Page Number: 
23

[from page 22]

In dealing with people, we frequently need to make statements about whole classes of people, or about a specific person without knowing what specific person we are talking about. In English we have, in addition to proper names, words that refer to people generally or even to specific unknown people. In mathematics we have specific numbers, $1$, $2$, $3$, ... $17$, ... $146$, etc., which correspond to the proper names of people. But we also need symbols to refer to classes of numbers, or to unknown numbers. For this purpose we must define new symbols. The symbols used are usually letters like $n$, $a$, $b$, $c$, $x$, $y$, etc., as the reader no doubt already knows.

There are a number of statements about numbers that are true no matter what specific number is involved, and we need to be able to make these statements clearly and as briefly as the ideas permit. For example, consider the following table:\[ \begin{align}
1 & = 1 \\
2 & = 2 \\
3 & = 3 \\
10 & = 10 \\
157 & = 157 \\
1136 & = 1136 \\
& and ~ so ~ on \end{align}
\] What English sentence will sum up what we are illustrating in this table?