Is it for sure that absolute value is NEVER negative?

From this: https://brilliant.org/discussions/thread/x0-find-x-dne-not-accepted/?newwindow=true

I looked into Quaternion $\Large\mathbb{H}$ and Octonion $\mathbb{O}$, and yep absolute value is still $\ge 0$...

Question

Is it for sure that absolute value is NEVER negative?

From this: https://brilliant.org/discussions/thread/x0-find-x-dne-not-accepted/?newwindow=true

I looked into Quaternion $\Large\mathbb{H}$ and Octonion $\mathbb{O}$, and yep absolute value is still $\ge 0$...

kainui · Answer

Yeah, this isn't that amazing, it's by definition. If for some reason what you did to get the absolute value resulted in something that wasn't positive then they would have to change the algorithm. 

Like for instance, suppose they forgot to put your city on a map, that doesn't mean your city doesn't exist, right? It's the same sort of idea. It's the place that matters, not the map of the place. Similarly, the absolute value is just the positive number, not whatever method you use to get there.

kainui · Answer

I didn't mean to sound sorta mean or anything by this haha. I really like talking about this sort of stuff. =D