equivalence class

Every ordered basis lives in one equivalence class or another.

Such an equivalence class is called an orbit (in ).

Do they also fall into a single equivalence class?

Real numbers are defined as the equivalence classes of this relation.

When the boundary is not known, we begin to get equivalence classes of phrases.

We shall show that each equivalence class of words contains exactly one reduced word.

Together, these equivalence classes are the elements of a quotient group.

One can simply take the equivalence classes as a base for the topology.

The equivalence classes are the circles with centre the origin.

Then we obtain the following much coarser equivalence class structure.

The equivalence classes of the new and of are shown below.

We can define the action of one equivalence class on another, and so we get a group.

For instance, there can be more than one Nielsen equivalence class of generators.

Charts map equivalence classes to points of a single patch.

Set of all equivalence classes for this relation is .

The number of elements in each equivalence class is the natural number n.

A representative set is designated for each equivalence class.

The group operation for the above equivalence class is as follows:

An equivalence class of valuations of a field is called a place.

The free object then consists of the set of equivalence classes.

We can collect function germs together to construct equivalence classes.

Can we find representatives for equivalence classes of processes?

Canonical forms are generally used to make operating with equivalence classes more effective.

In the other direction, suppose that R has finitely many equivalence classes.

Let denote the equivalence class to which a belongs.