- #1
boneill3
- 127
- 0
Homework Statement
Prove that if [itex] (X,\rho) [/itex]is a metric space then so is [itex](X,\bar\rho)[/itex], where
[itex]
\bar\rho:X \times X \Rightarrow R_{0}^{+}, (x,y) \Rightarrow \frac{\rho(x,y)}{1+\rho(x,y)}.
[/itex]
Homework Equations
I'm trying to prove the axiom that a metric space is positive definate.
The Attempt at a Solution
because given [itex] (X,\rho) [/itex] is a metric space is it enough to say that [itex](X,\bar\rho)[/itex], cannot be [itex]< 0 [/itex] because [itex] (X,\rho) [/itex] cannot be [itex]< 0 [/itex] ? ie the limit of [itex](X,\bar\rho)[/itex] is 0 as [itex] (X,\rho) [/itex] tends to zero ?
Last edited: