(Or "whole number") One of the numbers in the set
..., -3, -2, -1, 0, 1, 2, 3, ...
There are an infinite number of integers, though each one is finite.
An inductive definition of an integer is a number that is either zero or an integer plus or minus one. An integer has no fractional part. If written as a real number, e.g. 42.0, the part after the decimal point will be zero.
A natural number is a non-negative integer.
Computers usually store integers in binary. Natural numbers can be stored as unsigned integers and integers that may be negative require a sign bit and typically use twos complement representation. Other representations have been used, such as binary-coded decimal.