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Quote: Zermelo's axioms for set theory: extensionality, elementary sets, separation, union, choice, infinity
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sets
Topic:
infinity and infinitesimal
Quotation Skeleton
Axiom 1. (Axiom of extensionality.) … Every set is determined by its elements. … [p. 202] Axiom II. (Axiom of elementary sets … ) There exists a (fictitious) set, the null … there exists a set {a} containing a and … always exists a set {a,b} containing as elements … Axiom of separation [Every propositional function on a domain defines a subset of the domain] … Axiom of the power set … Axiom of the union … [p. 204] Axiom of choice … it is always possible to choose a single … [of a set of sets] and to combine all the chosen elements … into a set … Axiom of infinity … There exists in the domain at least one … [and for] each of its elements a it also … Google-1 Google-2
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Group: sets (7 topics, 148 quotes)
Topic: infinity and infinitesimal (37 items)