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An integer is a number that can be written without a fractional or decimal component. For example, 21, 4, and −2048 are integers; 9.75, 5½, and √2 are not integers. The set of integers is a subset of the real numbers, and consists of the natural numbers (0, 1, 2, 3, ...) and the negatives of the non-zero natural numbers (−1, −2, −3, ...).
The name derives from the Latin integer (meaning literally "untouched," hence "whole": the word entire comes from the same origin, but via French). The set of all integers is often denoted by a boldface Z (or blackboard bold , Unicode U+2124 ?), which stands for Zahlen (German for numbers, pronounced [?tsa?l?n]).
The integers (with addition as operation) form the smallest group containing the additive monoid of the natural numbers. Like the natural numbers, the integers form a countably infinite set. In algebraic number theory, these commonly understood integers, embedded in the field of rational numbers, are referred to as rational integers to distinguish them from the more broadly defined algebraic integers.

More here :http://en.wikipedia.org/wiki/Integer

a integer is a number that can be written  with out fractional or decimal