# Introduction

Elementary algebra is a system for talking about numbers
without having to say, or even know, exactly what the numbers are.
You do this by using some other symbol to stand for each number.
This symbol could be anything that doesn't already have a meaning,
usually a letter like *x*, *A*, or *n*.
You can also use letters from other languages,
like φ (Greek) or ℵ (Hebrew),
entire words like `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 real 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*

for all real numbers *a* and *b*.
Or if all you know about a real 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* can and 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 the length and *w* stands for the width.
These examples don't really need algebra,
because you can deal with them using ordinary words.
But more complicated problems really need symbols, or you'll get lost.

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This web page was written in 2007 and 2008 by Toby Bartels.
Toby reserves no legal rights to it.
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is
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.