What is a number line? You might reasonably think that it is a line with numbers on it, like this:

But when mathematicians draw a number line, the numbers are not actually on the line. A number's location is marked like this:

On a number line, a number represents a point on the line, and every point on the line represents a number. So you might think a number line would look like this:

However, this is not quite correct. The numbers need to be in order from smallest to largest, or, as a mathematician might say, from least to greatest. The next line shows this progression from right to left.

But the preceding example is still not the number line used in mathematics. The conventional way to draw a number line is horizontal, with numbers increasing from left to right.

But something is wrong with...