Regular expression notation clarification
Usually, $\Sigma^*$ denotes the set of all strings of length zero or more over the alphabet $\Sigma$. Thus, $\Sigma^* = \{\epsilon, a, b, c, aa, ab, ac, ba, bb, bc, ca, cb, cc, aaa, \ldots\}$, where $\epsilon$ denotes the empty string.

$\Sigma^+$ is the set of all strings of length $1$ or more over the alphabet $\Sigma$.  Thus, $\Sigma^+ := \Sigma^* - \{\epsilon\} = \{a,b,c,aa,\ldots\}$.