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- Axiom_schema_of_replacement abstract "In set theory, the axiom schema of replacement is a schema of axioms in Zermelo–Fraenkel set theory (ZFC) that asserts that the image of any set under any definable mapping is also a set. It is necessary for the construction of certain infinite sets in ZFC. The axiom schema is motivated by the idea that whether a class is a set depends only on the cardinality of the class, not on the rank of its elements. Thus, if one class is "small enough" to be a set, and there is a surjection from that class to a second class, the axiom states that the second class is also a set. However, because ZFC only speaks of sets, not proper classes, the schema is stated only for definable surjections, which are identified with their defining formulas.".
- Axiom_schema_of_replacement thumbnail Axiom_schema_of_replacement.svg?width=300.
- Axiom_schema_of_replacement wikiPageID "52387".
- Axiom_schema_of_replacement wikiPageRevisionID "600002314".
- Axiom_schema_of_replacement hasPhotoCollection Axiom_schema_of_replacement.
- Axiom_schema_of_replacement subject Category:Axioms_of_set_theory.
- Axiom_schema_of_replacement type Abstraction100002137.
- Axiom_schema_of_replacement type AuditoryCommunication107109019.
- Axiom_schema_of_replacement type AxiomsOfSetTheory.
- Axiom_schema_of_replacement type Communication100033020.
- Axiom_schema_of_replacement type Maxim107152948.
- Axiom_schema_of_replacement type Saying107151380.
- Axiom_schema_of_replacement type Speech107109196.
- Axiom_schema_of_replacement comment "In set theory, the axiom schema of replacement is a schema of axioms in Zermelo–Fraenkel set theory (ZFC) that asserts that the image of any set under any definable mapping is also a set. It is necessary for the construction of certain infinite sets in ZFC. The axiom schema is motivated by the idea that whether a class is a set depends only on the cardinality of the class, not on the rank of its elements.".
- Axiom_schema_of_replacement label "Aksjomat zastępowania".
- Axiom_schema_of_replacement label "Axiom schema of replacement".
- Axiom_schema_of_replacement label "Axioma da substituição".
- Axiom_schema_of_replacement label "Ersetzungsaxiom".
- Axiom_schema_of_replacement label "Esquema axiomático de reemplazo".
- Axiom_schema_of_replacement label "Schema di assiomi di rimpiazzamento".
- Axiom_schema_of_replacement label "Schéma d'axiomes de remplacement".
- Axiom_schema_of_replacement label "Схема преобразования".
- Axiom_schema_of_replacement label "替代公理".
- Axiom_schema_of_replacement sameAs Schéma_nahrazení.
- Axiom_schema_of_replacement sameAs Ersetzungsaxiom.
- Axiom_schema_of_replacement sameAs Esquema_axiomático_de_reemplazo.
- Axiom_schema_of_replacement sameAs Schéma_d'axiomes_de_remplacement.
- Axiom_schema_of_replacement sameAs Schema_di_assiomi_di_rimpiazzamento.
- Axiom_schema_of_replacement sameAs Aksjomat_zastępowania.
- Axiom_schema_of_replacement sameAs Axioma_da_substituição.
- Axiom_schema_of_replacement sameAs m.0ds27.
- Axiom_schema_of_replacement sameAs Q1361825.
- Axiom_schema_of_replacement sameAs Q1361825.
- Axiom_schema_of_replacement sameAs Axiom_schema_of_replacement.
- Axiom_schema_of_replacement wasDerivedFrom Axiom_schema_of_replacement?oldid=600002314.
- Axiom_schema_of_replacement depiction Axiom_schema_of_replacement.svg.
- Axiom_schema_of_replacement isPrimaryTopicOf Axiom_schema_of_replacement.
