Subsets in a sentence

A divisio is not an extensional definition, but an exhaustive list of subsets of a set, in the sense that every member of the "divided" set is a member of one of the subsets.

A partition of a set S is a set of nonempty subsets of S such that every element x in S is in exactly one of these subsets.

For any infinite sets A and B, if there is an injection from A to B then there is an injection from subsets of A to subsets of B. Thus for any infinite cardinals A and B, : If A and B are finite, the stronger inequality : holds.

For instance, a lattice is a partially ordered set in which all finite subsets have both a supremum and an infimum, and a complete lattice is a partially ordered set in which all subsets have both a supremum and an infimum.

For this reason, one considers instead a smaller collection of privileged subsets of X. These subsets will be called the measurable sets.

Graphs Graphs have path connected subsets, namely those subsets for which every pair of points has a path of edges joining them.

In other words, the power set of the empty set is the set containing the empty set and the power set of any other set is all the subsets of the set containing some specific element and all the subsets of the set not containing that specific element.

It must assign 0 to the empty set and be ( countably ) additive: the measure of a 'large' subset that can be decomposed into a finite (or countable) number of 'smaller' disjoint subsets, is the sum of the measures of the "smaller" subsets.

Rather, one observes pockets of dense connections (direct interactions) among small subsets of components, but only loose connections between these densely connected subsets.

Standardized subsets Several subsets of Unicode are standardized: Microsoft Windows since Windows NT 4.0 supports WGL-4 with 652 characters, which is considered to support all contemporary European languages using the Latin, Greek, or Cyrillic script.

This equivalence is a consequence of the facts that compact subsets of Hausdorff spaces are closed, and closed subsets of compact spaces are compact.

While compact subsets of Hausdorff spaces are always closed, this is not true for paracompact subsets.

Upon close of the transaction, we certainly expect to apply asset level financing on certain subsets of their portfolio.

The funds track a series of indexes that include duration-constrained subsets of U.S. Treasurys.

The latest round of relief is part of a strategy by the White House to take smaller, targeted actions for certain subsets of borrowers after the Supreme Court struck down a far more ambitious plan to wipe out $400 billion in debt last year.

While serotonin is often billed as a “feel-good brain chemical,” Lowry notes that certain subsets of serotonin neurons can, when activated, prompt anxiety-like responses in animals.

Ashton asked Hahn if people like pregnant women, children, people with kidney failure and other subsets of people who were not represented in the phase three clinical vaccine trials will be advised to take the vaccine.

Businesses in subsets of the industry such as fuel shippers, oilfield service companies and Alyeska Pipeline Service Co. offered comments about the regulations being too rigid, unclear or outdated.

Several subsets of Christians support Biden over Trump, including 52 percent of Catholics and 88 percent of Black Protestants.

It has three subsets: Remotely Piloted Aircraft (RPA), Autonomous Aircraft, and Model Aircraft.