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And so, I need to cheat a little bit on the drawing and make sure that this minimum occurs right here.
所以，我需要在画时作点弊,以确保最小值出现在这儿。
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I thought I still have to work for another 30, 40 years. I need to do something else.
我原本想，我还必须工作三四十年。但我需要做点别的事情。
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So, you need some reference points to be able to tell you, OK, this temperature is 550 degrees Smith, whatever.
你需要定要一些参考点,它们告诉你，“这个温度是550史密斯氏度“之类。
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This says, I need a second argument to it, and that second argument better be a point so I can do the comparison.
这里我需要第二个参数，第二个参数最好是一个点,这样我就能做比较了。
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I don't know if you know how a spark plug works, but for the electrical current to fly into operation in a spark plug, the two points of contact have to be gapped.
我不知道你们是否知道,火花塞是怎样工作的，在电流通入火花塞中使它运转之前，两个接触点之间需要有空隙。
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I don't always do that but I'd like to, ; and I can if you come at 11:30. Bring your books; I'm going to be talking about the texts and I hope you'll have them open.
当然我并不是经常这样，但我还是会尽力，你们需要在11点30分到，带上自己的书;,我会做一些关于课文的讲解,我希望由你们来开始讲。
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The second point to clear up is that there's really three different issues that might interest us.
需要解决的第二点是,有三种不同的观点,也许能够引起我们的兴趣
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If he's gone above the monopoly price we need to be a little bit more careful.
如果它高于垄断价格了,我们需要小心点
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One last word of encouragement, I'll say it again, there's a lot of words in this chapter, there's a lot of concepts, focus on the things that I talked about in class not the details, the basic concepts.
最后再说点鼓励你们的话吧,这一章涉及到很多名词,有很多概念,需要关注的不是我讲的细节,而是基本概念
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So if you haven't clicked in yet, or if you want to change your answer, keep in mind that you might need to jot down, - for example, a Lewis structure before you can answer this question.
如果你还没有点答案，或者你想改变你的答案，记住你也许需要在回答问题前写点东西，比如画一画Lewis结构,来得到最终。
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But, a few things to note.
还有一小点需要提出的是。
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get back to the initial point is going to require some input from outside, like heat or extra work or extra heat or something because you've done an irreversible process.
如果要逆转它,回到初始点，就需要外界的投入，比如额外的功，额外的热量等等,因为你进行了一个不可逆过程。
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In binary search-- ah, there's that wonderful phrase, this is called a version of binary search just like you saw bin-- or bi-section methods, - when we were doing numerical things- in binary search, I need to keep track of the starting point and the ending point of the list I'm looking at.
就是当我们处理数字的时候，所称的二分检索，在二分法搜索中,我需要记录区间的开始点和尾点，初始化的时候就是-,问题输入的开始点和尾点，当我开始做测试的时候,我想要做的就是去取中值点。
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Knowing what iambic pentameter is, is not a gift of birth, but rather something that comes through a little bit of practice, which means we have to work at it a little bit.
没有谁是生来就知道抑扬五音步格诗，是需要努力才能知道的，这说明我们必须在这个上面花点功夫。
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There's a line segment, it's got a starting point and ending point.
做一个线段，需要一个，开始点和一个结束点。
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So we found precisely one point on this best response picture, and there's a lot of points to find, and it's 20 past 12, so we better get going.
现在我们只找到了最佳对策曲线上的一点,我们还需要找到更多的点,现在12点20了,我们得快点了
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It's got a start point, it's got an end point.
这需要一个开始点，和一个结束点。
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Remember last time, I said that there's different kinds of complexity in our code, and I suggested for simple branching programs, the amount of time it takes to run that program is, in essence, bounded by the number of instructions, because you only execute each instruction at most once.
但是这里有个很重要的点,记得上节课，我提过在我们的代码中，有不同种类的复杂度，而且我还说了对于简单的分支程序,运行这种程序需要的总体时间,大体上，是和指令的数目相关的,因为每个指令只会被执行最多一次。
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But there's an important point here.
但是这儿有一个重要的点我需要提一下。
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Deep equality, we get to define, that's what I did by writing same point.
我们需要自己定义，也就是我写比较是不是，同一个点的那个程序。
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The lowest possible temperature in the Celsius scale is minus 273.15 degrees Celsius. So that begs the notion of re-referencing our reference point, of changing our reference points.
在摄氏温标中,绝对零度是-273。15摄氏度5,这样，我们需要重新定义参考点,将零度的参考点取在绝对零度处，而不是0摄氏度处。
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So when I type, I'm sorry, I shouldn't say type, c point although I would have typed it, p dot x, here's what basically happens.
处于特定点的实例的这个概念，我知道它来自于这个类，这个类，when，I，write，因此当我输入，抱歉，我不该说输入的，当我写，虽然我需要输入它，p，x的时候。
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So I said that we want to be talking about valence electrons here, so that means if we're talking about, for example, the octet rule for an f f molecule where we have two fluorine atoms, we need to write the valence electrons as dots around them.
我说过我们在这要讨论的是价电子，这就意味着，如果我们要讨论，比如，关于两个氟原子组成的分子的八隅体规则,我们首先需要把价电子画成围绕在它们周围的点。
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I want to do this carefully and slowly, and before I even start, let me point out in passing that calculus is not going to help us here.
我要慢点仔细讲这部分,在我开始之前,我需要说明微积分,在这里是用不着的
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And just as there are innumerable human activities which require undistorted references if they are to be satisfied, so there are innumerable other human activities not less important which equally require distorted references or, more plainly, fictions.
就像无数的人类活动,需要真实的证据,如果要达到令人满意的效果，无数同等重要的,人类活动,也同样需要失真的参考,说得更明白点，就是需要虚构。
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