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Never ending story

机译:说不完的故事

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摘要

In anyone's book, infinity is pretty paradoxical. If you add one apple to an infinite pile of apples, you still have an infinite pile of apples―and it is exactly the same size as the original pile. If your bank has an infinite number of pounds in the vault, then you can pay in one pound, take out a million pounds, and the bank won't have lost any money. And that's just the beginning. There's even a way you can take out an infinite number of pounds, and the bank still won't have lost any money. If you are confused already, don't worry: that's just an indication that your brain is working as it should. When we start thinking about infinity we are on dangerous ground. But it's not just philosophically threatening -it's also a problem to mathematics. Mathematicians would gladly banish the infinite from their minds, were it not for one thing: infinity is far too useful to do without. Even if it doesn't really exist, mathematics reeks of infinity; in many ways, it is what makes mathematics tick.
机译:在任何人的书中,无穷大都是自相矛盾的。如果将一个苹果添加到无限大的苹果堆中,则仍然会有无限大的苹果堆-它的大小与原始堆完全相同。如果您的银行的保管库中有无数磅,那么您可以付一磅,取出一百万英镑,银行就不会损失任何钱。这仅仅是开始。甚至还有一种方法可以取出无数磅,而银行仍然不会损失任何钱。如果您已经感到困惑,请不要担心:这只是表明您的大脑正在正常工作。当我们开始考虑无限时,我们就处于危险境地。但这不仅是哲学上的威胁-这也是数学的问题。如果不是因为一件事,数学家会很乐意将无限性从他们的脑海中消除:无限远就非常有用。即使它不是真的存在,数学也有无限的可能性。在许多方面,这就是使数学产生变化的原因。

著录项

  • 来源
    《New scientist》 |2003年第2414期|p.28-33|共6页
  • 作者

    Ian Stewart;

  • 作者单位

    University of Warwick;

  • 收录信息 美国《科学引文索引》(SCI);美国《化学文摘》(CA);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 自然科学总论;
  • 关键词

  • 入库时间 2022-08-18 02:57:10

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