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\end{equation}  This appears fine "mathematically". But what of the interpretation. Does there exist quantities like s^+s and what do the mean? There exist eigenoperators \begin{equation}  r^+s|n>=\sqrt{n+\frac{1}{2}}|n> \\  s^+r|n>=\sqrt{n}|n>  \end{equation}  Which means a double application of s^+r is equal to the number operator N=a^+a. But, from the old definitions \begin{equation}  N=a^+a \\  N=s^+r^+sr=s^+r^+sr  \end{equation}  suppose that $a=xyz$ and $a^+=x^+y^+z^+$ or similar. We could define fractional operators for example \begin{equation}  z|n>=\sqrt[6]{n}|n-\frac{1}{3}> \\