## integerAny positive or negative whole number or zero: ...-3, -2, -1, 0, 1, 2, 3, ... "Integer" is Latin for "whole" or "intact." The set of all integers is denoted by Z, which stands for Zahlen (German for "number").
The integers are an extension of the natural
numbers to include negative numbers
and so make possible the solution of all equations of the form a
+ x = b, where a and b are natural numbers.
Integers can be added and subtracted, multiplied, and compared. Like the
natural numbers, the integers form a countably infinite set. However, the
integers don't form a field since, for instance,
there is no integer x such that 2x = 1; the smallest field
containing the integers is that of the rational
numbers. An important property of the integers is division with
remainder: given two integers a and b with b
not equal to 0, it is always possible to find integers q and r
such that a = bq + r, and such that 0
r < |b|. q is called the quotient
and r is called the remainder resulting from division
of a by b. The numbers q and r are uniquely
determined by a and b. From this follows the fundamental
theorem of arithmetic, which states that integers can be written
as products of prime numbers in an essentially
unique way. ## Related category• TYPES OF NUMBERS | |||||

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