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Convergence and distance

  1. Oct 7, 2011 #1
    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. jcsd
  3. Oct 7, 2011 #2
    What is your definition of "converges to"?
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