Let’s take a closer look at the numerical incidence properties of relations, concentrating on the assorted regularity conditions defined in the article on Relation Theory.
For example, has the property of being if and only if the cardinality of the local flag is equal to for all in coded in symbols, if and only if for all in
In like fashion, one may define the numerical incidence properties and so on. For ease of reference, a number of such definitions are recorded below.
Clearly, if any relation is on one of its domains and also on the same domain, then it must be on that domain, in short, at
For example, let and and consider the dyadic relation bigraphed below.
We observe that is 3-regular at and 1-regular at
- Peirce’s 1870 Logic of Relatives • Part 1 • Part 2 • Part 3 • References
- Logic Syllabus • Relational Concepts • Relation Theory • Relative Term