Changes

: <p><math>\begin{array}{lcrcl}

: <p><math>\begin{array}{lcrcl}

\operatorname{d}x_i ((u, v)) & = & (\!|\ x_i (u) & , & x_i (v)\ |\!) \\

\operatorname{d}x_i ((u, v)) & = & (\!|\ x_i (u) & , & x_i (v)\ |\!) \\

                             & = & x_i (u)       & + & x_i (v)      \\

                             & = &       x_i (u) & + & x_i (v)      \\

                             & = & x_i (v)       & - & x_i (u).      \\ \end{array}</math></p>

                             & = &       x_i (v) & - & x_i (u).      \\

\end{array}</math></p>

In the above transcription, the operator bracket of the form "<font face=system>(&nbsp;&hellip;&nbsp;,&nbsp;&hellip;&nbsp;)</font>" is a ''cactus lobe'', signifying ''just one false'', in this case among two boolean variables, while "+" is boolean addition in the proper sense of addition in GF(2), and is thus equivalent to "&ndash;", in the sense of adding the additive inverse.

In the above transcription, the operator bracket of the form <math>(\!| \ldots\ ,\ \ldots |\!)</math> is a ''cactus lobe'', in general signifying that just one of the arguments listed is false.  In the case of two arguments this is the same thing as saying that the arguments are not equal.  The plus sign signifies boolean addition, in the sense of addition in GF(2), and thus means the same thing in this context as the minus sign, in the sense of adding the additive inverse.

The above definition is equivalent to defining d''x''_''i''&nbsp;:&nbsp;(''B''&nbsp;&rarr;&nbsp;''X'')&nbsp;&rarr;&nbsp;'''B''' such that:

The above definition is equivalent to defining d''x''_''i''&nbsp;:&nbsp;(''B''&nbsp;&rarr;&nbsp;''X'')&nbsp;&rarr;&nbsp;'''B''' such that: