Sentence examples for relation on a from inspiring English sources

This definition is equivalent to the more usual one identifying the identity relation on a set A with the set of ordered pairs of the form <x,x> for x in A. The present definition proves more helpful in what follows.

A directed graph is a binary relation on a set \ V\).

The static and stagnation states are shown in - coordinates in Figure 6.9. Figure 6.11 shows this relation on a - diagram.

It has been analyzed independently the performance of two structural forms of the generalized model, i.e., a relation depending on an integration of the properties of the solvent and the ionic salt and a relation on a reduced property-basis.

Let be a binary relation on a set X and let A be a nonempty subset of X.

A binary relation on a set $A$ is a set of ordered pairs of elements of $A$, that is, a subset of $A\times A$.

For \(U \subseteq A\), let \(R\) be the binary relation on \(A + A = A \times \{0\} \cup A \times \{1\}\) given by It can be checked that \(R\) is an equivalence relation.

It therefore requires additional arguments to claim that among all possible order relations on a given set, one and only one has a special status.

After other attempts have failed, this one aims to improve our transatlantic relations on a case-by-case legislative basis.

Analytic relations on a dynamical orbit, 2008.

He also taught labor relations on a volunteer basis at the Xavier Labor Institute in New York City.