Can anyone explain to me how the following is true for any language?
$$L^+ = LL^* = L^*L$$
I'm confused because $L^*$ is the set of all words including the empty string, while $L^+$ is the set of all words excluding the empty string. I don't understand how concatenating $L^*$ with $L$ makes it equal to $L^+$. What happens to the empty string? Thank you.