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MyWikiBiz, Author Your Legacy — Sunday September 07, 2025
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{| align="center" cellspacing="8" width="90%"
 
{| align="center" cellspacing="8" width="90%"
| <math>\texttt{(} S \texttt{)} ~=~ -\!S ~=~ X_i - S\!</math>
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| <math>\texttt{(} S \texttt{)} ~=~ -\!S ~=~ X_j - S\!</math>
 
|}
 
|}
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In case of ambiguities that are not resolved by context, indices may be used as follows.
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{| align="center" cellspacing="8" width="90%"
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| <math>\texttt{(} S \texttt{)}_j ~=~ X_j - S\!</math>
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|}
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In any case, the intended term can always be written out in full, as <math>X_j - S.\!</math>
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<h3 align="center">Fragments</h3>
    
<pre>
 
<pre>
When there is occasion for ambiguities that are not resolved by context then one must resort to indices on the bars, as "(S)i", or revert to writing out the intended term in full, as "(Xi  S)".
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R : (S(T)).
 
R : (S(T)).
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Fragments
      
Finally, the set of triples of dyadic relations, with pairwise cartesian products chosen in a pre arranged order from a collection of three sets {X, Y, Z}, is called the "dyadic explosion" of {X, Y, Z}.  This object is denoted as "Explo (X, Y, Z; 2)", read as the "explosion of XxYxZ by 2s" or simply as "X, Y, Z, choose 2", and is defined as follows:
 
Finally, the set of triples of dyadic relations, with pairwise cartesian products chosen in a pre arranged order from a collection of three sets {X, Y, Z}, is called the "dyadic explosion" of {X, Y, Z}.  This object is denoted as "Explo (X, Y, Z; 2)", read as the "explosion of XxYxZ by 2s" or simply as "X, Y, Z, choose 2", and is defined as follows:
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