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Full Idea
Axiom of Unions: For every collection of sets there exists a set that contains all the elements that belong to at least one of the sets in the collection.
Gist of Idea
Unions: There is a set of all the elements which belong to at least one set in a collection
Source
Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15)
Book Ref
Clegg,Brian: 'Infinity' [Robinson 2003], p.206
13016 | The Axiom of Union dates from 1899, and seems fairly obvious [Cantor, by Maddy] |
13033 | Union: ∀F ∃A ∀Y ∀x (x ∈ Y ∧ Y ∈ F → x ∈ A) [Kunen] |
10876 | Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg] |