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herrkaefer

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"定理"
"herrkaefer" · 2011-12-18 · via herrkaefer

我被老师叫起来回答一道数学题。我胸有成竹,因为直接套用书里的一个定理就可以得到答案。那个定理是这么描述的:一个大立体形状A的内部套着一个小立体形状B,或者说B在A里,它们的形态是任意的,把它们一起向其它随便什么地方投影,观察它们的投影会发现,B的投影仍然在A的投影内部。

书里定理众多,我颇为自己一下就找到对的思路而自喜。然而在我轻松说出答案和依据的定理后,可能是因为定理和问题的关系如此直接的缘故,我瞬间又迷惑了,并再次从头读着这个短短的问题,希望在这站立着的短暂间隙里可以寻求出其它的解法,似乎冥冥的还有要推翻那个定理的召唤。

未待有任何头绪冒出,甚至连老师的评语还未听到,我醒来,并在醒的同时发现自己正延续着梦里的思考,而竟然可以接续梦里的记忆以继续这思考。

我“在”梦里,并和梦一起投影到现实。那么根据定理的描述,我仍“在”梦里。

我不敢动一动,生怕身体的移动会破坏梦里接续过来的记忆,不久之后,我顺利发现了定理的谬误。

(卡夫卡先生笑了笑,转身走了。 )

首先要定义什么是内部和外部。仅由边界和形状一般来讲无法定义内部,特别当空间有限的情况下。因为这是相对的,说B套着A也可以。如果空间是无限的,倒可以定义有限的一面为内部。

不过即使如此,那定理也是不成立的,还要定义投影。投影如果只作用于边界,结果可以是任意的,根本不保证内部还是内部。

也许用集合的方式重写才可以:B为A的子集,即B在A内部;投影为对集合所做的映射f,在像上满足f(B)仍是f(A)的子集,即投影后,B的像在A的像的内部。

这自然可以了。但前提是B和A是同质的,且B全部要属于A,不可遗漏。

我应该不是梦的一部分吧???所以我很可能(至少不是全部)不在梦中了,证明我醒了。哦,如此艰难的一个苏醒。