Given this language, I was supposed to find the Regular Expression that represented it. Having given up and getting the answer later (below) I couldn't understand the regular expression.
Given this answer:
Why is {1,2} and {2} part of the regular expression?
EDIT: I dont know if Understanding Regular Expressions is a more appropriate title. My issue is that I dont understand the solution for this given problem.
It seems that $L\{1,2\}$ in this syntax means that the expressions produces words of the form $w$ or $w\cdot v$ for $w,v\in L$. Hence the regular expression you presented produces the empty word ($\epsilon$), all words of length $1$ or $2$ (with $(0\mid 1)\{1,2\}$), and words of length $\geq 3$ with the third character being $0$. Another way to put it, a regular expression that produces the same language with less syntactic sugar is
$$\epsilon + (0+1) + (0+1)(0+1) + (0+1)(0+1)0(0+1)^*$$