this is for holding javascript data
Massimiliano Sala edited bits1.tex
over 7 years ago
Commit id: c0d6d4addde380be633d0c98f774da0f871d326f
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index 55dad9a..e3bf5a1 100644
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$$(2+3)+4=5+4=9=2+7=2+(3+4),$$
so we can write also $9=2+3+4$, omitting the parentheses. Actually, this holds for any three numbers in $\ZZ$.
\\
The same property also We claim that this holds
\emph{also} for the sum of bits. For example
$$
(1+0)+1=1+1=0=1+(0+1)=1+0+1.$$ (1+0)+1=1+1=0=1+(0+1)=1+0+1 \,.$$
The reader can verify
that it is true our claim for
each any $a,b,c \in \Fb$.\\
This property can be formalized by saying that both the sum in $\ZZ$ and the sum in $\Fb$ are \emph{associative}. In formulas, we say that $\forall a,b,c$ (which are elements of $\ZZ$ or of $\Fb$), we have
$$(a+b)+c=a+(b+c)=a+b+c.$$
\smallskip