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:

    “That anger can be expressed through words and non-destructive activities; that promises are intended to be kept; that cleanliness and good eating habits are aspects of self-esteem; that compassion is an attribute to be prized—all these lessons are ones children can learn far more readily through the living example of their parents than they ever can through formal instruction.”
    —Fred Rogers (20th century)

    “Truth is used to vitalize a statement rather than devitalize it. Truth implies more than a simple statement of fact. “I don’t have any whisky,” may be a fact but it is not a truth.”
    —William Burroughs (b. 1914)