Integer

An integer is a whole number, its negative, or zero. Integers have no fractional or decimal part.

Natural number: A counting number; conventions differ on whether zero is included. Positive integers extend the counting numbers by adding zero and negative values.
Integer addition: The operation combining two integers to produce their sum. Adding integers always produces another integer, including when signs differ.
Integer programming: Optimization in which some or all decision variables must take integer values. Its restrictions use integers to model indivisible choices such as people or vehicles.
Fraction: A number expressed as one integer divided by another nonzero integer. Fractions such as one-half are rational but not integers.
Zero: The integer that represents no quantity and serves as the additive identity. Zero is the integer separating positive values from negative values.
Integer multiplication: The operation combining integers through repeated addition and sign rules. Products remain integers, with signs determined by the factors.
Diophantine equation: A polynomial equation whose solutions are sought among integers. It asks when integer values satisfy equations exactly.
Irrational number: A real number that cannot be expressed as a ratio of integers. Irrational numbers lie outside the integers and even outside the rationals.
Negative number: A real number less than zero, representing a value below a chosen reference point. Negative integers form the below-zero part of the integer system.
Divisibility: The relation in which one integer is an exact multiple of another. Divisibility organizes integers into factors and multiples.

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