`length`

or `population`

,
or even nonsense symbols like ↵ or ◊.
I'll mostly use ordinary English letters.
So if you want to say
that it doesn't matter what order you add two numbers,
then rather than saying 3 + 4 = 4 + 3 (since they're both 7)
and 2 + 9 = 9 + 2 (since they're both 11) and so on,
you can just say
that *a* + *b* = *b* + *a* in general.
Or if all you know about a number
is that you get 5 when you add 2 to it,
then you can say that *x* + 2 = 5
and see if you can figure out what *x* is
(as it turns out, *x* must be 3).
Or if you know that the length of a box is twice its width,
then you can write this as *l* = 2*w*,
where *l* stands for length and *w* stands for width.
None of these examples really need algebra,
because you could deal with them using ordinary words.
But more complicated problems really need symbols, or you get lost.

Go back to the course homepage.

This web page was written in 2007 by Toby Bartels. Toby reserves no legal rights to it.

The permanent URI of this web page
is
`http://tobybartels.name/MATH-0950/2007f/introduction/`

.