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7 August, 12:18

Under which operations is the set of whole numbers {0,1,2,3 ... } closed

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  1. 7 August, 12:42
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    Checking with Addition:

    Let x, y be two whole numbers.

    Then, x + y is definitely a whole number.

    So, the set of whole numbers is closed under addition.

    Checking with Subtraction:

    Let x, y be two whole numbers.

    Then, x - y may or may not be a whole number.

    For example, if we take 3 and 2,

    3 - 2 = 1 is a whole number but if we take 2 and 5, then

    2 - 5 = - 3 is not a whole number.

    So, the set of whole numbers is not closed under subtraction.

    Checking with Multiplication:

    Let x, y be two whole numbers.

    Then, x * y is definitely a whole number.

    So, the set of whole numbers is closed under multiplication.

    Checking with Division:

    Let x, y be two whole numbers.

    Then, x / y may or may not be a whole number.

    For example, if we take 6 and 3,

    6/3 = 2 is a whole number.

    But, if we take 4 and 5,

    4/5 is not a whole number.

    So, the set of whole numbers is not closed under division.
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