# Convergence and distance

1. Oct 7, 2011

### BelaTalbot

1. The problem statement, all variables and given/known data
show that x_n converges to x if and only d(x_n, x) converges to 0.

2. Relevant equations
|x_n - x| < ε for all ε>0

3. The attempt at a solution
well d(x_n,x) converges to 0 if d(x_n,x)<ε
i just don't know how to relate that back to |x_n - x|

2. Oct 7, 2011

### kru_

What is your definition of "converges to"?