In the equation below, as E goes to zero, n approaches infinity.

【infinity】在下面的方程式中，E趋向于零时，n接近无穷大。

The limit as n approaches infinity-- I don't like that color.

n 接近无穷大时的极限——我不喜欢那种颜色。

So we have the limit as n approaches infinity.

所以当 n 接近无穷大时我们有极限。

So as that approaches infinity, your actual sampling distribution of the sample mean will approach a normal distribution.

因此，当它接近无穷大时，样本均值的实际抽样分布将接近正态分布。

Eventually, you can approach the molecular level for your measuring units and the answer for the river's length will end up approaching infinity.

最终，你的测量单位可以接近分子水平，而河流长度的答案最终将接近无穷大。

As x approaches infinity what does n approach?

当 x 接近无穷时，n 接近什么？

And so the limit as x approaches infinity, what does a approach?

所以当 x 接近无穷大时，极限是什么？

The limit as n approaches infinity-- let me write out this binomial coefficient.

n 接近无穷大时的极限——让我写出这个二项式系数。

It just keeps getting longer and longer as you approach infinity, and so an answer has to be given before you get to that point.

随着你逐渐接近无穷大，它会变得越来越长，所以在你到无穷大之前必须给出一个答案。

The central limit theorem says as n approaches, really as it approaches infinity, then is when you get the real normal distribution.

中心极限定理说当 n 接近时，实际上当它接近无穷大时，就是当你得到真正的正态分布时。

And then finally, what's the limit as n approaches infinity?

最后，当 n 接近无穷大时，极限是多少？

Now what's the limit as n approaches infinity of this thing right here?

现在这个东西的 n 接近无穷大的极限是多少？

As this approaches infinity, this term's going to approach 0.

当这接近无穷大时，这个术语将接近 0。

The limit as n approaches infinity of n choose k.

当 n 趋近于 n 的无穷大时，极限选择 k。

As your sample size becomes larger-- or you could even say as it approaches infinity.

随着你的样本量变大——或者你甚至可以说它接近无穷大。

You could, theoretically, go all the way down to the molecular level for your measurement unit but if you do that, the length of the coast seems to approach infinity.

理论上说，你可以一直将测量单位精确到分子水平，但如果你这样做，海岸的长度似乎会接近于无穷大。

And as you approach infinity they actually converge to each other.

当你接近无穷大时，它们实际上会聚在一起。

We're going to have k moments in time because n approaches infinity, these intervals become super super duper small.

我们将有 k 个时刻，因为 n 接近无穷大，这些间隔变得超级超级小。

Now, the next thing I want to touch on is what happens as n-- we know as n approaches infinity, it becomes more of a normal distribution.

现在，我接下来要谈的是当 n 发生的事情——我们知道当 n 接近无穷大时， 它变得更接近于正态分布。

That the limit as n approaches infinity of 1 plus a over n to the n is equal to e to the a.

当 n 接近无穷大时，极限 1 加 a 超过 n 到 n 等于 e 到 a。