Consider the identity

$\displaystyle 0 = \frac{1}{z-1} + \frac{1}{1-z} = \frac{1}{z}\frac{1}{1-\frac{1}{z}}+\frac{1}{1-z} = \sum_{n=1}^{infinity} \frac{1}{z^n} + \sum_{n=0}^{infinity}z^n=\sum_{-infinity}^{infinity} z^n$

Does this contradict the uniqueness of the Laurent Series?

due in 15 hours haha

thanks ahead of time if anyone does work on this