老外民科:暴雪与0.99999.。。。。

  • s
    smalldudu
    http://zh.wikipedia.org/w/index.php?title=0.999&variant=zh-cn

    随着互联网的崛起,关于0.999…的讨论已经冲出了教室,并走向了新闻组和信息版,包括那些名义上几乎与数学无关的信息版。在新闻组sci.math中,辩论0.999…是一项“受欢迎的运动”,也是常见问答集之一。[42]常见问答集涵盖了1⁄3、乘以10、还有极限的证明,也间接地提到了柯西序列。

    一个2003年版的报纸专栏The Straight Dope通过1⁄3和极限讨论了0.999…,并谈到了误解:

    我们当中的低级灵长类动物仍然在抗拒,说:0.999…其实不是表示一个数,而是表示一个过程。我们必须把那个过程停止下来,来寻找那个数,这样0.999… = 1的等式便土崩瓦解了。真是一派胡言。(The lower primate in us still resists, saying: .999~ doesn't really represent a number, then, but a process. To find a number we have to halt the process, at which point the .999~ = 1 thing falls apart. Nonsense.)[43]

    The Straight Dope在自己的信息版引用了另外一个不明的信息版中的讨论,那个信息版“大部分是关于视频游戏的”。0.999…的问题在暴雪娱乐的Battle.net论坛的头七年也是一个非常受欢迎的话题,以致于该公司在2004年的愚人节不得不发布了一则“新闻”,声明0.999…就是1:

    我们对永远停止对这件事的讨论感到十分激动。我们亲眼目睹了对0.999…是否等于1的痛心和关心,并对以下的证明最终为我们的顾客解决了问题感到十分自豪。(We are very excited to close the book on this subject once and for all. We've witnessed the heartache and concern over whether .999~ does or does not equal 1, and we're proud that the following proof finally and conclusively addresses the issue for our customers.)[44]

    然后便提供了两个证明,一个是极限的证明,另一个是乘以10的证明。

    Blizzard Entertainment® Announces .999~ (Repeating) = 1


    IRVINE, Calif. - APRIL 1, 2004 - At a press conference earlier today, Blizzard Entertainment® announced that .999~ does in fact equal 1. For seven and a half years, enthusiastic forum-goers have fervently debated the issue on the Battle.net® forums. Does .999~ equal 1? Does .999~ not equal 1? The popular forum topic reached its epic conclusion today, as Blizzard revealed the proof that finally brought an end to the discussion and thus resolved the conundrum that has plagued visitors to the forums for so long. "We are very excited to close the book on this subject once and for all," stated Mike Morhaime, Blizzard Entertainment president and co-founder. "We've witnessed the heartache and concern over whether .999~ does or does not equal 1, and we're proud that the following proof finally and conclusively addresses the issue for our customers." Consider:


    Proof:

    lim(m --> ∞) sum(n = 1)^m (9)/(10^n) = 1
    0.9999... = 1

    Thus x = 0.9999...
    10x = 9.9999...
    10x - x = 9.9999... - 0.9999...
    9x = 9
    x = 1.

    [本帖最后由 smalldudu 于 2009-8-2 23:27 编辑]
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