Think of a sequence of dots on a plane (or line). Let's suppose that they have the following property:

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:

Here are some sequences that are not Cauchy Sequences:

Cauchy sequences are a method used to construct the real numbers from the rational numbers.
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