1= .9999999999999999999.

  1. 1= .9999999999999999999.........

    Here it is...

    1/3= .33333333333...........

    2/3= .6666666666.........


    3/3= .9999999999.......


    1= .999999999........


    I think that this "paradox" means that there is a problem with our definition of infinity. At least, the definition needs to be refined. Does this mean that 1 is not equal to one, or is .9999999... another name for one? I think this topic needs to be adressed.
  2. jcsd
  3. mezarashi

    mezarashi 658
    Homework Helper

    Oh no, I remember a long one discussing this. Something about convergence, but I'll sit back and watch :)
  4. Gokul43201

    Gokul43201 11,046
    Staff Emeritus
    Science Advisor
    Gold Member

  5. HallsofIvy

    HallsofIvy 41,061
    Staff Emeritus
    Science Advisor

    Ouch! Another one. Demodocus- there is nothing wrong with "our" definition of infinity (actually, I can't speak for yours). Yes, 0.9999.... is just another name for 1 (that, I must say, is put very nicely). Our definition of "base 10 enumeration system" is such that 0.9999.... means the sum of the infinite series 9/10+ 9/100+ 9/100+ ... which is a geometric series that can be shown to converge to 1.
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