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We claim that this holds \emph{also} for the sum of bits. For example  $$ (1+0)+1=1+1=0=1+(0+1)=1+0+1 \,.$$  The reader can verify our claim for any $a,b,c \in \Fb$.\\  In Algebra, any Any  time we have a set and a sum operation which satisfies the general property $$ \forall a,b,c, \quad (a+b)+c\,=\,a+(b+c)\,=\,a+b+c \,,$$  we say that the operation is \emph{associative}.\\  Therefore, we can conclude that both the sum in $\ZZ$ and the sum in $\Fb$ are associative operations.