5 for details) shows that in a thin building parallelism is a transitive relation and thus is an

equivalence relation on the set of all the residues.

K] is said to be a NP-soft

equivalence relation if it is symmetric, transitive and reflexive.

In Section 3, we discuss a canonical way to put an

equivalence relation on P when it is a lattice and give three simple conditions which together imply that [chi](P, t) has nonnegative integral roots.

Assume that T is a nonempty closed subset of R and E is an

equivalence relation on T.

In this case, the word "means" functions as a Crel that establishes an

equivalence relation between "cupan," "cup" and actual cups.

We call [theta] the

equivalence relation ofthe extension and the equivalence classes of 9 the equivalence classes of the extension.

He pairs music and math concepts such as scales and modular arithmetic, octave identification and

equivalence relation, intervals and logarithms, equal temperament and exponents, overtones and integers, tone and trigonometry, and tuning and rationality.

Reflexive, symmetric, and transitive properties of a relation were also described for a relation on a set X, and an

equivalence relation was described as any relation on X that satisfies these three properties.

In the construction by Aharonov and Anandan one considers an open path in Hilbert space which is projected to a path in Ray space by use of the

equivalence relation in Eq.

Moreover, as Lewin's Chopin example demonstrates, a similar

equivalence relation is often assumed to play a role in tonal music.

Each story portrays an

equivalence relation visually and verbally without any student interaction.

The solution offered by Williamson's account is to replace the matching relation of the intiutive criterion by what he calls a "maximal M-relation", which is an

equivalence relation "included" in the matching relation than which no other similarly included

equivalence relation is "larger".