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Are all irrational numbers rational?

  1. Aug 30, 2006 #1
    Since pie is the ratio of the circumference of the circle to its diameter, isn't it possible that there exist a fraction for all nonrepeating going on forever decimal values?
     
  2. jcsd
  3. Aug 30, 2006 #2

    CRGreathouse

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    Short answer: No.

    Tongue-in-cheek answer: Yes, but the fraction would have at least one noninteger.

    Longer answer: You're wrongly assuming that a circle with rational circumference and diameter exists.
     
  4. Aug 30, 2006 #3

    mathwonk

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    ????? are all humans non human? are all m ortals immortal? are al....
     
  5. Aug 31, 2006 #4
    lol :rofl:
     
  6. Aug 31, 2006 #5

    HallsofIvy

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    The definition of "rational number" is that it can be written as a fraction with numerator and denominator integers. The "ratio of the circumference of the circle to its diameter" is not a ratio of integers.
     
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