in reply to .999999... == 1? (Somewhat OT)

Pshaw! And I suppose next you'll tell me that 0.0000... repeating is equal to 0 ;-) 
   MeowChow                                   
               s aamecha.s a..a\u$&owag.print
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Re:(jepri) .999999... == 1? (Somewhat OT)
by jepri (Parson) on Jul 25, 2001 at 04:30 UTC
    Proving that 0.00000 ... (infinite zeros) ... 00001 = 0 is more of a challenge.

    ____________________
    Jeremy
    I didn't believe in evil until I dated it.

[reply]

      Yes, especially since it's not. :)

      Consider:

      0.00000 ... 00001 > 0.00000 ... 000009

      Now if A > B and A = 0 than 0 > B so

      0 > 0.00000 ... 000009

      and we've found a positive number which is strictly less than zero.<blink><blink><twitch>

      The problem comes from specifying a last digit since one can always specify one more after that which isn't zero and get a 'really' different number.

[reply]
        You just have to choose the right number system.

        It is impossible to make sense out of jepri's comment in the usual real number system. It is quite possible to make sense out of it in both non-standard analysis and in Conway's surreal numbers. In both of those systems jepri's comment not only makes perfect sense, but the two numbers differ by an infinitesmal.

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