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And this is really interesting to think about because you can imagine in our body we have concentrations of all types of ions, and specifically, some seem very, very similar to each other.
这是非常令人感兴趣的,因为大家可以想象一下，在我们的体内我们有,一定浓度的任何类型的离子，而且特别地，其中有一些非常非常地相似。
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The message I'm trying to get to here, because I'm running you right up against time, is I have to be careful about what's a primitive step.
我想说的事情是，因为我正在跟大家讲算法时间复杂度，我们需要注意一个基本步骤的定义,如果我可以假设。
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We're going to do this in four, just for-- just because I think it works out better so everybody tap your foot with a four beat.
我们只做四拍,因为我觉得这样的效果更好,大家都用脚打四个拍子
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Now this is a little counterintuitive, because very often people underestimate the amount of calories in things, but what's important here is the-- the error, the size of the error.
这与我们的直觉有些相反,因为经常性地,大家低估了卡路里含量,重要的是,误差和误差的大小
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Now one reason it's a fun class, is the nice thing about teaching Game Theory quieten down folks- one thing about teaching Game Theory is, you get to play games, and that's exactly what we've just been doing now.
为什么这门课很有趣,因为学习博弈论,大家安静一下,在课堂上我们通过一些游戏来学习博弈,我们不刚做完一个游戏吗
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They wouldn't have said that because it doesn't sound we want to think that we invented this here but it actually was a new invention in a way because the United States has a different philosophy which the United States has been committed since its beginning to federalism.
他们不会说,因为它听起来不像,这里我们希望大家把它想成我们自己的发明,但是事实上，它确实是一个新的发明,因为美国有一个不同的哲学,这个哲学是，美国力图从一开始就,使自己成为联邦制度国家。
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The hacker editions -- we don't offer specific walkthroughs since we assume that that crowd generally is ready to dive into the PDF alone.
黑客版--我们不会提供走查的细节,因为我们假设大家都准备好了,独立地投入到PDF中。
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So let's listen to a track here, a sax solo and I am going to try to keep-- make some sense out of this-- because it gets more and more complex-- by following the electric bass underneath so let's listen to an old tape.
那么我们听一下这段音轨,一段萨克斯独奏,我会尽量从中,理出一些头绪,因为我们的音乐片段会越来越复杂,大家可以跟着底下电贝斯的节奏,好的,我们来一下老磁带
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