Below you will find example sentences with "ordered set". The examples show how this phrase is used in natural context and which words often surround it.

Ordered Set in a sentence

Corpus data

  • Displayed example sentences: 20
  • Discovered as a combination around: ordered
  • Corpus frequency in the collocation scan: 10
  • Phrase length: 2 words
  • Average sentence length: 28.9 words

Words in this phrase

ordered set

Meanings of words in this phrase

  • ordered can mean: In order, not messy, tidy. Frequent word
  • set can mean: To put (something) down, to rest. Very common word

Sentence profile

  • Phrase position: 6 start, 12 middle, 2 end
  • Sentence types: 20 statements, 0 questions, 0 exclamations

Usage patterns

These patterns show short text windows around the phrase in the example sentences:

a partially ordered set in which 2× a linearly ordered set a simply 1× a partial ordered set vs on 1× a partially ordered set is contained 1× a partially ordered set or poset 1× a partially ordered set poset p 1× a partially ordered set with greatest 1× a partially ordered set y that 1×

Sentence openings and endings

Common sentence openings:

a partial order 1× a set paired 1× a tuple is 1× a well ordered 1× an abstract polyhedron 1× clearly then the 1×

Common sentence endings:

a bigger one 1× a chain e 1× and an infimum 1× and lower bounds 1× be non empty 1× comprises all numbers 1×

Context words

These words often appear near this phrase in the example sentences:

partially 10× order 9× subset 7× totally 6× elements 5× chain 4× upper 3× poset 3× element 3× examples 3× numbers 3× cofinality 3×

Related phrases

instruction set empty set set aside set theory set forth skill set

Phrases around this combination

Just before it in the phrase index:

order requiring orange juice orange high orange county orange bowl oral tradition

Just after it in the phrase index:

ordinary citizens ordinary people ordinary shares oregon ducks oregon university organ donation

Other phrases with the same pattern

Same ending:

instruction set empty set skill set

Corpus analysis

  • The phrase "ordered set" has 2 words and usually appears in the middle in these examples. The average sentence has 28.9 words and is mostly made up of statements.
  • Around this phrase, patterns and context words such as a partially ordered set in which, a linearly ordered set a simply, partially, order and subset stand out.
  • In the phrase index, this combination connects with instruction set, empty set and set aside, linking the page to nearby combinations.

Example types with ordered set

This selection groups the examples by length and sentence type, making usage of the full phrase easier to scan:

Short example sentences

A tuple is an ordered set of attribute values. (9 words)

Every finite subset of a non-empty totally ordered set has both upper and lower bounds. (16 words)

Clearly then, the existence of an assignment of an ordinal to every well-ordered set requires replacement as well. (19 words)

Longer example sentences

A well-ordered set as topological space is a first-countable space if and only if it has order type less than or equal to ω 1 ( omega-one ), that is, if and only if the set is countable or has the smallest uncountable order type. (46 words)

For if Ω were consistent, then as a well-ordered set, a number δ would correspond to it which would be greater than all numbers of the system Ω; the number δ, however, also belongs to the system Ω, because it comprises all numbers. (44 words)

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. (41 words)

Example sentences (20)

A set paired with a total order is called a totally ordered set, a linearly ordered set, a simply ordered set, or a chain.

The question of whether any ordered subset of a partially ordered set is contained in a maximal ordered subset was answered in the positive by Hausdorff using the well-ordering theorem.

Thus, constructing the set of Dedekind cuts serves the purpose of embedding the original ordered set S, which might not have had the least-upper-bound property, within a (usually larger) linearly ordered set that does have this useful property.

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.

Then there exists a partially ordered set, or poset, P such that every totally ordered subset has an upper bound, and every element has a bigger one.

The restricted principle "Every partially ordered set has a maximal totally ordered subset" is also equivalent to AC over ZF.

Examples Examples of directed sets include: * The set of natural numbers N with the ordinary order ≤ is a directed set (and so is every totally ordered set ).

The cofinality of a set of ordinals or any other well-ordered set is the cofinality of the order type of that set.

Advertentie

An abstract polyhedron is a certain kind of partially ordered set (poset) of elements, such that adjacencies, or connections, between elements of the set correspond to adjacencies between elements (faces, edges, etc.) of a polyhedron.

A well-ordered set as topological space is a first-countable space if and only if it has order type less than or equal to ω 1 ( omega-one ), that is, if and only if the set is countable or has the smallest uncountable order type.

Examples * The cofinality of a partially ordered set with greatest element is 1 as the set consisting only of the greatest element is cofinal (and must be contained in every other cofinal subset).

Some authors use "(ultra)filter" of a partial ordered set" vs. "on an arbitrary set"; i.e. they write "(ultra)filter on X" to abbreviate "(ultra)filter of ℘(X)".

That is, : Note that the set X needs to be defined as a subset of a partially ordered set Y that is also a topological space in order for these definitions to make sense.

A partial order under which every pair of elements is comparable is called a total order or linear order; a totally ordered set is also called a chain (e.

A tuple is an ordered set of attribute values.

Clearly then, the existence of an assignment of an ordinal to every well-ordered set requires replacement as well.

Definition A partially ordered set (poset) P is said to satisfy the ascending chain condition (ACC) if every strictly ascending sequence of elements eventually terminates.

Empty chain as boundary case In the formulation of Zorn's lemma above, the partially ordered set P is not explicitly required to be non-empty.

Every finite subset of a non-empty totally ordered set has both upper and lower bounds.

For if Ω were consistent, then as a well-ordered set, a number δ would correspond to it which would be greater than all numbers of the system Ω; the number δ, however, also belongs to the system Ω, because it comprises all numbers.

Advertentie