Editing CauchySequence
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Think of a sequence of dots on a plane (or line). Let's suppose that they have the following property: * You give me a coin. * I can find a place to put the coin such that ** all but finitely many points are covered. * This works no matter how small the coin is. [[[>50 In effect, we are asking that the points approach a limit. The reason for stating it as we have is because the limit point might not be in the set itself. ]]] Such a sequence is called a Cauchy Sequence. Here are some examples on a line: * 1/2, 3/4, 7/8, 15/16, 31/32, ... * 1, 3/2, 7/5, 17/12, 41/29, 99/70 Here are some sequences that are *not* Cauchy Sequences: * 1, 2, 3, 1, 2, 3, 1, 2, ... * 1, 2, 3, 4, 5, 6, 7, 8, ... * 1, -1, 1, -1, 1, -1, ... Cauchy sequences are a method used to construct the real numbers from the rational numbers.