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Full Idea
Axiom of Pairing: For any two sets there exists a set to which they both belong. So you can make a set out of two other sets.
Gist of Idea
Pairing: For any two sets there exists a set to which they both belong
Source
Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15)
Book Ref
Clegg,Brian: 'Infinity' [Robinson 2003], p.205
13017 | Zermelo introduced Pairing in 1930, and it seems fairly obvious [Zermelo, by Maddy] |
13032 | Pairing: ∀x ∀y ∃z (x ∈ z ∧ y ∈ z) [Kunen] |
18851 | Pairing (with Extensionality) guarantees an infinity of sets, just from a single element [Rosen] |
10100 | Axiom of Pairing: for all sets x and y, there is a set z containing just x and y [George/Velleman] |
10875 | Pairing: For any two sets there exists a set to which they both belong [Clegg] |