list of axioms wikipedia - EAS
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List of axioms - Wikipedia
This is a list of axioms as that term is understood in mathematics, by Wikipedia page. In epistemology, the word axiom is understood differently; see axiom and self-evidence. Individual axioms are almost always part of a larger axiomatic system.
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Xem thêmTogether with the axiom of choice (see below), these are the de facto standard axioms for contemporary mathematics or set theory. They can be easily adapted to analogous theories, such as mereology.
• Axiom of extensionality...
Xem thêmWith the Zermelo–Fraenkel axioms above, this makes up the system ZFC in which most mathematics is potentially formalisable.
Equivalents of AC
• Hausdorff maximality theorem
• Well-ordering theorem...
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The logico-deductive method whereby conclusions (new knowledge) follow from premises (old knowledge) through the application of sound arguments (syllogisms, rules of inference) was developed by the ancient Greeks, and has become the core principle of modern mathematics. Tautologiesexcluded, nothing can be deduced if nothing is assumed. Axioms and postulates are thus the basic assumptions underlying a given body of deductive knowledge. They are accepted …
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