more from this thinker     |     more from this text

Single Idea 10875

[filed under theme 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II ]

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

The 5 ideas with the same theme [axiom for new sets by combination]:

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]