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
you might need math to know how to make a bridge
你可能需要数学知识,才知道如何建一座桥
The concept of regression goes back to the mathematician Gauss, who talked about fitting a line through a scatter of points.
回归这个概念要追溯到数学家高斯,讨论的是从若干散点中切合出一条直线
So I'm going to find for you this result using calculus in a different way.
我将为你们展示,用不同数学方法得到的结果
So for those people who took Intro Economics, which is most of you, this is a game, this a setting in which we have constant marginal costs.
大多数学过经济学导论的同学都知道,这里的边际成本是一个常数
As I suggested in talking about the example of math last time, it's not a silly view, even if it's not a view that we all take automatically.
就像我上次用数学举例一样,即便这不是一个我们都能接受的观点,这也不一定是个愚蠢的观点
So, that's sort of the mathematically how we get to a, but we can also just look at the graph here, because every time we go one wavelength we can see that we're back in a maximum.
这是就我们得到a的数学,办法,但我们可以直接,从图上看,因为每次我们,经过一个波长,都回到一个最大值。
It's a mathematical thing too.
那也和数学有关
Yeah, a lot of math, actually a lot of math.
很多数学类课程,非常多。
It's a math and science class. And I did really badly on the final. I got a C in the class.
它主要就是关于数学和科学的,我期末的时候考得特别差,只得了一个C。
So the object is a mathematical point.
这个物体就是一个数学意义上的点
you have a mathematically complete problem.
这个问题就转变为数学问题了
That's going to presumably be given--mathematically if we gave it a number, we'd slap a zero on that.
如果用数学解释,给它一个数字,给它一个零。
But the mathematicians told Dirac, "You cannot ignore the negative energy solution because it tells you there's a second solution and you cannot throw them out."
但数学家们告诉狄拉克,你不能忽略负的能量,因为数学告诉我有两个根,你不能随便丢掉
You do not have to wave your hands in the air if you're math phobic, but since some of you are, let me just get you all to take a deep breath.
如果你有数学恐惧症你不必举手示意,既然有人是,那么让我们深呼吸一下
It is true mathematically, you can add two numbers, but you've got to ask yourself,"What am I doing as a physicist when I add these two numbers?"
在数学上它是正确的,你可以引入这两个常数,但是你需要问问自己,当我引入这两个常数时,这么做有什么物理意义
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