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:
“Good gentlemen, look fresh and merrily.
Let not our looks put on our purposes,
But bear it as our Roman actors do,
With untired spirits and formal constancy.”
—William Shakespeare (1564–1616)
“The parent is the strongest statement that the child hears regarding what it means to be alive and real. More than what we say or do, the way we are expresses what we think it means to be alive. So the articulate parent is less a telling than a listening individual.”
—Polly Berrien Berends (20th century)