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.
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