maximal element

This leaves open the possibility that there are many maximal elements.

A set can have several maximal elements without having a greatest element.

The Smith set is the maximal element of the beat-or-tie order.

We first prove it for the case where X is chain complete and has no maximal element.

The infinite decimal numbers are the maximal elements within this order.

The set of maximal elements of a social preference is called the core.

Thus an admissible decision rule is a maximal element with respect to the above partial order.

While this relation is not necessarily transitive, it does always contain at least one maximal element.

If a poset has more than one maximal element, then these elements will not be mutually comparable.

The game starts with the maximal element (with four sides) in the center of the gaming board.

The existence of a maximal elements is proved via Zorn's lemma.

That is, we should regard a rule as choosing the maximal elements ("best" alternatives) of some social preference.

S is empty or every partial ordering of S contains a maximal element.

So, assume that has at least one element, and let be a maximal element of .

(the set of maximal elements of with respect to ):

It is a simplified version of this dynamic problem, where one requires to delete only the maximal element.

That is, it is a maximal element connected subgraph.

The dual notion is called maximal element.

However, if it has a greatest element, it can't have any other maximal element.

In this case, the unique maximal element can be shown to coincide with above, and is called the completion of .

In the sections below the difference between suprema, maximal elements, and minimal upper bounds is stressed.

Noetherian module: every nonempty collection of submodules has a maximal element.

Finding a maximal ideal is the same as finding a maximal element in P.

In general, if an ordered set S has a greatest element m, m is a maximal element.

Thus the cofinality of a finite partially ordered set is equal to the number of its maximal elements.