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In the case of a 2-adic relation <math>L \subseteq X_1 \times X_2 ~=~ X \times Y,</math> we can reap the benefits of a radical simplification in the definitions of the local flags.  Also in this case, we tend to refer to <math>L_{u \star 1}</math> as <math>L_{u \star X}</math> and <math>L_{v \star 2}</math> as <math>L_{v \star Y}.</math>

In the case of a 2-adic relation <math>L \subseteq X_1 \times X_2 = X \times Y,</math> we can reap the benefits of a radical simplification in the definitions of the local flags.  Also in this case, we tend to refer to <math>L_{u \star 1}</math> as <math>L_{u \star X}</math> and <math>L_{v \star 2}</math> as <math>L_{v \star Y}.</math>

In the light of these considerations, the local flags of a 2-adic relation ''L''&nbsp;&sube;&nbsp;''X''&nbsp;&times;&nbsp;''Y'' may be formulated as follows:

In the light of these considerations, the local flags of a 2-adic relation <math>L \subseteq X \times Y</math> may be formulated as follows:

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A sufficient illustration is supplied by the earlier example ''E''.

A sufficient illustration is supplied by the earlier example <math>E.\!</math>

<pre>

<pre>

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</pre>

</pre>

The local flag ''E''_3.''X'' is displayed here:

The local flag ''E''_3.''X'' is displayed here:

<pre>

<pre>

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</pre>

</pre>

The local flag ''E''_2.''Y'' is displayed here:

The local flag ''E''_2.''Y'' is displayed here:

<pre>

<pre>

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</pre>

</pre>

===Commentary Note 11.8===

===Commentary Note 11.8===