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# The arbitrarily designated domains <math>X_1 = X\!</math> and <math>X_2 = Y\!</math> that form the widest sets admitted to the dyadic relation are referred to as the ''domain'' or ''source'' and the ''codomain'' or ''target'', respectively, of the relation in question.
# The arbitrarily designated domains <math>X_1 = X\!</math> and <math>X_2 = Y\!</math> that form the widest sets admitted to the dyadic relation are referred to as the ''domain'' or ''source'' and the ''codomain'' or ''target'', respectively, of the relation in question.
# The terms ''quota'' and ''range'' are reserved for those uniquely defined sets whose elements actually appear as the first and second members, respectively, of the ordered pairs in that relation. Thus, for a dyadic relation <math>L \subseteq X \times Y,\!</math> we identify <math>\operatorname{Quo} (L) = \operatorname{Quo}_1 (L) \subseteq X\!</math> with what is usually called the ''domain of definition'' of <math>L\!</math> and we identify <math>\operatorname{Ran} (L) = \operatorname{Quo}_2 (L) \subseteq Y\!</math> with the usual ''range'' of <math>L.\!</math>
# The terms ''quota'' and ''range'' are reserved for those uniquely defined sets whose elements actually appear as the first and second members, respectively, of the ordered pairs in that relation. Thus, for a dyadic relation <math>L \subseteq X \times Y,\!</math> we identify <math>\operatorname{Quo} (L) = \operatorname{Quo}_1 (L) \subseteq X\!</math> with what is usually called the ''domain of definition'' of <math>L\!</math> and we identify <math>\operatorname{Ran} (L) = \operatorname{Quo}_2 (L) \subseteq Y\!</math> with the usual ''range'' of <math>L.\!</math>
A ''partial equivalence relation'' (PER) on a set <math>X\!</math> is a relation <math>L \subseteq X \times X\!</math> that is an equivalence relation on its domain of definition <math>\operatorname{Quo} (L) \subseteq X.\!</math> In this situation, <math>[x]_L\!</math> is empty for each <math>x\!</math> in <math>X\!</math> that is not in <math>\operatorname{Quo} (L).\!</math> Another way of reaching the same concept is to call a PER a dyadic relation that is symmetric and transitive, but not necessarily reflexive. Like the “self-identical elements” of old that epitomized the very definition of self-consistent existence in classical logic, the property of being a self-related or self-equivalent element in the purview of a PER on <math>X\!</math> singles out the members of <math>\operatorname{Quo} (L)\!</math> as those for which a properly meaningful existence can be contemplated.
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A "moderate equivalence relation" (MER) on the "modus" M c X is a relation on X whose restriction to M is an equivalence relation on M. In symbols, R c XxX such that R|M c MxM is an equivalence relation. Notice that the subset of restriction, or modus M, is a part of the definition, so the same relation R on X could be a MER or not depending on the choice of M. In spite of how it sounds, a moderate equivalence relation can have more ordered pairs in it than the ordinary sort of equivalence relation on the same set.
A "moderate equivalence relation" (MER) on the "modus" M c X is a relation on X whose restriction to M is an equivalence relation on M. In symbols, R c XxX such that R|M c MxM is an equivalence relation. Notice that the subset of restriction, or modus M, is a part of the definition, so the same relation R on X could be a MER or not depending on the choice of M. In spite of how it sounds, a moderate equivalence relation can have more ordered pairs in it than the ordinary sort of equivalence relation on the same set.
