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

Set Theory in a sentence

Corpus data

  • Displayed example sentences: 20
  • Discovered as a combination around: set
  • Corpus frequency in the collocation scan: 16
  • Phrase length: 2 words
  • Average sentence length: 26.3 words

Words in this phrase

set theory

Meanings of words in this phrase

  • set can mean: To put (something) down, to rest. Very common word
  • theory can mean: A description of an event or system that is considered to be accurate. Frequent word

Sentence profile

  • Phrase position: 12 start, 8 middle, 0 end
  • Sentence types: 20 statements, 0 questions, 0 exclamations

Usage patterns

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

and that set theory was quite 1× applications of set theory in other 1× axiom in set theory today it 1× axiomatic set theory was originally 1× axioms of set theory 1× bernays gödel set theory nbg morse 1× classical set theory classical set 1× combinatorial set theory main combinatorial 1×

Sentence openings and endings

Common sentence openings:

although the axiom 1× another example of 1× as a matter 1× axiomatic set theory 1× classical set theory 1× combinatorial set theory 1×

Common sentence endings:

actual completed infinities 1× alternative set theory 1× axiomatic set theory 1× describe their relationships 1× distinct from logic 1× foundations of mathematics 1×

Context words

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

naive 5× axiomatic 5× fraenkel 5× mathematics 5× zermelo 4× modern 4× term 3× axiom 3× systems 3× mathematical 3× logic 3× formal 3×

Related phrases

instruction set empty set string theory quantum theory set aside conspiracy theory set forth skill set ordered set literary theory

Phrases around this combination

Other phrases discovered around set:

empty set 20×

Just before it in the phrase index:

set forth set aside services segment services provider services ltd services inc

Just after it in the phrase index:

settle down settlement agreement seven assists seven counts seven days seven deadly

Other phrases with the same pattern

Same start:

set aside set forth

Same ending:

string theory quantum theory conspiracy theory literary theory scientific theory classical theory

Corpus analysis

  • The phrase "set theory" has 2 words and usually appears near the start in these examples. The average sentence has 26.3 words and is mostly made up of statements.
  • Around this phrase, patterns and context words such as and that set theory was quite, applications of set theory in other, naive, axiomatic and fraenkel stand out.
  • In the phrase index, this combination connects with instruction set, empty set, string theory and empty set, linking the page to nearby combinations.

Example types with set theory

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

Short example sentences

Axiomatic set theory was originally devised to rid set theory of such paradoxes. (13 words)

Classical set theory Classical set theory accepts the notion of actual, completed infinities. (13 words)

Combinatorial set theory main Combinatorial set theory concerns extensions of finite combinatorics to infinite sets. (15 words)

Longer example sentences

Gödel showed that the continuum hypothesis cannot be disproven from the axioms of Zermelo–Fraenkel set theory (with or without the axiom of choice), by developing the constructible universe of set theory in which the continuum hypothesis must hold. (39 words)

Nonetheless mathematics is often imagined to be (as far as its formal content) nothing but set theory in some axiomatization, in the sense that every mathematical statement or proof could be cast into formulas within set theory. (37 words)

Informal applications of set theory in other fields are sometimes referred to as applications of "naive set theory", but usually are understood to be justifiable in terms of an axiomatic system (normally Zermelo–Fraenkel set theory ). (36 words)

Example sentences (20)

Concerning the origin of the term naive set theory, Jeff Miller says, "Naïve set theory (contrasting with axiomatic set theory) was used occasionally in the 1940s and became an established term in the 1950s.

Informal applications of set theory in other fields are sometimes referred to as applications of "naive set theory", but usually are understood to be justifiable in terms of an axiomatic system (normally Zermelo–Fraenkel set theory ).

Other formalizations of set theory have been proposed, including von Neumann–Bernays–Gödel set theory (NBG), Morse–Kelley set theory (MK), and New Foundations (NF).

Although the axiom schema of replacement is a standard axiom in set theory today, it is often omitted from systems of type theory and foundation systems in topos theory.

It was one of the first mathematical journals with special emphasis on set theory, topology, theory of real functions, measure and integration theory, functional analysis, logic and foundations of mathematics.

Fuzzy set theory main In set theory as Cantor defined and Zermelo and Fraenkel axiomatized, an object is either a member of a set or not.

The term naive set theory is still today also used in some literature to refer to the set theories studied by Frege and Cantor, rather than to the informal counterparts of modern axiomatic set theory.

Another example of the syntactic approach is the Alternative Set Theory Vopěnka, P. Mathematics in the Alternative Set Theory.

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As a matter of convenience, usage of naive set theory and its formalism prevails even in higher mathematics including in more formal settings of set theory itself.

Axiomatic set theory was originally devised to rid set theory of such paradoxes.

Classical set theory Classical set theory accepts the notion of actual, completed infinities.

Combinatorial set theory main Combinatorial set theory concerns extensions of finite combinatorics to infinite sets.

Furthermore, a firm grasp of set theory's concepts from a naive standpoint is a step to understanding the motivation for the formal axioms of set theory.

Gödel showed that the continuum hypothesis cannot be disproven from the axioms of Zermelo–Fraenkel set theory (with or without the axiom of choice), by developing the constructible universe of set theory in which the continuum hypothesis must hold.

He always maintained that mathematics required set theory and that set theory was quite distinct from logic.

In modern set theory, it is common to restrict attention to the von Neumann universe of pure sets, and many systems of axiomatic set theory are designed to axiomatize the pure sets only.

In the modern era, musical set theory uses the language of mathematical set theory in an elementary way to organize musical objects and describe their relationships.

Its publication by Adolf Fraenkel in 1922 is what makes modern set theory Zermelo-Fraenkel set theory (ZFC).

Nonetheless mathematics is often imagined to be (as far as its formal content) nothing but set theory in some axiomatization, in the sense that every mathematical statement or proof could be cast into formulas within set theory.

Set theory While his contributions to logic include elegant expositions and a number of technical results, it is in set theory that Quine was most innovative.

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