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Math Help - Completeness versus Closedness.

  1. #1
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    Feb 2011
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    Completeness versus Closedness.

    i have in my lecture notes that complete is not equal to close,,, what does it mean ?
    and also i have this
    "Because with completeness, convergent infinite sums are defined it is possible to introduce smaller basis than the Hamel basis "
    as i know , when a general sentence of sequence is convergent to zero then it is possible that the series composed of that be convergent but according the above sentences completeness make a series convergent ,, why?
    and the other question why when the series converges it can introduce for us smaller basis than Hamel basis ?
    Last edited by Ackbeet; February 28th 2011 at 06:25 PM. Reason: Split off from Dual Space thread.
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