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With the computer today, you can, for the most part, not represent every possible number that mankind can think of.
在当今世界，大多数情况下，并不是要把每个数字,都精确表示出来。
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they want to, or they feel they want to be separate and different from the rest of Europe.
他们想要，或者他们觉得他们想要独立出来，与欧洲其他地方不一样。
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OK. Now, having done that, again I want to stress this idea and I'm going to write it out one more time, that there's a particular format here.
好，讲完了这些，我又想要强调一下这个思想,并且再一次把它写出来了，就是有一个特定的格式。
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We often feel like things bleed out of us and so people will systematically overestimate the extent to which other people notice their secrets.
我们通常会觉得我们的秘密要泄露出来,所以人们心里经常会觉得,别人都发现了他们的秘密。
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The tests will be written in the normal class period.
测试是要在常规的课堂时间写出来。
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So, in particular, what we're going to do to find out what quantity q1 maximizes this profits for each choice of q2.
所以我们要算出来在不同的q2下,q1取什么值才能最大化利润
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He does a great deal else in it, but I'm isolating this strand, which is what's relevant to what we're talking about.
他在书里还讲了很多别的东西，但我要把这点单拎出来，因为只有这一点和我们要讨论的相关。
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And so for many, many problems, especially on exams, especially on this first exam, you will be able to say that this is the relationship between internal energy and temperature.
对于很多问题，特别是考试中的问题，你们要能够说出来,这是内能与温度的关系。
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These are all real questions and I raise them now myself because they are questions I want you to be thinking about as you do your reading and work through this course.
这些都是很真实的问题,我现在提出来,因为这些是,我要你们思考的问题,在你们阅读时，还有在做本课的研究时。
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You figure that most of those boxes are being eaten by somebody or another, there's some waste that you might calculate in, but there--error gets introduced there trying to estimate that, so you get a number on that.
你的计算中大部分食品,都被人们吃了,浪费的那些也要计算进来,但其中的误差,也要估算出来,最后得出一个数字
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But then we have to ask-- so I'll throw the question out and we'll call it a day, start with this next time-- then we have to ask, ? would it really be better to know?
但是接下来我们要问-,我把问题提出来便结束今天的课程，下节课从这个问题开始-,接下来我们要问，知道了真的会更好吗？
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You know, speak even if you're not sure exactly what you're saying is totally correct,
即使你不能确定你讲的内容是否完全正确，你也要开口讲出来，
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and I don't know why I would go to his wedding now.
所以我看不出来现在我为什么要去参加他的婚礼。
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I want to mention that 5 you're going to get problem-set five is posted today, and I'll write which ones you can already do so far, because you don't have class on Monday.
我要指出的是,今天会贴出来习题集，我会给出你们现在可以做的题目，因为周一没有课。
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You shall not make yourselves unclean through any swarming thing that moves upon the earth. For I the Lord am He who brought you up from the land of Egypt to be your God: you shall be holy, for I am holy.
你们也不可在地上的爬物,污秽自己，我是把你们从埃及地领出来的耶和华,要作你们的神，所以你们要圣洁，因为我是圣洁的。
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You knew it was time to start clapping as soon as that chord hit that, it stopped going back and forth,tonic,dominant,just sitting there.
你知道在这个和弦出来的时候要拍手，然后停下来，来回的行进，而主音，属音，然后保持住。
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I'm going to print it and let's see what it prints.
我要将其打出来,我想显示下数组的内容。
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Again, same kind of reasoning says, given some value x, I happened to pick a small one here, what's an easy way to do this? Well, let's just start at one. That's my variable I'm going to change and check.
好，尤其是，让我们到这里来,让我给大家看看第二个例子,让我把这个注释掉，这是我要解决的，第二个问题，假设我想找到一些整数的,所有除数，我想要找出来这个数的所有的除数。
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Because it says, your program will still give you a value, but it may not be what you intended, and you can't always tell, and that may propagate it's way down through a whole bunch of other computations before it causes some catastrophic failure.
因为这意味着，你的程序依然会返回一个值，但是这个值可能不是你想要的，你可能还分辨不出来，而且这种情况会传播,结果会沿着正果计算过程传播下去,直到产生一个灾难性的错误。
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I've listed a sequence of modules, the things that I want to do.
我先把我要做的事情，作为一系列的模块列了出来。
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And, I will go through the actual line by line derivation not because I want to do derivations in class.
我们要仔细讨论实际的线,和推导出来的线,并不是我想在这节课做推导。
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But imagine I actually wanted to gather them together. I wanted to collect them, so I could do something with them.
把那些除数都显示出来,这很有用，但是请想想下我想要，把它们放在一块。
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Some people in this room might be hubs, and it is not impossible to find out.
这个教室里可能就人这样的人，要找出来很简单。
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So the four of you who chose numbers bigger than 67, whose names I'm not going to read out, maybe they were making a mistake.
所以那四位选择大于67的同学,我虽然不念出来你们的名字,但以后要注意啊
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So if I print e to f of soccer, it will print the string football.
如果我要显示soccer的e到f变换的话，打印出来的就是football了。
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And I don't actually know the periodic table entry for raisins. So I'll have to write it out.
我不知道葡萄干的周期表条目是什么,所以现在我要把它写出来。
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And I'll remind you, what I'm printing out there is first and last, with the range I'm looking over, and then just how many times the iteration called.
我要打印出来的是，每次的区间,也就是first和last指向的值，以及重复多少次了。
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So this of course relies on me having brought some money and we'll have to do this without dislodging the microphone.
要继续我得先拿出来点钱,但我还不能碰掉麦克风
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Right, so the things we want you to take away from this are, get into the habit of using pseudo code when you sit down to start a problem, write out what are the steps.
好，这儿我想大家明白的就是,养成解决问题时先写伪代码的好习惯,把步骤都写出来,我想要告诉你们的是一个好的程序员。
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