Axiom of Extensionality
المؤلف:
Devlin, K
المصدر:
The Joy of Sets: Fundamentals of Contemporary Set Theory, 2nd ed. New York: Springer-Verlag, 1993.
الجزء والصفحة:
...
18-2-2022
676
Axiom of Extensionality
The axiom of Zermelo-Fraenkel set theory which asserts that sets formed by the same elements are equal,
Note that some texts (e.g., Devlin 1993), use a bidirectional equivalent 
preceding "
," while others (e.g., Enderton 1977, Itô 1986), use the one-way implies 
. However, one-way implication suffices.
Using the notation 
(
is a subset of 
) for 
, the axiom can be written concisely as
where 
denotes logical AND.
REFERENCES
Devlin, K. The Joy of Sets: Fundamentals of Contemporary Set Theory, 2nd ed. New York: Springer-Verlag, 1993.
Enderton, H. B. Elements of Set Theory. New York: Academic Press, 1977.
Itô, K. (Ed.). "Zermelo-Fraenkel Set Theory." §33B in Encyclopedic Dictionary of Mathematics, 2nd ed., Vol. 1. Cambridge, MA: MIT Press, pp. 147-148, 1986.
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