equivalence relation

Conditions 1, 2, and 3 say that is an equivalence relation.

In the next step, one imposes a set of equivalence relations.

The points to be identified are specified by an equivalence relation.

Equality is both an equivalence relation and a partial order.

Suppose we have some set S of objects, with an equivalence relation.

This provides a strong backing to the theory that Equivalence relations can form without language.

Both these relations are equivalence relations on the set of points.

Equivalence relations are a ready source of examples or counterexamples.

This is just an equivalence relation and holds among all objects of the considered domain.

The kernel of f is the equivalence relation thus defined.

This does not define bijective maps and equivalence relations however.

This defines an equivalence relation on the set of almost homomorphisms.

Similarity is an equivalence relation on the space of square matrices.

Note that the equivalence relation generated in this manner can be trivial.

Equivalence relations can construct new spaces by "gluing things together."

One can form the quotient of a pointed space X under any equivalence relation.

There are four different equivalence relations which may be defined on the set of functions from to .

Let be a set with an equivalence relation .

Consider the following equivalence relation on formulae in the free variables "x",.

For example, an equivalence relation possesses cycles but is transitive.

Samuel formalized the concept of an adequate equivalence relation in 1958.

Theorem: Let be an incidence structure with two equivalence relations and on the set of points (see above).

With any there is an associated equivalence relation :

These are two properties of an equivalence relation.

Therefore, the "ordered" concept of parallelism does not form an equivalence relation on lines.