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

但是如果碰到不是我们常使用的整数的数字该怎么办呢？

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 大的整数。

You have a few minutes to choose four distinct positive whole numbers.

有几分钟时间可以选择 四个不同的正整数。

The 17th-century French mathematician Pierre de Fermat, states that you can't find numbers where: x to the n plus y to the n is equal to z to the n when n is a whole number greater than 2.

17世纪法国数家皮埃尔·德·费马指出，当n为大于2的整数时，不可能找到满足x的n次方加y的n次方等于z的n次方的数字。

So int is short for integer and that represents a whole number and str is short for string, so here we're subtracting a string from an integer, and Python doesn't know what to do with it.

int是整数的缩写，表示整数而str是字符串的缩写，所以这里我们减去一个整数的字符串，Python不知道如何处理它。

That's a nice round figure to deal with! OK, if you were to buy this insurance policy, your yearly fixed income from it would be 94.35 RMB.

这是一个很好筹算的整数。好的！如果想要买这项保险的话，那么将会每年得到固定数额收入是94.35人民币。

We could use that to figure out the empirical formula which is the simplest whole number formula.

我们可以用它来计算经验公式, 这是最简单的整数公式。

You've never seen a chemical formula written with anything aside from whole numbers down here.

从来没有见过一个化公式用除了整数以外的任何东西写下来。

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

有一个数分支叫做 “数论”，就是在研究整数之间的关系。

You see, the ratio of a circle's circumference to its diameter is what's known as an irrational number, one that can never be expressed as a ratio of two whole numbers.

为，圆周长和直径的比值是一个无理数，它无法用两个整数的比值来表示。

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 大的整数。

According to Pythagoras Theorem, the diagonal length would be square root of two; but try as he might, Hippasus could not express this as a ratio of two integers.

根据毕达哥拉斯的理论，这个正方形的对角线长度应该为根号二；但是无论希帕索斯如何尝试，都不能将根号二变为两个整数的比例形式。

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，平均数接近于 20 至 35 之间的某个整数。

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

它应该是从一到十的正整数。

So a round number splitting the difference is a focal point.

，一个取中间值的整数就成了焦点。

And while we're at it, why is it so close to an even 40,000 km?

而既然提到这个话题，为何它又如接近整数的4万公里呢？

Is it 17% or are they nice round numbers?

是17%，还是他们选用了整齐的整数？

So, each of these cases is categorised on four metrics with a standard integer scale.

，每个案例都依据四个标准指标进行分类，采用标准的整数评分体系。

Daltons's atomic theory began when he expanded French chemist's Joseph Louis Proust's Law of Definite Proportions, to develop the Law of Multiple Proportions, which says elements combine in simple, whole number ratios of their masses.

道尔顿的原子理论始于他对法国化家约瑟夫·路易·普鲁斯特的定比定律的扩展，从而提出了倍比定律，该定律指出元素以简单的整数质量比相结合。

And so most of these chi-squared-- the reason why we have these weird numbers like this instead of whole numbers or easy-to-read fractions is it is actually driven by the p value.

，这些卡方分布中的大多数——我们得到这些奇怪的数字而不是整数或易于阅读的分数的原实际上是由p值驱动的。