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    Wikipedia
    https://en.wikipedia.org › wiki › Integer

    Integer - Wikipedia

    History

    The word integer comes from the Latin integer meaning "whole" or (literally) "untouched", from in ("not") plus … See more

    Algebraic properties

    Like the natural numbers, is closed under the operations of addition and multiplication, that is, the sum and product of any two integers is an integer. However, with the inclusion of the negative natural numbers (and importantly, … See more

    Order-theoretic properties

    is a totally ordered set without upper or lower bound. The ordering of is given by: :... −3 < −2 < −1 < 0 < 1 < 2 < 3 < .... An integer is positive if it is greater than zero, and negative if it is less than zero. Zero is defined as … See more

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    Construction

    In elementary school teaching, integers are often intuitively defined as the union of the (positive) natural numbers, zero, and the negations of the natural numbers. This can be formalized as follows. First construct the set of natur… See more

    Computer science

    An integer is often a primitive data type in computer languages. However, integer data types can only represent a subset of all integers, since practical computers are of finite capacity. Also, in the common two's complement representation, … See more

    Cardinality

    The set of integers is countably infinite, meaning it is possible to pair each integer with a unique natural number. An example of such a pairing is
    (0, 1), (1, 2), (−1, 3), (2, 4), (−2, 5), (3, 6), . . . ,(1 − k, 2k … See more

    Footnotes

    1. ^ More precisely, each system is embedded in the next, isomorphically mapped to a subset. The commonly-assumed set-theoretic containment may be obtained by constructing the reals, discarding … See more

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