Thread: Help with proving metric space

Hi All, i'm getting lost here

Let (X,d) be a metric space. Show that (X,c) is a metric space where c(x,y) = d(x,y)/(d(x,y)+1).

It's just the triangle inequality that I can't seem to nut out!

Any help would be much appreciated!

Thanks!

Originally Posted by metric89

Let (X,d) be a metric space. Show that (X,c) is a metric space where c(x,y) = d(x,y)/(d(x,y)+1).
It's just the triangle inequality that I can't seem to nut out!

Lemma
If then

Then let

Originally Posted by metric89

Hi All, i'm getting lost here

Let (X,d) be a metric space. Show that (X,c) is a metric space where c(x,y) = d(x,y)/(d(x,y)+1).

It's just the triangle inequality that I can't seem to nut out!

Any help would be much appreciated!

Thanks!

O.K

We have:

.

Now if you can prove that:

AND

,Then you are done

Start with : AND