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- Ideal_(set_theory) abstract "In the mathematical field of set theory, an ideal is a collection of sets that are considered to be \"small\" or \"negligible\". Every subset of an element of the ideal must also be in the ideal (this codifies the idea that an ideal is a notion of smallness), and the union of any two elements of the ideal must also be in the ideal.More formally, given a set X, an ideal I on X is a nonempty subset of the powerset of X, such that: if A ∈ I and B ⊆ A, then B ∈ I, and if A,B ∈ I, then A∪B ∈ I.Some authors add a third condition that X itself is not in I; ideals with this extra property are called proper ideals.Ideals in the set-theoretic sense are exactly ideals in the order-theoretic sense, where the relevant order is set inclusion. Also, they are exactly ideals in the ring-theoretic sense on the Boolean ring formed by the powerset of the underlying set.".
- Ideal_(set_theory) wikiPageID "12633368".
- Ideal_(set_theory) wikiPageLength "5894".
- Ideal_(set_theory) wikiPageOutDegree "32".
- Ideal_(set_theory) wikiPageRevisionID "643507049".
- Ideal_(set_theory) wikiPageWikiLink Bijection.
- Ideal_(set_theory) wikiPageWikiLink Boolean_algebra_(structure).
- Ideal_(set_theory) wikiPageWikiLink Boolean_ring.
- Ideal_(set_theory) wikiPageWikiLink Cartesian_product.
- Ideal_(set_theory) wikiPageWikiLink Category:Set_theory.
- Ideal_(set_theory) wikiPageWikiLink Cofinality.
- Ideal_(set_theory) wikiPageWikiLink Complement_(set_theory).
- Ideal_(set_theory) wikiPageWikiLink Counting_measure.
- Ideal_(set_theory) wikiPageWikiLink Equivalence_class.
- Ideal_(set_theory) wikiPageWikiLink Equivalence_relation.
- Ideal_(set_theory) wikiPageWikiLink Filter_(mathematics).
- Ideal_(set_theory) wikiPageWikiLink Finite_set.
- Ideal_(set_theory) wikiPageWikiLink Ideal_(order_theory).
- Ideal_(set_theory) wikiPageWikiLink Ideal_(ring_theory).
- Ideal_(set_theory) wikiPageWikiLink Image_(mathematics).
- Ideal_(set_theory) wikiPageWikiLink Large_set_(combinatorics).
- Ideal_(set_theory) wikiPageWikiLink Lebesgue_measure.
- Ideal_(set_theory) wikiPageWikiLink Meagre_set.
- Ideal_(set_theory) wikiPageWikiLink Measure_(mathematics).
- Ideal_(set_theory) wikiPageWikiLink Natural_density.
- Ideal_(set_theory) wikiPageWikiLink Natural_number.
- Ideal_(set_theory) wikiPageWikiLink Ordinal_number.
- Ideal_(set_theory) wikiPageWikiLink Power_set.
- Ideal_(set_theory) wikiPageWikiLink Real_number.
- Ideal_(set_theory) wikiPageWikiLink Set_theory.
- Ideal_(set_theory) wikiPageWikiLink Sigma-ideal.
- Ideal_(set_theory) wikiPageWikiLink Stationary_set.
- Ideal_(set_theory) wikiPageWikiLink Subset.
- Ideal_(set_theory) wikiPageWikiLink Symmetric_difference.
- Ideal_(set_theory) wikiPageWikiLink Union_(set_theory).
- Ideal_(set_theory) wikiPageWikiLink W._Hugh_Woodin.
- Ideal_(set_theory) wikiPageWikiLinkText "Ideal (set theory)".
- Ideal_(set_theory) wikiPageWikiLinkText "ideal (set theory)#Terminology".
- Ideal_(set_theory) wikiPageWikiLinkText "ideal".
- Ideal_(set_theory) wikiPageWikiLinkText "ideals".
- Ideal_(set_theory) wikiPageUsesTemplate Template:Cite_book.
- Ideal_(set_theory) subject Category:Set_theory.
- Ideal_(set_theory) hypernym Collection.
- Ideal_(set_theory) type Book.
- Ideal_(set_theory) comment "In the mathematical field of set theory, an ideal is a collection of sets that are considered to be \"small\" or \"negligible\".".
- Ideal_(set_theory) label "Ideal (set theory)".
- Ideal_(set_theory) sameAs Q5987925.
- Ideal_(set_theory) sameAs Ideal.
- Ideal_(set_theory) sameAs m.02wyyl4.
- Ideal_(set_theory) sameAs Q5987925.
- Ideal_(set_theory) wasDerivedFrom Ideal_(set_theory)?oldid=643507049.
- Ideal_(set_theory) isPrimaryTopicOf Ideal_(set_theory).