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

Dayanara Terry 2022-07-02 Answered
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 0
We also learned that x 2 0. For example:
( 5 ) 2 = 25 0
The 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 = 4
These 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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Answers (1)

Jordin Church
Answered 2022-07-03 Author has 11 answers
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'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.
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