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I might be wrong, but I thought absolute values weren't positive or negative?
I don't understand this argument. I've heard high school teachers decree it as a mathematical truth before.
Do we all agree absolute value is a function from reals to reals? If so, the absolute value of any real number is nonnegative. It can be zero or any positive numbers.
Case closed, right?
It's like taking a signed int and turning it into an unsigned int though. It doesn't become positive it just loses its sign.
They're not negative, thus they're positive.
It was my understanding that it's like velocity vs speed. Positive/Negative numbers have a directional component, that is that they are above or below zero. Absolute values, however, lack a direction. They're a value, but they don't tell you if the value is positive or negative.
Absolute value shows only distance from the 0 value on the number line without the direction. All distances are positive when viewed without direction.
What about non binary numbers?
Those are just complex.
If your task is to turn any number that could be negative into positive then you would use abs right?
I'd use a pencil. I'm too out-of-shape to have abs, particularly ones I could do math with.
If you're out of shape then you can use your abs for non-Euclidean geometries
Technically true, but they are always graphed in positive quadrants.