Let (M,d) be a metric space. Define a new metric as $\displaystyle p(x,y)=\frac{d(x,y)}{1+d(x,y)}$ and prove that $\displaystyle p(x,z)\leq p(x,y)+p(y,z)$
**Sorry just had a huge breakthrough, this is now solved**
Let (M,d) be a metric space. Define a new metric as $\displaystyle p(x,y)=\frac{d(x,y)}{1+d(x,y)}$ and prove that $\displaystyle p(x,z)\leq p(x,y)+p(y,z)$
**Sorry just had a huge breakthrough, this is now solved**