| 词汇 | example_english_axiom-of-choice |
| 释义 | axiom of choicecollocation in Englishmeanings of axiomand choiceThese words are often used together. Click on the links below to explore the meanings. Or, see other collocations with choice. 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 at axiom choice noun uk /tʃɔɪs/ us /tʃɔɪs/ an act or the possibility ... See more at choice Examples of axiom of choiceThese 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 the axiomofchoice is equivalent to stating that every surjective function has a right-inverse. Assuming the axiomofchoice, this factorization is unique up to equivalence. To prove that this definition actually preserves composition of relations, one needs the axiomofchoice. In certain other categories (topoi), the exponential functor is a relator only if the internal axiomofchoice is satisfied. Generally, these models do not validate the axiomofchoice for propositions taken over hierarchies of extensional functionals. The proofs of these stronger statements require the axiomofchoice, whereas those we need have constructive proofs. Assuming the axiomofchoice, it can be shown that any set is projective. They conjecture that although such rules exist, proof of their existence involves some version of the axiomofchoice. If we have just one, then we may need to employ something like the axiomofchoice to ensure there is such a proposition. For the examples given below we assume either that this constructive definition is used or that the axiom of description (equivalently, the axiomofchoice for types) is assumed. We use the axiomofchoice here. We shall use a strong version of the axiomofchoice to enhance the simplicity of the proof, even if the result holds also for weak versions of it. We consider the full axiomofchoice and the axiom of descriptions, or unique choice - the former leads to classical logic, whereas the second is constructively valid. 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 propositional axiomofchoice. The band was named after the mathematical concept, the axiomofchoice. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Under the assumption of the axiomofchoice, this transfinite sequence includes every cardinal number. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Another argument against the axiomofchoice is that it implies the existence of objects that may seem counterintuitive. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. This second definition makes sense without the axiomofchoice. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. 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. Want to learn more? Go to the definition of axiom Go to the definition of choice See other collocations with choice |
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