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    is it true that the sum of the absolute values of the two numbers is equal to the absolute value of the sum of the numbers.

    0  Views: 341 Answers: 1 Posted: 9 years ago

    1 Answer

    No it is not true. See below:



    abs(2-2)=0 NOT equal to abs(2)+abs(-2)=4

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    The above is technically correct, though the more thorough answer is as follows;
    no because the absolute value of the sum is LESS THEN OR EQUAL TO the sum of the absolute values. The simple proof the the fact that |A+B|<=|A|+|B| is called the triangular inequality.
    When A and B (or for that matter an infinite number of them) are both positive (or all) or both negative (or all) then they inequality is actually equal, if however any of the numbers have different signs then any other number, the inequality is less then.


     


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