Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Can somebody explain this to me?

  1. Jan 14, 2007 #1
  2. jcsd
  3. Jan 14, 2007 #2


    User Avatar
    Staff Emeritus
    Science Advisor

    There are lots of threads on here discussing "0.99...=1." Try searching!
  4. Jan 14, 2007 #3


    User Avatar
    Science Advisor
    Homework Helper

    the point is there is a difference bewteen a real number and the numerals used to represent it.

    just as 1/2 = 2/4, there are more decimals than there are reals, and1.000, and .99999 represent the same real.

    one way to see this is to define the real number represented by an infinite decimal as the smallest number not smaller than any of the finite decimal approximations. then one eventually sees that the smallest number not smaller than.9, .99, .999, ..... is 1.00000.

    if one does not eventually see this, one continues to post it here ad infinitum.
  5. Jan 14, 2007 #4


    User Avatar
    Science Advisor

    The definition of the decimal representation 0.a1a2a3... is the limit of the sequence 0.a1, 0.a1a2, 0.a1a2a3, ...
    In particular, 0.999... means the limit of the sequence 0.9, 0.99, 0.999, 0.9999, .... Since that is a geometric sequence, it is easy to show that its limit is [itex]\frac{0.1}{1- .9}= 1.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook