this is for holding javascript data
Giancarlo Rinaldo edited bits1.tex
over 7 years ago
Commit id: 63419456467c6217d3508535abcdb6e394714d87
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Consider now $2,3 \in \ZZ$. We know that $2\cdot 3=3\cdot 2=6$ and this holds for every pair of integers.
We claim the same for bits, since for example
$$ 0\cdot 1\,=\,1\cdot
0\,=\,1\,.$$ 0\,=\,0\,.$$
We leave, as an exercise to the reader, to verify this for each $a,b \in \Fb$.\\
Again, this property can be formalized by saying that both the product in $\ZZ$ and the product in $\Fb$ are \emph{commutative}. In formulas, we say that for any $ a,b$ (which are elements of $\ZZ$ or of $\Fb$), we have
$$a\cdot b=b\cdot a.$$