Thread: 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

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.

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 but