It's 0.
By definition, the absolute value of a number [tex]x[/tex] is
[tex]|x|=\begin{cases}x&\text{for }x\ge0\\-x&\text{for }x<0\end{cases}[/tex]
so it follows that |0| = 0.
Intuitively, the quantity [tex]|a-b|[/tex] can be thought of as "the distance between the numbers [tex]a[/tex] and [tex]b[/tex] on the real line". If [tex]a=b=0[/tex], asking about |0| is the same as asking "how far away is 0 from 0 on the number line?" to which we answer, 0.
