A language $L$ is defined recursively according to the following rules:$  L$If $w  L$, then $bw  L$ and $waa  L$I am not sure if strings from this language should mix from this definition. Would strings only consist of $bbbb$ and $aaaa$, or can it also consist of $bbaa$, $aabb$, and so on?
How to read this inductive language definition?
formal languages;induction;mathematical foundations
The recursive definition implies that a word $w$ is in $L$ if there is a sequence $w_0,\ldots,w_n=w$ such that $w_0$ is the empty word and for each $i=1,\ldots,n$, either $w_i = bw_{i-1}$ or $w_i = w_{i-1}aa$. This, in turn, implies that $L = b^*(aa)^*$.