They're just adding integers on each downbeat.

只是在每个强拍上加一个整。

Why that integer and what exactly does 0 represent?

什麽是这个整，而 0 又代表什麽？

He labeled these hypothetical integers p and q.

他將這兩個假設的整數 命名為 p 及 q 。

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，也被称自然。

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。

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，都可以表示这些字之和。

Good, Mom. I think I really nailed those integers.

挺好的 老妈 我觉得整题我做得不错。

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，何处偏离的指针以及遇到带符号整溢出时该怎么办。

So integers, again, are implemented in C as these things ints.

同样，整在C中实现int。

And it turns out that int, for instance, integers in C, only use 32 bits.

结果是int，C中的整，只使用32位。

But they on CS50 IDE, and most modern systems, an integer is only 32 bits.

但他们在cs50ide上，以及大多现代系统中，一个整只有32位。

I think what this means is that percent i recall was for integers.

我想这意味着我记得的百分比是整。

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

因此，p 可以 2a 表示，a 是一個整數。

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

从提示用户输入正整的用户处获取整。

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

它返回一个我声明的整类型的值。

Recall that integers, of course, can be represented in decimal or in binary.

当然，整可以用十进制或二进制表示。

And here, I'm going to go ahead and " Get negative integer from user."

在这里，我要继续 “从用户处获取负整。”

And so there's this problem with integers too.

所以整也有这个问题。

Interestingly, even though we can't express irrational numbers as ratios of integers, it is possible to precisely plot some of them on the number line.

有趣的是，即便我们无法将无表示称整的比，我们却可以将它准确表现在图形之中。

So an integer or a real number you'd expect to square it and it to be a positive value or perhaps zero right?

所以对于一个整或实，它的平方你会认结果是一个非负，对吗？