This " discrete infinity" is often said to be the hallmark of human language.

这种“离散无穷大”常被认为是人类语言的标志。

So that's a great example of something that's infinite.

这是无穷大的一个很好的例子。

It was an old-fashioned battering ram propelled with infinite power.

那是古代的攻城机，被无穷大的力量推动一样。

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，n接近无穷大。

Basically, when you try to combine them, the equations break, they give infinities, they just don't produce answers or calculations that you can use that you can work with.

基本，着把它们结合起来，方程会断裂，会给出无穷大的数，不会生你可以使用的答案或计算结果。

Our best theory of space and time, Einstein's theory of general relativity, says that space and time become infinitely curved, that the centre of the hole becomes infinitely dense.

目前最好的论，也就是爱因斯坦的广义相对论，告诉我们被无限扭曲使得黑洞中心的密度变得无穷大。

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。

But having infinity equal to zero is ultimately not all that useful to mathematicians, or anyone else.

但是无穷大等于 0 对于数学家或其他任何人来说最终并不那么有用。

Georg Cantor called this level of infinity aleph-zero.

George Cantor称这个水平为无穷大阿列夫零。

The curvature of space becomes infinite, density becomes infinite, and our rules just don't make sense.

间的曲度变得无穷大，紧密程度也无穷大，那我们的规则就不再适用。

The most important infinity that I study is that the universe is infinite.

我所研究的最重要的无穷大就是宇宙是无限的。

In their newest course, you can expand your mind with the paradoxes and beauties of infinity.

在他们最新的课程中，你可以用无穷大的悖论和美丽来拓展你的思维。

Reckoning with infinity is one of the major accomplishments of mathematics.

用无穷大计算是数学的主要成就之一。

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。

So if they can do that, couldn't we just make up a new rule, say, that the symbol infinity means one over zero, and see what happens?

所以，如果他们可以那样做的话，我们不能创建一个新的规则吗，即，无穷大等于 1/0，看看会怎样？

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.

论说，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。

We use infinities all the time when we're making predictions in physics, and it turns out that the size of the universe is infinite.

我们在物学中做预测，我们一直使用无穷大，事实证明宇宙的大小是无限的。

Start with basic counting and work your way up to the many types of infinity culminating in the profundity of Cantor's theorem.

从基本的计数开始，一直到许多类型的无穷大，最终达到康托尔定的深奥程度。

Infinity is not just a concept in our minds.

无穷大不仅仅是我们头脑中的一个概念。

So depending on what you've used, your answer for the length of this river could range anywhere from 300 kilometers to infinity.

所以根据你使用的方法，这条河的长度可以从 300 公里到无穷大不等。