#topologicaldual — Public Fediverse posts

#LogicalGraphs • 15
• https://oeis.org/w/index.php?title=Logical_Graphs&stable=0&redirect=no#Duality

We have treated in some detail various forms of the #InitialEquation or #LogicalAxiom whose text expression is \(``\texttt{((}~\texttt{))}~=~".\) For comparison, let's record the plane-embedded and #TopologicalDual 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
• https://oeis.org/w/images/b/b4/Logical_Graph_Figure_7_Visible_Frame.jpg

#Logic #Peirce

#LogicalGraphs • 15
• https://oeis.org/w/index.php?title=Logical_Graphs&stable=0&redirect=no#Duality

We have treated in some detail various forms of the #InitialEquation or #LogicalAxiom whose text expression is \(``\texttt{((}~\texttt{))}~=~".\) For comparison, let's record the plane-embedded and #TopologicalDual 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
• https://oeis.org/w/images/b/b4/Logical_Graph_Figure_7_Visible_Frame.jpg

#Logic #Peirce

#LogicalGraphs • 15
• https://oeis.org/w/index.php?title=Logical_Graphs&stable=0&redirect=no#Duality

We have treated in some detail various forms of the #InitialEquation or #LogicalAxiom whose text expression is \(``\texttt{((}~\texttt{))}~=~".\) For comparison, let's record the plane-embedded and #TopologicalDual 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
• https://oeis.org/w/images/b/b4/Logical_Graph_Figure_7_Visible_Frame.jpg

#Logic #Peirce

#LogicalGraphs • 15
• https://oeis.org/w/index.php?title=Logical_Graphs&stable=0&redirect=no#Duality

We have treated in some detail various forms of the #InitialEquation or #LogicalAxiom whose text expression is \(``\texttt{((}~\texttt{))}~=~".\) For comparison, let's record the plane-embedded and #TopologicalDual 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
• https://oeis.org/w/images/b/b4/Logical_Graph_Figure_7_Visible_Frame.jpg

#Logic #Peirce

#LogicalGraphs • 9
• https://oeis.org/w/index.php?title=Logical_Graphs&stable=0&redirect=no#Duality

From the #AlphaGraph and its text expression we turn to representing their common form in computer memory, where it can be manipulated with the greatest of ease. We begin by transforming the alpha graph into its #TopologicalDual. Planar regions of the alpha graph are mapped into points (or nodes) of the #DualGraph & boundaries between those planar regions are mapped into lines (or edges) connecting those points.

#Logic #Peirce #AlphaGraphs #Duality