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大老李聊数学(全集)

19. 数学家比较了两个“无限”--有关连续统假设

17 Sep 2017

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      关于无限集,可能好多听众也了解过一些,比如你可能听过这个比喻,就是如果一个旅馆有无穷多个房间,而且住满了,那么又来了一个旅客,怎么让他入住呢。如果是有限个房间的旅馆,那当然是没办法了,但是有无穷多个房间的旅馆的话,没有问题,老板胸有成竹,他一声令下,请所有住客注意,如果你现在是第n号房间,请你搬到第n+1号房间。然后新来的旅客就顺利入住了第1号房间。然后忽然又来了无穷多个旅客了,怎么办呢。老板还是不慌不忙,发了一道新指令,请所有第n号房间的住客搬到第2n号房间,然后瞬间就发现所有奇数号房间都腾出来了,新来的无穷多个旅客就顺利入住了。       无限集世界很奇妙,连续统假设更烧脑。p与t的定义: 

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