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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 \,\text{at}\, 1}</math> as <math>L_{u \,\text{at}\, X}</math> and <math>L_{v \,\text{at}\, 2}</math> as <math>L_{v \,\text{at}\, Y}.</math>

In the case of a 2-adic relation <math>L \subseteq X_1 \times X_2 = X \times Y,</math> it is possible to simplify the notation for local flags in a couple of ways.  First, it is often easier in the 2-adic case to refer to <math>L_{u \,\text{at}\, 1}</math> as <math>L_{u \,\text{at}\, X}</math> and <math>L_{v \,\text{at}\, 2}</math> as <math>L_{v \,\text{at}\, Y}.</math>  Second, the notation may be streamlined even further by writing <math>L_{u \,\text{at}\, 1}</math> as <math>u \cdot L</math> and <math>L_{v \,\text{at}\, 2}</math> as <math>L \cdot v.</math>

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:

In 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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<math>\begin{array}{lll}

<math>\begin{array}{lll}

L_{u \,\text{at}\, X}

L_{u \,\text{at}\, X}

& = &

& = &

\{ (x, y) \in L : x = u \}

\{ (x, y) \in L : x = u \}

\text{the set of all ordered pairs in}~ L ~\text{incident with}~ u \in X.

\text{the set of all ordered pairs in}~ L ~\text{incident with}~ u \in X.

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\\[9pt]

L_{v \,\text{at}\, Y}

L_{v \,\text{at}\, Y}

& = &

& = &

\{ (x, y) \in L : y = v \}

\{ (x, y) \in L : y = v \}