deletions | additions       diff --git a/Splitting the Num.tex b/Splitting the Num.tex  index 7025f26..a8a6451 100644  --- a/Splitting the Num.tex  +++ b/Splitting the Num.tex 
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Letting $\theta=\frac{\pi}{3}=\varphi$. It is still true that $-n\cdot-n=n^2$.  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_{|}} = -\hat{e_{+}}\exp(-i\varphi) \\  \end{equation}  The components then transform according to the algebra with Cayley table  \begin{equation}  \begin{array}{| c | c c c |} 
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\end{array}  \end{equation}  It needs to be true that from equation ...  $-n \cdot -n =n^2$  A suggested Cayley table by D.Worthy is  \begin{equation}  \begin{array}{| c | c c c |} 
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\end{array}  \end{equation}  There is a suggested set of angles in which $\theta=\varphi=\frac{\pi}{3}$ for symmetric properties by R.Garner. 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_{|}} = -\hat{e_{+}}\exp(-i\varphi) \\  \end{equation}