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, if for every set C, C is a member of A if and only if C is a member of B, then A is equal to B.
(It is not really essential that C here be a set — but in ZF, everything is. See Ur-elements below for when this is violated.)
The converse, of this axiom follows from the substitution property of equality.
Read more about this topic: Axiom Of Extensionality
Famous quotes containing the words formal and/or statement:
“On every formal visit a child ought to be of the party, by way of provision for discourse.”
—Jane Austen (1775–1817)
“I think, therefore I am is the statement of an intellectual who underrates toothaches.”
—Milan Kundera (b. 1929)