Is there a number whose absolute value is negative?I've recently started to think about this, and I'm sure a couple of you out there have, too.In Algebra, we learned that | x | ≥ 0 , no matter what number you plug in for x. For example: | − 5 | = 5 ≥ 0We also learned that x 2 ≥ 0. For example: ( − 5 ) 2 = 25 ≥ 0The exception for the x 2 rule is imaginary numbers (which we learn later on in Algebra II). Imaginary numbers are unique, in that their square is a negative number. For example: 4 i 2 = − 4These imaginary numbers can be used when finding the "missing" roots of a polynomial equation.My question to you is this: Is there any number whose absolute value is negative, and how could it be used?

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Is there a number whose absolute value is negative?I&#039;ve recently started to think about this, and I&#039;m sure a couple of you out there have, too.In Algebra, we learned that   |  x  |  ≥  0 , no matter what number you plug in for x. For example:  |  −  5  |  =  5  ≥  0We also learned that       x    2    ≥  0. For example:  (  −  5      )    2    =  25  ≥  0The exception for the       x    2   rule is imaginary numbers (which we learn later on in Algebra II). Imaginary numbers are unique, in that their square is a negative number. For example:  4      i    2    =  −  4These imaginary numbers can be used when finding the &quot;missing&quot; roots of a polynomial equation.My question to you is this: Is there any number whose absolute value is negative, and how could it be used?

Jordin Church · Accepted Answer

If such a number were allowed to exist, it could not be a part of         R    n  , with   n  ∈  N, because the absolute value of any such number is             x      1      2        +          x      2      2        +    …    +          x      n      2        ≥  0, since       x    i    ∈  R. But could it be part of         R    a  , with   a  ∈        Q    +    ⋆    ∖  N? Unfortunately, such factional-order sets have yet to be studied. Or perhaps part of something else altogether ? We don&#039;t know.In my opinion, this is the real question... because, if someone were to find a “practical” use for such a quantity (inside mathematics itself, at the very least), then people would allow it to exist, and study it, and research it, just like they did with the imaginary unit i.

Is there a number whose absolute value is negative? I've recently started to think about this, and

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