deletions | additions       diff --git a/Splitting the Num.tex b/Splitting the Num.tex  index 2adba3e..1b44298 100644  --- a/Splitting the Num.tex  +++ b/Splitting the Num.tex 
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that is by definition. It is a requirement of the theory that when $\theta=\varphi=0$, then, $\hat{e_{-}}=\hat{e_{|}}=\hat{e_{+}}$ and equation [ABOVE] reduces back to $-n=-n$.  If one required the numbers to be held on the complex plane then the basis elements are \begin{equation}  \hat{e_{-}} = \hat{e_{+}}\exp(i\theta) -\hat{e_{+}}\exp(i\theta)  \\ \hat{e_{|}} = \hat{e_{+}}\exp(-i\varphi) -\hat{e_{+}}\exp(-i\varphi)  \\ \end{equation}