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Number Lines

We can visualise positive numbers as the distances to points on a line, measured to the right of some chosen "zero point" called the origin.

Negative numbers can then be thought of as corresponding to distances measured to the left of the origin:

We call this a number line.

For any number x, the number -x (called the negative of x) is the number which is the same distance from the origin as x, but on the opposite side. Note that this is also true when x itself is a negative number, for example -(-2) = 2.

Since the effect of placing a minus sign before a number is to "reflect" the number about the origin, it follows that for any number x (positive or negative):

-(-x) = x

That is, two successive "reflections" take you back to where you started.

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