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 + afor 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 = 5and 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 = 2w,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.
The permanent URI of this web page
is
http://tobybartels.name/MATH-0950/2008SP/introduction/
.