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Thread: Simple question about limits points

  1. #1
    Ant
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    Simple question about limits points

    This may seem a little trivial but I'd still like to get clarification if possible:

    Given the sequence An = 2

    Does there exist infinitely many limits points (all of which are equal to 2) or do you say that there exist only one limit point (2)?
    Last edited by mr fantastic; Jan 10th 2011 at 01:06 PM. Reason: Restored deleted question.
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  2. #2
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    There is just one limit to a sequence.

    There can be values in the sequence equal to the limit, but the limit is just a number.

    The limit of a sequence (if it exists) is by definition a number, L, such that you can always find a tail of the sequence in which all values are as close to L as you want it.

    As a matter of fact, you can use the definition of a sequence limit to prove that it is unique.
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