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So there was a good question in Wednesday's class about the de Broglie wavelength and if it can actually go to infinity.
在周三的课上有个关于德布罗意波波长的问题,非常好，就是它能不能到无穷大。
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And, we're going to look at what happens as the chloride ion moves from infinity in towards the positive ion.
然后我们要看一下,当氯离子从无限远处逐渐靠近,这个正离子会发生什么。
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If I had taken as my interpolation scheme, my white curve here, I could go to infinity and have the equivalent of absolute zero being at infinity, minus infinity.
要注意，如果我们采用，像图中白线这样的插值方案的话,我就可以一直降温下去,相应的绝对零度点。
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So the mathematical notions of infinity or logical notions like logical entailment are beyond a child of this age.
因此,对于无限这个数学概念,或者是,像逻辑蕴涵这样的逻辑概念,超出了该年龄阶段儿童的理解范围
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Because we know as we go to infinity, even though the density gets smaller and smaller and smaller, we still have electron density very far away from the nucleus.
因为我们知道即使到了无穷远处，尽管电子密度会变得非常非常非常小，但我们仍然有一定的电子密度，无论离原子核多远。
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But, you know, in 2D, the options are not just left and right or north and south, but infinity of possible directions in which I could go those 5 km.
但在二维空间中,不仅可以向左向右或者向南向北,我在走那5公里的时候可以有无数个方向
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Well, the energy at infinity is zero -K and the energy in the ground state is minus K.
无限远处的能量值为,而基态能量值为。
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Well, the infinity mechanism, and many of you will be familiar with this from mathematics or computer science, is recursion.
这种无限机制是递归的,你们许多人会在数学与计算机科学中,熟悉这个词
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You have to learn them one by one, but you could produce a virtual infinity of sentences.
你必须一个个的去学习这些词,但你却可以创造出实际上无限的句子
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And, being he described as an infinity of indivisible particles, which he dubbed atoms from the Greek.
他将原子描述为无限的极微小的,粒子，他用德语给原子命名。
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This is infinity. Let's call this 3, 2, 1.
它是无穷大的，我们叫它3，2，1吧。
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STUDENT: Why doesn't wavelength go to infinity as it stops, like a standing .
学生：当它停下来时,它的波长为什么,不趋于无穷大呢，就像一个。
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It's just like if you restrict me to only a subset of numbers, only the odd numbers, still there's an infinity of odd numbers.
这就像,如果你把我限制在数字的子集,只是奇数,但奇数的数量却仍然是无限多的
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So, grammar can be restricted but still give rise to an infinity of possible sentences.
所以,语法是有些局限,但仍然能产生无限可能的句子
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And in fact, language allows us to produce a virtual infinity of sentences.
事实上,语言使得我们能够,创造出近乎无限的句子
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Infinity is the force when we're thinking about it and our brains, negative infinity is when we actually plug it into the equation here, and the reason is the convention that the negative sign is just telling us the direction that the force is coming together instead of pushing apart.
说力有多大时，我们想到的,是无穷大，而方程解出来的,是负无穷，这是因为习惯上,我们用负号表示力的方向,是相互吸引而不是相互排斥的,所以我们可以用库仑定律。
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Yeah. So, the force actually goes to infinity, and specifically it goes to negative infinity.
是的，力变成无穷大，更具体说是负无穷大。
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That's why the infinity.
这是无穷的原因。
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So it tails off to infinity.
所以，它在无穷远处几乎为。
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And here you get a potential infinity of sentences.
这样你就能得到潜在的无限数量的句子
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At infinity, there's no stored potential energy, and it drops off more and more negative as one over R.
在无限远处，没有储存的势能，并且它向负方向减少，当距离超过R时。
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So, we just talked about the force law to describe the interaction between a proton and an electron. You told me that when the distance went to infinity, the force went to zero. What happens instead when the distance goes to zero? What happens to the force?
我们刚刚讨论了描述质子,和电子之间相互作用力的定律,当距离变为无穷时,力变为零，那当距离变为,零时会发生什么？,这时候力是多少？
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DNA also has this sort of combinatorial system where you have a finite number of, I guess, bases or amino acids that could combine to a possible infinity of strings of DNA strings.
脱氧核糖核酸也拥有这种组合系统,你的生物基础或氨基酸数量是有限的,但却能组合出,几乎无限的脱氧核糖核酸螺旋结构
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But also unlike n, l cannot have just any value, we can't go into infinity.
但不像n，l，不能取所有整数，不能到正无穷。
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This is E equals zero. N equals infinity.
这是第N个能级，能量为。
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Then we go negative and we go through zero again, which correlates to the second area of zero, that shows up also in our probability density plot, and then we're positive again 0 and approach zero as we go to infinity for r.
并且再次经过,这和，第二块等于0的区域相关联,这也在,我们的概率密度图里反映出来了，然后它又成了正的,并且当r趋于无穷时它趋于。
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And finally up here we have n equals infinity.
最终我们让n等于无限大。
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When n equals infinity, r equals infinity.
当n为无限大时，r也为无限大。
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The ionization energy must then be nothing more than, that is the energy to go from the ground state here to n equals infinity, so that would be the energy at state infinity minus the energy of the ground state.
这个电离能一定不会大于，从基态到n为无限大时的能量,而是等于,无限远处的能量减去基态能量。
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