19.1.1.11 Properties of Metric Spaces

Condition: let \ (\ rho (m, n) = \ left \ {\ begin {array} {c} 1+ (m+n)^{-1}, \ quad m \ neq n \\ 0, \ quad m = n \ end}, m, n \ in \ Mathbb {n} \ right. Is pair \ ((\ mathbb {n}, \ rho) \) - metric space?