We come now to the special cases of dyadic relations known as functions. It will serve a dual purpose in the present exposition to take the class of functions as a source of object examples for clarifying the more abstruse concepts of Relation Theory.
To begin, let us recall the definition of a local flag of a
-adic relation
In the case of a dyadic relation it is possible to simplify the notation for local flags in a couple of ways. First, it is often more convenient in the dyadic case to refer to
and
as
and
respectively. Second, the notation may be streamlined even further by making the following definitions:
In light of these conventions, the local flags of a dyadic relation may be comprehended under the following descriptions:
The following definitions are also useful:
A sufficient illustration is supplied by the earlier example
![]() |
(35) |
The local flag of
is displayed here:
![]() |
(36) |
The local flag of
is displayed here:
![]() |
(37) |
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