in reply to Re:(jepri) .999999... == 1? (Somewhat OT)
in thread .999999... == 1? (Somewhat OT)

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.

  • Comment on Re: Re:(jepri) .999999... == 1? (Somewhat OT)

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Re (tilly) 3 .999999... == 1? (Somewhat OT)
by tilly (Archbishop) on Jul 25, 2001 at 22:53 UTC
    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.

[reply]

      :) OK, OK. It makes sense in infinitesimal analysis (which came out of topos theory) too. But if you start switching number systems all bets are off.

      Thanks for the pointer to surreal numbers.

      FWIW, my booklist contains a good descriptive book on infinitesimal analysis.

[reply]

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