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Get to know Cofinality better with 8 real example sentences, the meaning.

Rare word

Cofinality in a sentence

Cofinality meaning

  1. The least of the cardinalities of the cofinal subsets of a partially ordered set.
  2. The property of being cofinal.

Using Cofinality

  • The main meaning on this page is: The least of the cardinalities of the cofinal subsets of a partially ordered set. | The property of being cofinal.
  • In the example corpus, cofinality often appears in combinations such as: the cofinality, cofinality of, of cofinality.

Context around Cofinality

  • Average sentence length in these examples: 24.8 words
  • Position in the sentence: 5 start, 2 middle, 1 end
  • Sentence types: 8 statements, 0 questions, 0 exclamations

Often before:

different 1×

Often after:

depends 1× introduced 1×

Sentence patterns with Cofinality

These short patterns come directly from the example sentences and show how the word is often embedded:

0 the cofinality of any 1× 1 the cofinality of any 1× concept of cofinality that hausdorff 1× examples the cofinality of a 1× have different cofinality 1× is the cofinality of b 1× is the cofinality of the 1× notion of cofinality introduced by 1×

Sentence openings and endings

Common sentence openings:

the cofinality of 2× examples the cofinality 1× if two cofinal 1× in 1904 hausdorff 1× of fundamental importance 1× this demonstrates that 1×

Common sentence endings:

for aleph exponentiation 1× have different cofinality 1× infinite regular cardinal 1× its maximal elements 1× of that set 1× other cofinal subset 1×

Words around Cofinality

Just before it in the word index:

cofinal 5 cofield 8 cofie 5 cofidis 6 coffs 84 coffren 2

Just after it in the word index:

cofinite 2 cofiwch 2 coforge 3 cofound 3 cofounded 24 cofounder 96

Similar in corpus frequency:

aargau 11 abacos 11 abboud 11 abbreviate 11 abdelkader 11 abdomens 11

Corpus analysis for Cofinality

  • In this selection, "cofinality" usually appears near the start of the sentence. The average example has 24.8 words, and this corpus slice is mostly made up of statements.
  • Around the word, different, depends and introduced stand out and add context to how "cofinality" is used.
  • Recognizable usage signals include 0 the cofinality of any and 1 the cofinality of any. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "cofinality" sits close to words such as aargau, abacos and abboud, which helps place it inside the broader word index.

Example types with cofinality

The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:

Short example sentences

Of fundamental importance to the whole theory is the concept of cofinality that Hausdorff introduced. (15 words)

Thus the cofinality of a finite partially ordered set is equal to the number of its maximal elements. (18 words)

This demonstrates that the cofinality depends on the order; different orders on the same set may have different cofinality. (19 words)

Longer example sentences

In 1904 Hausdorff published the recursion named after him: For each non-limit ordinal we have This formula was, together with the later notion of cofinality introduced by Hausdorff, the basis for all further results for Aleph exponentiation. (38 words)

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). (33 words)

The cofinality of 0 is 0. The cofinality of any successor ordinal is 1. The cofinality of any nonzero limit ordinal is an infinite regular cardinal. (26 words)

Example sentences (8)

The cofinality of 0 is 0. The cofinality of any successor ordinal is 1. The cofinality of any nonzero limit ordinal is an infinite regular cardinal.

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

This demonstrates that the cofinality depends on the order; different orders on the same set may have different cofinality.

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).

If two cofinal subsets of B have minimal cardinality (i.e. their cardinality is the cofinality of B), then they are order isomorphic to each other.

In 1904 Hausdorff published the recursion named after him: For each non-limit ordinal we have This formula was, together with the later notion of cofinality introduced by Hausdorff, the basis for all further results for Aleph exponentiation.

Of fundamental importance to the whole theory is the concept of cofinality that Hausdorff introduced.

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

Common combinations with cofinality

These word pairs occur most frequently in English texts:

Frequently asked questions

How do you use "cofinality" in a sentence?
An example: "The cofinality of 0 is 0. The cofinality of any successor ordinal is 1. The cofinality of any nonzero limit ordinal is an infinite regular cardinal." This page contains 8 example sentences with the word "cofinality" from authentic English texts.
What does "cofinality" mean?
Cofinality means: The least of the cardinalities of the cofinal subsets of a partially ordered set.
How many example sentences with "cofinality" are there?
Voorbeeldzinnen.info contains 8 example sentences with "cofinality", drawn from a database of millions of English sentences.