Axiom:Axiom of Pairing

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Axiom

Set Theory

For any two sets, there exists a set to which only those two sets are elements:

$\forall A: \forall B: \exists x: \forall y: \paren {y \in x \iff y = A \lor y = B}$

Thus it is possible to create a set that contains as elements any two sets that have already been created.


Class Theory

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

  • Results about the axiom of pairing can be found here.