Does Convergence of d(x_n, x) to 0 Imply x_n Approaches x?

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Homework Statement


show that x_n converges to x if and only d(x_n, x) converges to 0.


Homework Equations


|x_n - x| < ε for all ε>0




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|
 
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What is your definition of "converges to"?
 

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