foundation of mathematics

collocation in English

meaningsoffoundationandmathematics

These words are often used together. Click on the links below to explore the meanings. Or,see other collocations withmathematicsorfoundation.
foundation
noun
uk
/faʊnˈdeɪ.ʃən/us
/faʊnˈdeɪ.ʃən/
an occasion when an organization, state, etc. ...
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mathematics
noun[U]
uk
/ˌmæθˈmæt.ɪks/us
/ˌmæθˈmæt̬.ɪks/
the study of numbers, shapes, and space using reason and usually a special system of symbols and rules for ...
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(Definition offoundationandmathematicsfrom theCambridge English Dictionary© Cambridge University Press)

Examplesoffoundation of mathematics

These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.
This grew from the increasingly popular assertion in the late 20th century that no onefoundationofmathematicscould be ever proven to exist.
From
Wikipedia
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In this view, logic is the properfoundationofmathematics, and all mathematical statements are necessary logical truths.
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In thefoundationofmathematics, nominalism has come to mean doing mathematics without assuming that sets in the mathematical sense exist.
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Regardless of the major, all students start with the first year, called the core building a firmfoundationofmathematics, statistics and economics.
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Functional programming, e.g. type free lambda calculus, originated as a theoreticalfoundationofmathematics.
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Certain categories called topoi (singular "topos") can even serve as an alternative to axiomatic set theory as afoundationofmathematics.
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Church demonstrated that it could serve as afoundationofmathematicsand it was referred to as a higher-order logic.
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Lesniewski consciously derived his mereology as an alternative to set theory as afoundationofmathematics, but did not work out the details.
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If one agrees that set theory is an appealingfoundationofmathematics, then all mathematical objects must be defined as sets of some sort.
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It touches upon such topics as time and identity, free will, perception, change, memory, consciousness, language, thefoundationofmathematicsand the limits of reason.
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His lectures were generally on the foundations of mathematics, and were very popular with students.
From theCambridge English Corpus
Skolem's result showed this is not possible, creating doubts about the use of set theory as afoundationofmathematics.
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From the conceptual point of view, some of the major ideas about thefoundationofmathematicsare conveyed with reasonable accuracy, although sometimes errors, mistakes and inaccuracies occur.
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Wikipedia
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It offered rigorous formal techniques for characterizing the rules, based on approaches to the foundations of mathematics and computability developed earlier in the century.
From theCambridge English Corpus
The need for such procedures - in present day terminology we would call them algorithms - arose with the crisis of the foundations of mathematics around 1900.
From theCambridge English Corpus
In general, logical laws lie at the foundations of mathematics.
From theCambridge English Corpus
The canonicalfoundationofmathematicsis axiomatic set theory, with a background logic consisting of first-order logic with identity, with a universe of discourse consisting entirely of sets.
From
Wikipedia
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The foundations of mathematics, which in turn are the foundations of much scientific work, lie in the primary schools.
From the
Hansard archive
Example from the Hansard archive. Contains Parliamentary information licensed under theOpen Parliament Licence v3.0
These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.
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