axiom of pairing
For any and there exists a set that contains exactly and .
The Axiom of Pairing is one of the axioms of Zermelo-Fraenkel set theory. In symbols, it reads:
Using the Axiom of Extensionality, we see that the set is unique, so it makes sense to define the pair
Using the Axiom of Pairing, we may define, for any set , the singleton
We may also define, for any set and , the ordered pair
Note that this definition satisfies the condition
We may define the ordered -tuple recursively
Title | axiom of pairing |
---|---|
Canonical name | AxiomOfPairing |
Date of creation | 2013-03-22 13:42:43 |
Last modified on | 2013-03-22 13:42:43 |
Owner | Sabean (2546) |
Last modified by | Sabean (2546) |
Numerical id | 7 |
Author | Sabean (2546) |
Entry type | Axiom |
Classification | msc 03E30 |
Synonym | pairing |