So, the curious thing about recursion is that pretty much always can you implement this idea of doing the same thing again and again and again but with smaller bytes each time.
可见,递归算法中新奇的一点是,为了实现一个想法,你可以一遍又一遍地做相同的事情,但每次的规模都会有所减小。
One way to think about this intuitively if the derivative is very large the function is changing quickly, and therefore we want to take small steps.
关于这个方法很直观的一点想法是,如果导数非常大,函数也就变化的非常快,因此我们想一小步一小步的来。
People have long thought that these kinds of things happen only in Japan but that's not true at all; it's happening right now in the U.S.
人们一直认为,这种事情只会在日本发生,但这种想法一点儿也不对;,它现在正发生在美国。
When Thoreau sits on his little stool outside his cabin at Walden Pond and he hears the train go by over the ridge, and he puts his hands over his ears he doesn't want to hear it-- he's representing something.
在瓦尔登湖的木屋外,梭罗坐在他的小凳子上,他听到火车的声音穿越桥梁,他捂住了耳朵,他一点也不想听到这个声音,他代表着某种想法
Or, for that matter, if you've got some quick reactions or thoughts or responses to the arguments that I'm laying out and you want to share them with the class as a whole, then very much I want to invite you to do this.
或者,关于那一点,如果你很快有回应,以及关于那个争论的想法或者反应,那么我会敞开胸怀,如果你想和全班同学分享这个,我会非常想邀请你这样做的。
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