Could someone clarify this picture in Spivak, illustrating $|x - a| < \frac{|a|}{2}$?

Question

It's not really clear to me what the picture is trying to illustrate. If we mark $a$ to be the largest vertical bar, then how many of these unit bars is $a$ supposed to be? $4$?

Answer 1

The largest (middle) vertical bar is $0$ and each unit bar has length $\dfrac{|a|}2$.

If $a>0$, $a$ is the second vertical bar on the right starting from the middle.

If $a<0$, $a$ is the second vertical bar on the left starting from the middle.

The values that $x$ can take is contained in one of the greyed areas, depending on the sign of $a$.