deletions | additions       diff --git a/Dirac notation.tex b/Dirac notation.tex  index 862f8c2..7e844fb 100644  --- a/Dirac notation.tex  +++ b/Dirac notation.tex 
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\end{equation}  etc. The bigger the closing number the larger the spread from the expectation.  The state representation as substates remains constant, and with that the number $5$ can be seen as no more than a linear combination of $2$ and $3$... Trying this with other numbers ... \begin{equation}  \ket{3}=(0\ket{2}+2\ket{3}) \\  \ket{3}=(3\ket{2}+0\ket{3}) \\  \ket{5}=(2\ket{2}+2\ket{3}) \\  \ket{5}=(5\ket{2}+0\ket{3}) \\  \ket{7}=(1\ket{2}+4\ket{3}) \\  \ket{7}=(4\ket{2}+2\ket{3}) \\  \ket{7}=(7\ket{2}+0\ket{3}) \\  \ket{11}=(2\ket{2}+6\ket{3}) \\  \ket{11}=(5\ket{2}+4\ket{3}) \\  \ket{11}=(8\ket{2}+2\ket{3}) \\  \ket{11}=(11\ket{2}+0\ket{3}) \\  \ket{13}=(1\ket{2}+8\ket{3}) \\  \ket{13}=(4\ket{2}+6\ket{3}) \\  \ket{13}=(7\ket{2}+4\ket{3}) \\  \ket{13}=(10\ket{2}+2\ket{3}) \\  \ket{13}=(13\ket{2}+0\ket{3}) \\  \end{equation}  Ah... there are multiple ways of expressing states... Some of them are iffy. Is zero a valid coefficient... We could remove these, but they are somewhat feasible, sometimes you look for a particle and there isn't one? They also will have a high spread associated with them.  Interesting, that there (at the moment appears to be $n$ ways to generate the $n^{th}$ prime vector.