Changes

====Note 3====

====Note 3====

Last time we computed what will variously be called the ''difference map'', the ''difference proposition'', or the ''local proposition'' <math>\operatorname{D}f_p</math> for the proposition <math>f(x, y) = xy\!</math> at the point <math>p\!</math> where <math>x = 1\!</math> and <math>y = 1.\!</math>

Last time we computed what will variously be called

the "difference map", the "difference proposition",

or the "local proposition" Df_p for the proposition

f(x, y) = xy at the point p where x = 1 and y = 1.

In the universe U = X x Y, the four propositions

In the universe <math>U = X \times Y,</math> the four propositions <math>xy,~ x\texttt{(}y\texttt{)},~ \texttt{(}x\texttt{)}y,~ \texttt{(}x\texttt{)(}y\texttt{)}</math> that indicate the "cells", or the smallest regions of the venn diagram, are called ''singular propositions''.  These serve as an alternative notation for naming the points <math>(1, 1),~ (1, 0),~ (0, 1),~ (0, 0),\!</math> respectively.

xy, x(y), (x)y, (x)(y) that indicate the "cells",

or the smallest regions of the venn diagram, are

called "singular propositions".  These serve as

an alternative notation for naming the points

<1, 1>, <1, 0>, <0, 1>, <0, 0>, respectively.

Thus, we can write Df_p = Df|p = Df|<1, 1> = Df|xy,

Thus, we can write Df_p = Df|p = Df|<1, 1> = Df|xy,

so long as we know the frame of reference in force.

so long as we know the frame of reference in force.