In the Eden of the East opening, there are a lot of quotes from different sources. The only one I know the origin of is "The abuse of greatness is when it disjoins remorse from power," which is from Julius Caesar by William Shakespeare. I don't know what the other quotes that show up on the screen are from or are in reference to. Can someone tell me?


Question: Need help with a subsets problem
Answer: The subsets of $X$ not containing $1$ are the subsets of $\{2,3,...,n\}$. This set has $2^{n-1}$ susbsets, because it has $n-1$ elements. The sets that do contain $1$ are all the subsets of $X$ that don't not contain $1$ (double negative!). There are $2^n$ subsets of $X$ and $2^{n-1}$ don't contain $1$, so the remaining $2^n-2^{n-1}=2^{n-1}$ must contain $1$.