deletions | additions       diff --git a/bits1.tex b/bits1.tex  index 2f61b85..422f418 100644  --- a/bits1.tex  +++ b/bits1.tex 
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It is of utmost interest to observe that bits behave like rational numbers rather than integers.   Indeed, $1 \cdot 1=1$ in $\Fb$, but we cannot find any bit $b$ such that $1 \cdot b = b \cdot 1 =1$.  \\  We can formalize this property, saying that each nonzero element of $\QQ$ (respectively $\Fb$) has a \emph{multiplicative inverse}, i.e.  $$\forall i.e.\\  $\forall  a \in \QQ\setminus \{0\}\, (\textrm{ \{0\}(\textrm{  resp } \Fb\setminus \{0\}),\, \exists \{0\}),\exists  a^{-1} \in \QQ\setminus \{0\}\, \{0\}  (\textrm{ respectively } \Fb\setminus \{0\}) \textrm{ s.t. } a\cdot a^{-1} =a^{-1} \cdot a =1. $$ $  In $\Fb$, the (multiplicative) inverse of $1$ is $1$ and $0$ has no (multiplicative) inverse  (but keep in mind that the opposite of $0$ exists: $-0=0$ in $\Fb$).  \\