axiom of choice
collocation in Englishmeaningsofaxiomandchoice
These words are often used together. Click on the links below to explore the meanings. Or,see other collocations withchoice.
axiom
noun[C]
uk/ˈæk.si.əm/us/ˈæk.si.əm/
formal
a statement or principle that is generally accepted to be true, but need not ...
See more ataxiom
choice
noun
uk/tʃɔɪs/us/tʃɔɪs/
an act or the possibility ...
See more atchoice
(Definition ofaxiomandchoicefrom theCambridge English Dictionary© Cambridge University Press)
Examplesofaxiom of choice
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.
It is well-known that theaxiomofchoiceis equivalent to stating that every surjective function has a right-inverse.
From theCambridge English Corpus
Assuming theaxiomofchoice, this factorization is unique up to equivalence.
From theCambridge English Corpus
To prove that this definition actually preserves composition of relations, one needs theaxiomofchoice.
From theCambridge English Corpus
In certain other categories (topoi), the exponential functor is a relator only if the internalaxiomofchoiceis satisfied.
From theCambridge English Corpus
Generally, these models do not validate theaxiomofchoicefor propositions taken over hierarchies of extensional functionals.
From theCambridge English Corpus
The proofs of these stronger statements require theaxiomofchoice, whereas those we need have constructive proofs.
From theCambridge English Corpus
Assuming theaxiomofchoice, it can be shown that any set is projective.
From theCambridge English Corpus
They conjecture that although such rules exist, proof of their existence involves some version of theaxiomofchoice.
From theCambridge English Corpus
If we have just one, then we may need to employ something like theaxiomofchoiceto ensure there is such a proposition.
From theCambridge English Corpus
For the examples given below we assume either that this constructive definition is used or that the axiom of description (equivalently, theaxiomofchoicefor types) is assumed.
From theCambridge English Corpus
We use theaxiomofchoicehere.
From theCambridge English Corpus
We shall use a strong version of theaxiomofchoiceto enhance the simplicity of the proof, even if the result holds also for weak versions of it.
From theCambridge English Corpus
We consider the fullaxiomofchoiceand the axiom of descriptions, or unique choice - the former leads to classical logic, whereas the second is constructively valid.
From theCambridge English Corpus
Instead, topoi, being governed by propositions as mono types, admits only the usual existential quantifier of intuitionistic logic with no internal existence property, and hence no propositionalaxiomofchoice.
From theCambridge English Corpus
The band was named after the mathematical concept, theaxiomofchoice.
From
Wikipedia
Under the assumption of theaxiomofchoice, this transfinite sequence includes every cardinal number.
From
Wikipedia
Another argument against theaxiomofchoiceis that it implies the existence of objects that may seem counterintuitive.
From
Wikipedia
This second definition makes sense without theaxiomofchoice.
From
Wikipedia
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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