Then, in Section 3 we discuss the notion of parallel residues and describe the buildings in which parallelism is an equivalence relation
Since we want a poset, it is necessary to require two more properties of our equivalence relation
A triple (t, E, [alpha]) is called a time scale if t is a nonempty closed subset of r and E is an arranged equivalence relation
This can be seen as further support for the RFT approach as Barnes et al suggested that symbol-referent relations (in natural language) are functionally similar to equivalence relations
in a matching-to-sample context.
Overall, most participants indicated that they would include more examples in the lesson, including more examples of equivalence relations
, more mathematical examples, and more examples generated and constructed by students in the classroom.
Clearly, T/I relation is an equivalence relation
Let R be an equivalence relation
, where its partition of U is given by
This internal category will be a groupoid precisely when the given reflexive and transitive relation R is symmetric, so that if in C every internal category is an internal groupoid, then all of its internal reflexive and transitive relations are equivalence relations
The following theorem due to Hivert and Nzeutchap  shows that an equivalence relation
This sentence has an air of authority about it; the concept of an equivalence relation
is well established in many fields and is intersubjectively defined as a (Type 1) relation that is symmetric, reflexive, and transitive.
Now let m : X' [right arrow] X be a monomorphism in C such that the monomorphism U(m) is normal to the equivalence relation
R in D, namely such that we have a discrete fibration in D:
As described above, when an equivalence relation
is established, arbitrary stimuli are substitutable for one another such that a = b.