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Definition of Extensionality
1. Noun. (philosophy) The principle that objects are equal if and only if their observed properties are the same, regardless of internal processes that lead to those properties. ¹
2. Noun. (mathematics functional analysis) The principle that functions are equal if and only if they operate on the same domain and for any given element of the domain the result of each of the functions is the same. ¹
3. Noun. (mathematics set theory) The principle, codified in the axiom of extensionality, that sets are equal if and only if they contain the same elements. ¹
¹ Source: wiktionary.com
Definition of Extensionality
1. [n -TIES]
Lexicographical Neighbors of Extensionality
Literary usage of Extensionality
Below you will find example usage of this term as found in modern and/or classical literature:
1. Prolegomena to the Study of Hegel's Philosophy and Especially of His Logic by William Wallace (1894)
"... and yet not leave it behind, in the infinitely-various modes of its two great
and conspicuous attributes of consciousness and extensionality. ..."
2. The Praxis of Alain Badiou by Paul Ashton, A J Bartlett, Justin Clemens (2006)
"... in which the primacy of extensionality and the ubiquity of actual infinities
reign supreme. It is interesting to observe, however, ..."
3. The Concept of Model: An Introduction to the Materialist Epistemology of by Alain Badiou (2007)
"There, we find the event defined in such a way that its identity cannot be
established by the set-theoretic axiom of extensionality, the only means that ..."
4. Basic Concepts of Mathematics by Elias Zakon (2001)
"... and anti-symmetry of the inclusion relation, respectively; (c) is also called
the axiom of extensionality.3 A set A may consist of a single element p; ..."
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