And any positive integer, up to a certain limit, can be expressed as a sum of these numbers.

在一定范围内的任何正整数，都可以表示为这些数字之和。

The first two aren't very interesting: all ones, and then the positive integers, also known as natural numbers.

开头两条并不是很有趣，全都是 1。接下来是正整数，也被称为自然数。

It should be a number from one to ten, a positive integer.

它应该是从一到十的正整数。

And doesn't have to be a positive integer anymore.

并且不再必须是一个正整数。

This week, we're 'gonna see what happens when we add positive and negative integers together.

本周，我们将看看将正整数和负整数相加时会发生什么。

So this is a function that's only going to get a positive integer.

所以这个函数只能得到一个正整数。

Get an integer from the user prompting them for a positive integer.

从提示用户输入正整数的用户处获取整数。

It doesn't take any inputs, it just gets a positive integer from the human.

它不需要任何输入，只需要从人类那里得到一个正整数。

If you, don't a positive integer the binomial theorem, Newton's binomial theorem will give you an infinite sum.

如果你不知道二项式定理中的正整数，牛顿二项式定理将给出一个无穷和。

The standard binomial theorem insist that you apply it only when N is a positive integer, which makes sense.

标准二项式定理坚持只有当 N 为正整数时才应用它，这是有道理的。

On a horizontal number line, do positive integers go to the left of zero, or to the right of the zero?

在水平数轴上，正整数是在零的左边还是在零的右边？

The last episode was on positive and negative integers If you didn't happen to see it, you can check it out here.

上一集是关于正整数和负整数的， 如果你没有碰巧看到它，你可以在这里查看。

Like for all positive integers it was just a finite set of terms and now we've got an infinite set of terms.

就像对于所有正整数来说，它只是一组有限的项，而现在我们得到了一组无限的项。

And how can you get a distribution where the sum is exactly 1 greater than the number of non-zero positive integers being added together?

以及如何获得总和恰好比加在一起的非零正整数的数量大 1 的分布？

It doesn't have to be a positive integer, it doesn't have to be a negative integer it doesn't have to be an integer.

- 它不必是正整数，它不必是负整数，它不必是整数。

But once you get outside of the triangle with positive integers, you never hit N minus N because N is not a positive integer, so you get this infinite series.

但一旦你走出正整数三角形，你永远不可能达到 N 减 N，因为 N 不是正整数，所以你得到了这个无限系列。

In this coordinate system, the derivative is described with an infinite matrix that's mostly full of zeroes, but which has the positive integers counting down on this offset diagonal.

在这个坐标系中 导数是用一个无限矩阵来描述的这个矩阵大部分都是0 但是在这个偏移对角线上有正整数在倒数。