Problem with mbox command

Question

I have the following simple code which causes some problems, would be great if someone could point out what is going wrong here:

\begin{compactenum}

\item Perform addition over all bits
  \[
  $\mbox{for~} j \in \{0 \ldots 7\} $ \\
  $r_j = 8 \cdot a_j + 4 \cdot b_j + 2 \cdot x_j + 1 \cdot y_j$
  \]                

 \end{compactenum}     

LaTeX outputs the following error message:

! Missing $ inserted.
<inserted text> 
                $
l.822       $\mbox{for~} j \in
                           \{0 \ldots 7\} $ \\

Answer 1

Inside \[ ... \] you cannot use the math mode again. If you want two lines then use align* from amsmath or the same without \[...\] :

  $\mbox{for~} j \in \{0 \ldots 7\} $ \\
  $r_j = 8 \cdot a_j + 4 \cdot b_j + 2 \cdot x_j + 1 \cdot y_j$