Number (mathematics)

A number is an abstract mathematical object used to represent quantity, position, or measurement. Different number systems extend what operations and solutions are possible.

Natural number: A number used for counting; conventions differ on whether natural numbers include zero. Natural numbers provide the basic counting numbers from which broader systems are developed.
Addition: An arithmetic operation that combines quantities to produce a sum. Addition combines numbers while preserving the system's rules and closure properties.
Irrational number: A real number that cannot be expressed as a ratio of two integers. Irrationals distinguish the real numbers from the rational numbers.
Measurement: The process of assigning values to quantities by comparison with units or standards. Measurements use numbers to express magnitudes, though physical precision is limited.
Philosophy of mathematics: The philosophical study of mathematics, including its objects, knowledge, and methods. The status of numbers is a central question about mathematical objects.
Integer: A whole number, its negative, or zero. Integers extend counting numbers to include subtraction results such as −3.
Multiplication: An arithmetic operation that scales one quantity by another to produce a product. Multiplication reveals how number systems handle products, inverses, and distributive laws.
Transcendental number: A number that is not a root of any nonzero polynomial with integer coefficients. Transcendental numbers form a narrower class within the real and complex numbers.
Numeral system: A writing system for representing numbers using symbols and rules. Numeral systems encode numbers; the symbols are not the abstract numbers themselves.
Platonism in mathematics: The view that mathematical objects exist independently of human thought and language. Platonism treats numbers as discoveries rather than inventions.

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