Does Min(d1,d2) Satisfy Triangle Inequality?

[Daveyboy]

d₁ and d₂ are metrics on a space X. Does min(d₁,d₂) satisfy the triangle inequality.

I think it does not but I am having a hard time finding a counter example.

 

[Bacat]

Try looking at the special case of the triangle inequality where equality holds.

 

[Daveyboy]

Oh neat this works: euclidean and discrete metric d_min(0,2)=1
d_min(0,1)=1
d_min(1,2)=1
does not satisfy the triangle inequality.

 

[Dick]

dmin(0,2)<=dmin(0,1)+dmin(1,2). 1<=1+1. I think it does work.