- #1
RenOdur
- 5
- 0
Homework Statement
the actual problem is to show that d(x,y)=d1(x,y)/[1+d1(x,y)] expresses a distance in R^n if d1(x,y) is a distance in R^n.Based on theory I have to show that
i) d(x,y)>=0 ,
ii)d(x,y)=d(y,x) and
iii)d(x,y)<= d(x,z)+d(z,y)
i've proven the first two so basically how can i get from d1(x,y)<= d1(x,z)+d1(z,y)(the above three statements apply for d1(x,y) since d1(x,y) is already a distance in R^n ) to d1(x,y)/[1+d1(x,y)]<=d1(x,z)/[1+d1(x,z)]+d1(z,y)/[1+d1(z,y)] ?