31 October 2013

Controversial Question of the Week

This question provoked a certain amount of contoversy at the Green Linnet this week:
True or false: 0.999… (recurring) = 1?
Info ou intox: 0,999… (à l'infini) = 1?
What do you think? Qu'en pensez-vous?
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2 comments:

  1. Nicolas D.01 November, 2013 01:40

    I can't see how 0,999 ad nauseam could equal 1. It would be infinitely close, but not equal. Equal means there's no difference whatsoever, which is false in that case.

    At least, that's my take on it, even though admittedly my maths are getting rusty...

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  2. Páraic Maguire01 November, 2013 03:00

    That's what most people say, including myself, when they hear the question. But it's not correct.

    In fact 0.999... and 1 are simply two ways to express the same number. Here's one proof (there are many):

    n = 0.999...
    10n = 9.999...
    10n - n = 9.999... - 0.999...
    9n = 9
    n = 1

    QED (or in vf: CQFD)

    ReplyDelete