Positive Operator Value Measurement Question I'm attempting to understand some of the characteristics of Posiitive Operator Value Measurement (POVM). For instance in Nielsen and Chuang, they obtain a set of measurement operators $\{E_m\}$ for states $|\psi_1\rangle = |0\rangle, |\psi_2\rangle = (|0\rangle + |1\rangle)/\sqrt{2}$. The end up obtaining the following set of operators:
\begin{align*}
E_1 &\equiv \frac{\sqrt{2}}{1+\sqrt{2}} |1\rangle \langle 1 |, \\
E_2 &\equiv \frac{\sqrt{2}}{1+\sqrt{2}} \frac{(|0\rangle - |1\rangle) (\langle 0 | - \langle 1 |)}{2}, \\
E_3 &\equiv I - E_1 - E_2
\end{align*} 
Basically, I'm oblivious to how they were able to obtain these. I thought that perhaps they found $E_1$ by utilizing the formula:
\begin{align*}
E_1 = \frac{I - |\psi_2\rangle \langle \psi_2|}{1 + |\langle \psi_1|\psi_2\rangle|}
\end{align*}
However, when working it out, I do not obtain the same result. I'm sure it's something dumb and obvious I'm missing here. Any help on this would be very much appreciated.
Thanks.

Yes, those are the results but you have the subindexes swaped.
