So, we've used $3 billion as a nice big round number.

因此取个整我已经花掉30亿美元 。

It might've been 42, but I rounded down.

其实有 42 小时，不过我四舍五入取整了。

Why that integer and what exactly does 0 represent?

为什麽是这个整，而 0 又代表什麽？

I multiplied my check by seven and it revealed a nearly round number. Mystery solved.

我把奖金目乘以七正好接近一个整，谜底解开了。

But what about if something's not quite those round numbers that we often use.

但是如果碰到不是我用的整的该怎么办呢？

In programming, we refer to these numbers as integers.

在编程中，我将这称为整。

These sorts of relationships between integers are studied in a branch of math called number theory.

有一个学分支叫做 “论”，就是在研究整之间的关系。

If everyone playing comes to this same conclusion, no one will guess higher than 67.

如果每个人都在博弈中得出同样的结论，没人会猜比 67 大的整。

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，都可以表示为这之和。

You might say, imagine somebody who spends his eternity counting the integers--1, 2, 3, 4, 5, 6.

比方说 有人用他无限的生命整 一二三四五六。

Since everyone can figure this out, it wouldn't make sense to guess anything higher than 67.

既然每个人都明白这个道理，那就没有理由去猜比 67 大的整。

That's not a whole number, though. And we don't have bits of gold coins coming out of the bag.

不过，这就不是一个整了，而且那个袋子里出来的金币可没有零碎的。

So to the 1st power you move it one to the right and you get 60.

它并不是以时速60英哩" 整" 的时速前进的。 我只知道我的车速介於两个整间。

Last episode, we talked about integers, positive whole numbers and their opposites.

上一集，我讨论了整、正整及其相反。

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

本周，我将看看将正整和负整相加时会发生什么。

The figure was rounded off to make it easier for you. The options were: about 700; 1,200 or 1,600.

以整计，方便你选择。选项有：约700个、1200个、1600个。

Is that going from all the integers to the odd ones?

是从所有整到奇吗？

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，也被称为自然。

When this game is played in real-world settings, the average tends to be somewhere between 20 and 35.

当这个博弈在真实世界中发生时，平均接近于 20 至 35 之间的某个整。

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

它应该是从一到十的正整。