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How do you use Hyperreals in a sentence? See 7 example sentences showing how this word appears in different contexts, plus the exact meaning.

Rare word

Hyperreals in a sentence

Related words

Hyperreals | Hyperreal

Hyperreals meaning

plural of hyperreal

Using Hyperreals

  • The main meaning on this page is: plural of hyperreal
  • In the example corpus, hyperreals often appears in combinations such as: the hyperreals, hyperreals or, hyperreals are.

Context around Hyperreals

  • Average sentence length in these examples: 27.4 words
  • Position in the sentence: 3 start, 3 middle, 1 end
  • Sentence types: 7 statements, 0 questions, 0 exclamations

Often before:

limited 1× infinitesimal 1×

Sentence patterns with Hyperreals

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

and the hyperreals are those 1× of infinitesimal hyperreals are external 1× of limited hyperreals or the 1× of the hyperreals and is 1× r of hyperreals is constructed 1× sense for hyperreals and hold 1× that the hyperreals were logically 1× the hyperreals or nonstandard 1×

Sentence openings and endings

Common sentence openings:

all the arithmetical 1× ball p 31 1× includes an axiomatic 1× the hyperreals or 1× the only properties 1× the set of 1×

Common sentence endings:

hyperreals is constructed 1× mathematical society 1984 1× number of terms 1× out of sets 1× over these sets 1× the ordinary reals 1×

Words around Hyperreals

Just before it in the word index:

hyperrealistic 5 hyperrealist 2 hyperrealism 2 hyperreal 20 hyperquant 4 hyperproductive 2

Just after it in the word index:

hypersaline 4 hyperscale 20 hyperscaler 3 hyperscalers 8 hyperscreen 2 hypersense 2

Similar in corpus frequency:

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

Corpus analysis for Hyperreals

  • In this selection, "hyperreals" usually appears near the start of the sentence. The average example has 27.4 words, and this corpus slice is mostly made up of statements.
  • Around the word, limited and infinitesimal stand out and add context to how "hyperreals" is used.
  • Recognizable usage signals include and the hyperreals are those and of infinitesimal hyperreals are external. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "hyperreals" sits close to words such as aaba, aafc and aaib, which helps place it inside the broader word index.

Example types with hyperreals

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

With this identification, the ordered field *R of hyperreals is constructed. (11 words)

All the arithmetical expressions and formulas make sense for hyperreals and hold true if they are true for the ordinary reals. (21 words)

Ball, p. 31 In the 1960s, Abraham Robinson proved that the hyperreals were logically consistent if and only if the reals were. (22 words)

Longer example sentences

The set of limited hyperreals or the set of infinitesimal hyperreals are external subsets of V(*R) ; what this means in practice is that bounded quantification, where the bound is an internal set, never ranges over these sets. (38 words)

The only properties that differ between the reals and the hyperreals are those that rely on quantification over sets, or other higher-level structures such as functions and relations, which are typically constructed out of sets. (36 words)

Includes an axiomatic treatment of the hyperreals, and is freely available under a Creative Commons license * Keisler, H. Jerome: An Infinitesimal Approach to Stochastic Analysis, vol. 297 of Memoirs of the American Mathematical Society, 1984. (35 words)

Example sentences (7)

The set of limited hyperreals or the set of infinitesimal hyperreals are external subsets of V(*R) ; what this means in practice is that bounded quantification, where the bound is an internal set, never ranges over these sets.

All the arithmetical expressions and formulas make sense for hyperreals and hold true if they are true for the ordinary reals.

Ball, p. 31 In the 1960s, Abraham Robinson proved that the hyperreals were logically consistent if and only if the reals were.

Includes an axiomatic treatment of the hyperreals, and is freely available under a Creative Commons license * Keisler, H. Jerome: An Infinitesimal Approach to Stochastic Analysis, vol. 297 of Memoirs of the American Mathematical Society, 1984.

The hyperreals, or nonstandard reals, *R, are an extension of the real numbers R that contains numbers greater than anything of the form : (for any finite number of terms).

The only properties that differ between the reals and the hyperreals are those that rely on quantification over sets, or other higher-level structures such as functions and relations, which are typically constructed out of sets.

With this identification, the ordered field *R of hyperreals is constructed.

Common combinations with hyperreals

These word pairs occur most frequently in English texts:

Frequently asked questions

How do you use "hyperreals" in a sentence?
An example: "The set of limited hyperreals or the set of infinitesimal hyperreals are external subsets of V(*R) ; what this means in practice is that bounded quantification, where the bound is an internal set, never ranges over these sets." This page contains 7 example sentences with the word "hyperreals" from authentic English texts.
What does "hyperreals" mean?
Hyperreals means: plural of hyperreal
How many example sentences with "hyperreals" are there?
Voorbeeldzinnen.info contains 7 example sentences with "hyperreals", drawn from a database of millions of English sentences.