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MyWikiBiz, Author Your Legacy — Wednesday November 20, 2024
Jump to navigationJump to search→Duality : logical and topological: redo spaces -- TeX "~" doesn't work here anymore
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This can be written inline as <math>{}^{\backprime\backprime} \texttt{(~(~)~)} = \quad {}^{\prime\prime}\!</math> or set off in a text display as follows:
This can be written inline as <math>{}^{\backprime\backprime} \texttt{( ( ) )} = \quad {}^{\prime\prime}\!</math> or set off in a text display as follows:
{| align="center" cellpadding="10"
{| align="center" cellpadding="10"
| width="33%" | <math>\texttt{(~(~)~)}\!</math>
| width="33%" | <math>\texttt{( ( ) )}\!</math>
| width="34%" | <math>=\!</math>
| width="34%" | <math>=\!</math>
| width="33%" |
| width="33%" |
This ritual is called ''traversing'' the tree, and the string read off is called the ''traversal string'' of the tree. The reverse ritual, that passes from the string to the tree, is called ''parsing'' the string, and the tree constructed is called the ''parse graph'' of the string. The speakers thereof tend to be a bit loose in this language, often using ''parse string'' to mean the string that gets parsed into the associated graph.
This ritual is called ''traversing'' the tree, and the string read off is called the ''traversal string'' of the tree. The reverse ritual, that passes from the string to the tree, is called ''parsing'' the string, and the tree constructed is called the ''parse graph'' of the string. The speakers thereof tend to be a bit loose in this language, often using ''parse string'' to mean the string that gets parsed into the associated graph.
We have treated in some detail various forms of the initial equation or logical axiom that is formulated in string form as <math>{}^{\backprime\backprime} \texttt{(~(~)~)} = \quad {}^{\prime\prime}.~\!</math> For the sake of comparison, let's record the plane-embedded and topological dual forms of the axiom that is formulated in string form as <math>{}^{\backprime\backprime} \texttt{(~)(~)} = \texttt{(~)} {}^{\prime\prime}.\!</math>
We have treated in some detail various forms of the initial equation or logical axiom that is formulated in string form as <math>{}^{\backprime\backprime} \texttt{( ( ) )} = \quad {}^{\prime\prime}.~\!</math> For the sake of comparison, let's record the plane-embedded and topological dual forms of the axiom that is formulated in string form as <math>{}^{\backprime\backprime} \texttt{( )( )} = \texttt{( )} {}^{\prime\prime}.\!</math>
First the plane-embedded maps:
First the plane-embedded maps:
