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The basic idea that we need to talk about convergence is to find a way of saying when two things are close. A metric space is something in which this makes sense. Definitions . ... (The triangle inequality) For all x, y, z X, d(x, y) + d(y, z) d(x, z). A metric space is a set X together with such a metric. ... The fact that these two proofs are ... ................
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