Changes

Next let's re-examine the ''numerical incidence properties'' of relations, concentrating on the definitions of the assorted regularity conditions.

Next let's re-examine the ''numerical incidence properties'' of relations, concentrating on the definitions of the assorted regularity conditions.

For instance, <math>L\!</math> is said to be <math>^{\backprime\backprime} c\text{-regular at}~ j \, ^{\prime\prime}</math> if and only if the cardinality of the local flag <math>L_{x \,\text{at}\, j}</math> is equal to <math>c\!</math> for all <math>x \in X_j,</math> coded in symbols, if and only if <math>|L_{x \,\text{at}\, j}| = c</math> for all <math>x \in X_j.</math>

For example, <math>L\!</math> is said to be <math>^{\backprime\backprime} c\text{-regular at}~ j \, ^{\prime\prime}</math> if and only if the cardinality of the local flag <math>L_{x \,\text{at}\, j}</math> is equal to <math>c\!</math> for all <math>x \in X_j,</math> coded in symbols, if and only if <math>|L_{x \,\text{at}\, j}| = c</math> for all <math>x \in X_j.</math>

In a similar fashion, one can define the numerical incidence properties <math>^{\backprime\backprime}(< c)\text{-regular at}~ j \, ^{\prime\prime},</math> <math>^{\backprime\backprime}(> c)\text{-regular at}~ j \, ^{\prime\prime},</math> and so on.  For ease of reference, I record a few of these definitions here:

In a similar fashion, it is possible to define the numerical incidence properties <math>^{\backprime\backprime}(< c)\text{-regular at}~ j \, ^{\prime\prime},</math> <math>^{\backprime\backprime}(> c)\text{-regular at}~ j \, ^{\prime\prime},</math> and so on.  For ease of reference, a few of these definitions are recorded below.

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