Axiom of Pairing - Formal Statement

Formal Statement

In the formal language of the Zermelo–Fraenkel axioms, the axiom reads:

or in words:

Given any set A and any set B, there is a set C such that, given any set D, D is a member of C if and only if D is equal to A or D is equal to B.

or in simpler words:

Given two sets, there is a set whose members are exactly the two given sets.

Read more about this topic:  Axiom Of Pairing

Famous quotes containing the words formal and/or statement:

    This is no argument against teaching manners to the young. On the contrary, it is a fine old tradition that ought to be resurrected from its current mothballs and put to work...In fact, children are much more comfortable when they know the guide rules for handling the social amenities. It’s no more fun for a child to be introduced to a strange adult and have no idea what to say or do than it is for a grownup to go to a formal dinner and have no idea what fork to use.
    Leontine Young (20th century)

    It is commonplace that a problem stated is well on its way to solution, for statement of the nature of a problem signifies that the underlying quality is being transformed into determinate distinctions of terms and relations or has become an object of articulate thought.
    John Dewey (1859–1952)