
Prime number	A number with exactly two positive divisors.
Composite number	A number that can be factored into a product of smaller integers. Every integer greater than one is either prime or composite.
Square number	A numbers that can be written as the square of an integer.
There are many other famous integer sequences, such as the sequence of Fibonacci numbers, the sequence of factorials, the sequence of perfect numbers, and so forth.
Algebraic numbers
Algebraic number	Any number that is the root of a non-zero polynomial with rational coefficients.
Transcendental number	Any real or complex number that is not algebraic. Examples include e and π.
Quadratic surd	An algebraic number that is the root of a quadratic equation. Such a number can be expressed as the sum of a rational number and the square root of a rational.
Constructible number	A number representing a length that can be constructed using a compass and straightedge. These are a subset of the algebraic numbers, and include the quadratic surds.
Algebraic integer	An algebraic number that is the root of a monic polynomial with integer coefficients.