# Why d is not a metric

## Homework Statement

If d= sup{|f(x)-g(x)|} where f, g are contuous function from R to R, why is d not a metric

## The Attempt at a Solution

quasar987
Homework Helper
Gold Member
Take f(x)=x, g(x)=0. then d(f,g)=infinity. So d is not a map into R.

why infinity is not a map into R?

quasar987