Knowing how to order $\{a,b,c,0\}$ implies knowing how to order $\{a,b,c,0,-a,-b,-c\}$?

Question

Suppose I have $4$ real numbers $\{a,b,c,0\}$ and I know

• that they are all different

• how to order them from smallest to largest, e.g., I know that $b<a<0<c$

Does this imply that I know how to order from smallest to largest $\{a,b,c,0,-a,-b,-c\}$?

Answer 1

No, because you don't know how to compare $c$ to $-a$ and $-b$.

It's only possible if $0$ is either the smallest or the largest of the four.

Answer 2

You can iff all are greater or smaller than zero.

Otherwise consider $$-2<-1<0<c$$ If $c=1.5$ then $-c$ will be between $a$ and $b$; if $c=3$ then $-c$ will be on the far left...