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So sometimes the extra solution is very interesting and you should always listen to the mathematics when you get extra solutions.
所以有时候这些增根的意义很耐人寻味,当你解出增根的时候,别忘了想一想它的数学含义
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but they're still really good at like teaching, but sometimes a little bit crazy. Like... like very strange personalities.
但是他们还是很擅长教学，但是有时候有点疯狂，比如性格有点奇怪。
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So this is actually the most straightforward, so sometimes it's nice to end with the easiest concept, and that's what we're doing here.
这应该是最明显的一个，有时候用最简单的内容来结束是很好的，这也正是我们在做的。
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and that something that happens was often very mysterious, very akin, I think, sometimes to inspiration.
而这种想法，常常是神秘的，有时候，与“灵感“很相似。
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But you know, sometimes what seems to be the virtuous may not necessarily be, so that would be an example.
但是现在你们知道了,有时候看起来低脂的食物并不一定低脂,这是个很好的例子
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but it's important to get some peace and quiet sometimes, so I do go to Central Park for that.
但有时候得到一些平静和安宁也很重要，这种时候我就会去中央公园。
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I guess some days at Yale can be very busy. Do you think those busy days happen a lot?
我想有时候在耶鲁会很忙。你觉得经常很忙吗？
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And,also,because he just sat around and played cards all the time and ate and drank, he became quite a large man,and occasionally he would get up and go and look at the relics of Marie Antoinette, and then he'd go back and play cards for big stakes; he was a big-time gambler.
而且,由于他只是坐在那儿,整日玩牌,饮酒作乐,他变得很肥,有时候他站起来,去看看玛丽王后的遗物,然后又回来豪赌,他是个有名的赌徒
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Because sometimes it's useful to think about the payoffs, as coming from "i's" own choice and everyone else's choices.
因为有时候考虑在i和对手,在不同选择下的收益是很有必要的
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And you know, sometimes you run into people that you haven't seen in a while, so it's nice.
你知道，有时候你碰上一些好久不见的人，这很好。
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So sometimes you'd see they'd make statues of Isis look like statues of Artemis back home.
有时候看到他们在建艾西斯的神像,很像故乡阿尔忒弥斯的神像。
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If we want to know the total heat added to the system, we can measure it, which is the straightforward thing, but sometimes you want to calculate in advance, or sometimes you want to calculate it on an exam.
如果想知道给系统的总热量，我们可以测量，这是很直接的事情，但有时候我们想事先计算它，或者需要在考试中计算。
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So literary can sometimes be very abstract like mathematics, and therefore, if someone says make me a movie, showing me what the square of minus two means that is going to be a challenge.
文学有时候也可以很抽象,像数学，因此如果有人说,给我做一部电影吧,给我展示一下负二的平方,那将是一个挑战。
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Sometimes the notion is that it is just terrible for everybody with actual pain and suffering, and others have a notion of a wonderful kind of a heaven in which marvelous things happen to you, sometimes spiritual, sometimes physical depending on the religion.
有时候一些观念是很可怕的,每个人死后,都要受苦受难,而另一些观念就很美好,有一个美妙天堂,在那里你会有非凡的体验,或是精神上的,或是肉体上的,不同的宗教里说法不同
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And sometimes people get angry at you and don't want to talk to you,
有时候人们会对你很生气，不想和你说话，
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And I think in some cases, it could be a very good investment
而且有时候我觉得这是很好的投资。
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I guess living with roommates can be very difficult sometimes.
有时候跟室友一起住不是很方便。
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Because sometimes paintings that are very detailed or realism,
因为有时候图画很精细或很现实主义。
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and to some degree, I miss studying those things.
有时候，我还是很怀念学习那些理科内容的。
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and yeah, kind of one day, I'll be smart,
有时候，我会打扮得很漂亮，
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and sometimes she's just a pain in the neck.
而且有时候，她很讨厌。
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You know, it's good. But it's corrupt sometimes.
它的确很棒，但是它有时候也很腐败。
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and just you know, it's very unstressful sometimes,
而且你知道，有时候很没有压力，
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because it, that kind of sucks sometimes.
因为它，它有时候真的很糟糕。
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It's a little difficult sometimes,
有时候我会觉得很困难，
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Sometimes the questions are worded quite differently, so I just want to sum up here the different ways they could be worded.
有时候问题表述的很不一样，所以我只是希望能,汇总不同的表述方式。
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This is also important though for Roman politics, because if you're if a freedman, - or even if you're a free person-- sometimes see freemen would connect themselves to a powerful Roman who was higher status than them, because they could use him for important things.
同时对罗马政治也很重要，因为即使是自由人，甚至是自由民-,有时候也会依附有权有势,地位高于他们的罗马人，以谋求他们的帮助。
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She is sometimes fun.
有时候，她很有趣。
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