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Translations for „axiom of choice“ in the English » German Dictionary (Go to German » English)

Monolingual examples (not verified by PONS Editors)

English
However, specifying an isomorphism requires the axiom of choice.
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Such theorems may depend on non-constructive foundational material such as the axiom of infinity, the axiom of choice, or the law of excluded middle.
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Meanwhile, the negation of the axiom of choice is, curiously, an NF theorem.
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The band was named after the mathematical concept, the axiom of choice.
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As this could be done for any proposition, this completes the proof that the axiom of choice implies the law of the excluded middle.
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Assuming the axiom of choice, the union of a countable set of countable sets is itself countable.
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The statement that every vector space has a basis is equivalent to the axiom of choice.
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Furthermore, assuming the axiom of choice, the free abelian groups are precisely the projective objects in the category of abelian groups.
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Indeed, their existence is a non-trivial consequence of the axiom of choice.
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References to particular axioms typically then occurs only when tradition demands it, e.g. the axiom of choice is often mentioned when used.
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