He labeled these hypothetical integers p and q.

他將這兩個假設的數 命名為 p 及 q 。

Thus, p could be expressed as 2a, where a is an integer.

因此，p 可以 2a 表示，a 是一個數。

Why that integer and what exactly does 0 represent?

为什麽是这个数，而 0 又代表什麽？

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”，就是在研究数之间的关系。

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数，都可以表示为这些数字之和。

In programming, we refer to these numbers as integers.

在编程中，我们将这些数字称为数。

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。接下来是正数，也被称为自然数。

Programming languages have some undefined behaviors, such as what to do with misaligned pointers or when encountering signed integer overflows.

编程语言有一些未定义行为，例如如何处理偏离的指针以及遇到符号数溢出时该怎么办。

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

它应该是从一到十的正数。

And the higher frequency bins are just integer multiples of this frequency.

较高频率的 bin 只是该频率的数倍。

So you could represent any positive integer this way.

因此您可以用这种方式表示任何正数。

Is a woman a thinking unit at all, or a fraction always wanting its integer?

一个女人到底是一个思维单位， 还是一个总是想要它的数的分数？

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

上一集，我们讨论了数、正数及其相反数。

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

是从所有数到奇数吗？

And an integer, recall, in CS50 IDE is 4 bytes.

在cs50ide中，一个数是4字节。

It returns a value I claim that is of type integer.

它返回一个我声明的数类型的值。

Remember the fields have to be blitable, bytes, floats, integers, stuff like that.

请记住，字段必须是可直接传送的、字节、浮点数、数等。

Here for example we're just checking for two values, two integer values, being the same.

例如，在这里我们只是检查两个值，两个数值是否相同。

A positive integer has a value that's greater than 0.

一个正数有一个大于 0 的值。

For a lot of instruments, the most common overtones are integer multiples of the fundamental frequency.

对于许多乐器来说，最常见的泛音是基频的数倍。