Most recent change of CauchySequence

Edit made on August 30, 2008 by GuestEditor at 13:34:41

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WW
HEADERS_END
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.