deletions | additions       diff --git a/Prime Factors.tex b/Prime Factors.tex  index e633efd..c405a57 100644  --- a/Prime Factors.tex  +++ b/Prime Factors.tex 
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\prod_{p \in \mathbb{P}} p^{-\infty} = \prod_{p \in \mathbb{P}} \prod_{k=1}^{\infty} \frac{1}{p} = \infty  \end{equation}  The useful property of these results in that integer fractions can be expressed as states $|1,-1,0,..>=\frac{2}{3}$ for example. The operation of addition for states is not simple!  \subsection{Operators}  Now to include bosonic style operators. Counting could be performed from 1 as \begin{equation}  a^+_1|0,0>=|1,0> \\  a^+_2a_1|1,0>=|0,1> \\  a^+_1a^+_1a_2|0,1>=|2,0> \\  a^+_3a_1a_1|2,0>=|0,0,1> \\  a^+_2a^+_1a_3|0,0,1>=|1,1>  \end{equation}