Jon Awbrey · @Inquiry
129 followers · 624 posts · Server mathstodon.xyz
Jon Awbrey · @Inquiry
109 followers · 499 posts · Server mathstodon.xyz
Jon Awbrey · @Inquiry
100 followers · 428 posts · Server mathstodon.xyz

• 15
oeis.org/w/index.php?title=Log

We have treated in some detail various forms of the or whose text expression is \(``\texttt{((}~\texttt{))}~=~".\) For comparison, let's record the plane-embedded & forms of the axiom whose text expression is \(``\texttt{(}~\texttt{)(}~\texttt{)}=\texttt{(}~\texttt{)}".\)

Figure 7 reproduces the planar form of the equation we first saw in Figure 1.

Figure 7
oeis.org/w/images/b/b4/Logical

#Peirce #logic #topologicaldual #logicalaxiom #initialequation #LogicalGraphs

Last updated 2 years ago

Jon Awbrey · @Inquiry
96 followers · 408 posts · Server mathstodon.xyz
Jon Awbrey · @Inquiry
96 followers · 397 posts · Server mathstodon.xyz

• 10
oeis.org/w/index.php?title=Log

Figure 4 illustrates the mapping of to by overlaying the alpha graphs of Figure 2 with their corresponding dual graphs.

Figure 4. Alpha Graphs and Dual Graphs for the Second
oeis.org/w/images/3/3f/Logical

It is usual to think of ourselves as observing alpha graphs from the outermost region of the plane and we mark that by mapping that region to a node singled out as the “root” of the dual.

#Peirce #logic #initialequation #dualgraphs #alphagraphs #LogicalGraphs

Last updated 2 years ago