Recursively defining the set of bit strings set having more zeros than ones Question: 
Recursively define the set of bit strings that have more zeros than ones.
I tried it this way:
$\Sigma\subset \{0,1\}^*$
Basis step: $0 \in \Sigma$
Recursive step: For any $x\in \Sigma$, $00x1\in L$
Is it a valid answer?

It might be a little late to answer but this would be another way to answer it.
Basic Step: $0 \in S$.
Recursive Step: If $x, y \in S$ then $xy \in S$, $x1y \in S$, $1xy \in S$, $xy1 \in S$.
