\Bigg{ and \Bigg} are errors; it should be \Bigg\{ and \Bigg\}, respectively.
Actually, there's no need to \Bigg (pun intended) -- \bigg is the correct size for the fractional term at hand. Thus, you should enter the displayed equation as follows:
\[
\biggl\{\biggl| \frac{f_i(x_i+h)-f_i(x-k)}{h} \biggr|\biggr\}
\]
Note that I use \biggl and \biggr instead of just \bigg for the "fence symbols". For the present equation this makes no difference in appearance. However, there would be a major difference if the fractional expression were preceded by a unary minus (or plus) symbol.
\Biggl\{\biggl|...\biggr|\Biggr\}. And don’t use$$! – GuM Aug 10 '16 at 09:32\{ ... \}not{...}, also consider using\Biggl ... \Biggrin order to get the correct classes. – daleif Aug 10 '16 at 09:32\[ ... \]preferable to$$ ... $$? – GuM Aug 10 '16 at 09:43