Thread: metrics

Supoose that f -> X where D is any set and x is any metric space with metric d. We can define a function d*xD->R given by:
d*(x,y) = d(f(x),f(y)) for any x,y in D. If f is injective prove that d* is a metric on D!

Any help would be great!

sorry its f: D -> X
and later on d*: DxD -> R.
the weird smiley faces come sometimes..

Originally Posted by really.smarty

Supoose that f -> X where D is any set and x is any metric space with metric d. We can define a function d*xD->R given by:
d*(x,y) = d(f(x),f(y)) for any x,y in D. If f is injective prove that d* is a metric on D!

There is really one of the three properties that is not trival.
If that mean .
Does that mean f(x)=f(y)? And what does that mean?

if f(x) = f(y) that means the first three parts are satisfied for metrics.
1. not negative.
2. d(x,y) = 0 iff x=y
3. d(x,y) = d(y,x)

i am more concerned with how to show the triangle inequality for this question?

Originally Posted by really.smarty

i am more concerned with how to show the triangle inequality for this question?

and i would go about proving that statement how?

than you again.