668. What is $|a|$, if $a<0$: will it be $a$ or $-a$?
$\triangleright$ It seems tempting to say that the modulus is $a$ (after all, the modulus is a "number without a sign," while $-a$ has a "minus" sign), but this is incorrect. Since $a$ is negative, the modulus must be positive. To find the modulus, one must choose the positive (more precisely, non-negative) number from the two numbers $a$ and $-a$, and in this case, it is $-a$. $\triangleleft$

Using the modulus sign, the formula for distance can be written as follows: the distance between points with coordinates $a$ and $b$ is $|a-b|$.