Axiom:Axiom of Pairing/Class Theory

Axiom

Let $a$ and $b$ be sets.

Then the class $\set {a, b}$ is likewise a set.

Also known as

The Axiom of Pairing is also known as the Axiom of the Unordered Pair.

Some sources call it the Pairing Axiom.

Also see

• Definition:Doubleton Class

• Doubleton Class can be Formed from Two Sets, which demonstrates the fact that the class $\set {a, b}$ can be created in the first place

Sources

• 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $2$: Some Basics of Class-Set Theory: $\S 4$ The pairing axiom: $A_4$ [Pairing axiom]