Proof and other Dilemmas: When is One Thing Equal to Some Other Thing?
Proof and other Dilemmas: When is One Thing Equal to Some Other Thing?
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证明和其他困境：什么时候一件事等于另一件事？
DOI：
10.5948/upo9781614445050.015
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
B. Mazur
中科院分区：
文献类型：
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作者：
B. Mazur
一个人做数学不可能超过十分钟而不以某种方式与平等的狡猾概念作斗争。滑，因为对象呈现给我们的方式几乎从来没有，也许永远不会，立即告诉我们-没有进一步的评论-当他们中的两个被认为是平等的。例如，如果我们试图将真实的数定义为小数，然后必须提到20 = 19.999这样的别名，我们甚至会看到这一点。. .这一事实对于那些将商品定价为19.99美元的商家来说并不陌生。
One can’t do mathematics for more than ten minutes without grappling, in some way or other, with the slippery notion of equality. Slippery, because the way in which objects are presented to us hardly ever, perhaps never, immediately tells us–without further commentary–when two of them are to be considered equal. We even see this, for example, if we try to define real numbers as decimals, and then have to mention aliases like 20 = 19.999 . . . , a fact not unknown to the merchants who price their items $19.99.