Axiom·A02
Pairing
Any two objects can be gathered into a set.
The set
is the pair
of D003.
In words
For any a, b, there is a set P where for every x, x belongs to P exactly when x equals a or x equals b.
This is a ZFC axiom: it is assumed, not proven. Everything below it in a proof chain ultimately rests here.
Remarks
Guarantees the unordered pair of D003 exists for any
. Taking
yields the singleton
.
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