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0.999...=1 project

  1. Mar 18, 2005 #1
    Need urgent help

    :approve: sorrypeople if this annoys u but please don't close this thread. i need urhent help with my 0.999...=1 project and i have a new thing my teacher told me would help, but i don't understand!!!!!!!!!!!!!!!!!!
    0.9=1- 1/10(fraction)
    0.99=1-1/100(fraction)
    0.999=1- 1/1000(fraction)
    .
    .
    .
    .
    .
    1-(approaches zero)=1

    sequence and series.
    ______________________
    Also, any background information and/or history and/or opinions and/or information would be very greatly appreciated!!!!!!!!!!!!!!!!!!!!!!!1 o:)
     
  2. jcsd
  3. Mar 18, 2005 #2

    matt grime

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    Science Advisor
    Homework Helper

    OPinions are not required. The real numbers are by construction somewhere where convergent sequences of rationals have unique limits. the sequence 0.99..9 with n nines converges to 1, that is what the above states - the distance from it to 1 is 10^{-n} which converges to zero.

    so 0.999... the infinite string of nines which, by definition also represents the limit of that sequence mustbe equal to one by fiat.
     
  4. Mar 24, 2005 #3
    Let x = 0.999999...
    10x = 9.999...=9+0.999...=9+x
    10x - x = 9
    9x = 9
    x=1

    0.999... = 1
     
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