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Explore Extensionality through 7 example sentences from English, with an explanation of the meaning. Ideal for language learners, writers and word enthusiasts.

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Extensionality in a sentence

Extensionality meaning

  1. The principle that objects are equal if and only if their observed properties are the same, regardless of internal processes that lead to those properties.
  2. The principle that functions are equal if and only if they operate on the same domain and for any given element of the domain the result of each of the functions is the same.
  3. The principle, codified in the axiom of extensionality, that sets are equal if and only if they contain the same elements.

Using Extensionality

  • The main meaning on this page is: The principle that objects are equal if and only if their observed properties are the same, regardless of internal processes that lead to those properties. | The principle that functions are equal if and only if they operate on the same domain and for any given element of the domain the result of each of the functions is the same. | The principle, codified in the axiom of extensionality, that sets are equal if and only if they contain the same elements.
  • In the example corpus, extensionality often appears in combinations such as: of extensionality, extensionality in.

Context around Extensionality

  • Average sentence length in these examples: 22.4 words
  • Position in the sentence: 2 start, 3 middle, 2 end
  • Sentence types: 7 statements, 0 questions, 0 exclamations

Sentence patterns with Extensionality

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

axiom of extensionality 1× axiom of extensionality in this 1× axiom of extensionality is generally 1× axiom of extensionality the axiom 1× axiom of extensionality to show 1× principle of extensionality in set 1× see also extensionality for a 1×

Sentence openings and endings

Common sentence openings:

however we say 1× interpretation we can 1× see also extensionality 1× the axiom of 1× the principle of 1× while this approach 1×

Common sentence endings:

a general overview 1× an adjustment instead 1× axiom of extensionality 1× in this context 1× of set theory 1× one empty set 1×

Words around Extensionality

Just before it in the word index:

extensional 21 extension 3.882 extensible 39 extensibility 20 extends 1.219 extending 1.607

Just after it in the word index:

extensionally 2 extensions 710 extensionthe 2 extensive 4.011 extensively 990 extenso 2

Similar in corpus frequency:

aaba 10 aafc 10 aaib 10 aalbers 10 abbate 10 abbesses 10

Corpus analysis for Extensionality

  • In this selection, "extensionality" usually appears in the middle of the sentence. The average example has 22.4 words, and this corpus slice is mostly made up of statements.
  • Recognizable usage signals include axiom of extensionality and axiom of extensionality in this. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "extensionality" sits close to words such as aaba, aafc and aaib, which helps place it inside the broader word index.

Example types with extensionality

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

See also * Extensionality for a general overview. (7 words)

Interpretation We can use the axiom of extensionality to show that there is only one empty set. (17 words)

While this approach can serve to preserve the axiom of extensionality, the axiom of regularity will need an adjustment instead. (20 words)

Longer example sentences

Most of the axioms of equality still follow from the definition; the remaining one is : and it becomes this axiom that is referred to as the axiom of extensionality in this context. (32 words)

The principle of extensionality in set theory assures us that any matching pair of curly braces enclosing one or more instances of the same individuals denote the same set. (29 words)

The axiom of extensionality is generally uncontroversial in set-theoretical foundations of mathematics, and it or an equivalent appears in just about any alternative axiomatisation of set theory. (28 words)

Example sentences (7)

However, we say that two sets which differ only in that one has duplicate members are in fact exactly identical (see Axiom of extensionality ).

Interpretation We can use the axiom of extensionality to show that there is only one empty set.

Most of the axioms of equality still follow from the definition; the remaining one is : and it becomes this axiom that is referred to as the axiom of extensionality in this context.

See also * Extensionality for a general overview.

The axiom of extensionality is generally uncontroversial in set-theoretical foundations of mathematics, and it or an equivalent appears in just about any alternative axiomatisation of set theory.

The principle of extensionality in set theory assures us that any matching pair of curly braces enclosing one or more instances of the same individuals denote the same set.

While this approach can serve to preserve the axiom of extensionality, the axiom of regularity will need an adjustment instead.

Common combinations with extensionality

These word pairs occur most frequently in English texts:

  • of extensionality 6×
  • extensionality in 2×

Frequently asked questions

How do you use "extensionality" in a sentence?
An example: "However, we say that two sets which differ only in that one has duplicate members are in fact exactly identical (see Axiom of extensionality )." This page contains 7 example sentences with the word "extensionality" from authentic English texts.
What does "extensionality" mean?
Extensionality means: The principle that objects are equal if and only if their observed properties are the same, regardless of internal processes that lead to those properties.
How many example sentences with "extensionality" are there?
Voorbeeldzinnen.info contains 7 example sentences with "extensionality", drawn from a database of millions of English sentences.