Let (x_n) and (y_n) be sequences in a metric space X. Suppose that x_n converges to a and y_n converges to b. Prove that d(x_n, y_n) converges to d(a, b).
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|d(x_n, y_n) - d(a,b)|
We need to relate this to the hypothesis, so I think perhaps subtracting and adding d(x_n, a) would help...but still I can't figure out how to prove the result...
Any help is appreciated!