Second, recursively defining general binary trees. A node can now have $0,1$ or $2$ children. These may not be balanced and all the leaves may not be on the same level of the tree. This definition can also capture full binary trees. This is a tricky definition and you can $$make$-$up$$ some notation or have $$cases$$ by using logical AND or OR in your definition.

An example that recursively defines a set of binary strings $(\{0,1,00,01,10,11,000,001,010,011,100,...\})$ might look like

B$(1)=0$ OR B$(1)=1($now there are $2$ base cases$)$

B$($n$)=$ B$($n$-1)0$ OR B$($n$-1)1($now there are $2$ rules and I claim that the symbols B$($n$-1)0$ and B$($n$-1)1$ are concatenated together$)$