# Thread: show violation of metric definition

1. ## show violation of metric definition

Let he function # : PxP->R be defined as
#((x1,y1),(x2,y2))=((x2-x1)^3+(y2-y1)^3)^(1/3)

Show that # violates all four conditions that define a metric

2. Originally Posted by nikie1o2
Let he function # : PxP->R be defined as
#((x1,y1),(x2,y2))=((x2-x1)^3+(y2-y1)^3)^(1/3)

Show that # violates all four conditions that define a metric
You really need to learn to use LaTeX!

Metrics are non-negative. Find points that give a negative value.

3. Originally Posted by nikie1o2
Let he function # : PxP->R be defined as
#((x1,y1),(x2,y2))=((x2-x1)^3+(y2-y1)^3)^(1/3)

Show that # violates all four conditions that define a metric
For the second condition note that $(-1,0)\ne(1,0)$ but $\#((-1,0),(1,0))=0$