All these numbers, whether positive or negative, have the known appellation of whole numbers, or integers, which consequently are either greater or less than nothing.
所有这些数，无论正负，都有一个通称：whole numbers 或 integers，也就是整数；因此，整数可以大于零，也可以小于零。
We call them integers, to distinguish them from fractions, and from several other kinds of numbers, of which we shall hereafter speak.
我们称它们为整数，是为了把它们同分数以及以后要谈到的其他种类的数区别开来。
For instance, 50 being greater by an entire unit than 49, it is easy to comprehend that there may be, between 49 and 50, an infinity of intermediate numbers, all greater than 49, and yet all less than 50.
例如，50 比 49 大一个完整单位；所以很容易明白，在 49 与 50 之间可以有无穷多个中间数，它们都大于 49，却又都小于 50。
We need only imagine two lines, one 50 feet, the other 49 feet long, and it is evident that an infinite number of lines may be drawn, all longer than 49 feet, and yet shorter than 50.
只要想象两条线，一条长 50 英尺，另一条长 49 英尺，就很明显：可以画出无穷多条线，它们都长于 49 英尺，却短于 50 英尺。
整数之间还有分数和其他数；欧拉用线段长度说明这一点。
49 和 50 是相邻整数。
但 49.5 在它们之间。
49.1、49.01、49.001 也都在它们之间。
所以研究数不能只停在整数。