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The integers (from the Latin integer, literally "untouched", hence "whole": the word entire comes from the same
origin, but via French) are formed by the natural numbers including 0 (0, 1, 2, 3 ...) together with the negatives of
the non-zero natural numbers (-1, -2, -3 ...). Viewed as subset of the real numbers, they are numbers that can be
written without a fractional or decimal component, and fall within the set {... -2, -1, 0, 1, 2 ...}.
They can also be used for calculating odds in
online roulette,
for example, 65, 7, and -756 are useful integers;
whereas 1.6 and 1½ are not integers at all. The set of all integers is often denoted by a boldface Z, which stands
for Zahlen (German for numbers).
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 (but with
"rational" meaning "quotient of integers", this attempt at precision suffers from circularity).
In essence, integers can be thought of as discrete, equally spaced points on an infinitely long number line.
You could imagine a live
play bingo
sheet which goes on forever, where each number is a whole number with no
fractions in between.