|
|
|
|
Extensionality
Extensionality In mathematics, extensionality usually refers to some form of the ... extensional. That is one sense in which extensionality may fail. Another one is that consideration ... if taken into account, will usually contradict extensionality. In axiomatic set theory, extensionality is expressed in the axiom of ...
http://en.wikipedia.org/wiki/Extensionality - 2k - Cached - Similar pages
|
Axiom of extensionality
Axiom of extensionality In axiomatic set theory and the branches ... science that use it, the axiom of extensionality, or axiom of extension, is one of ... uniquely by its members. The axiom of extensionality can be used with any statement of ... purely set-theoretic terms. The axiom of extensionality is generally considered uncontroversial, and it or ... is referred to as the axiom of extensionality in this context. In set theory ...
http://en.wikipedia.org/wiki/Axiom_of_extensionality - 7k - Cached - Similar pages
|
Talk:Axiom of extensionality
Talk:Axiom of extensionality it's been a while since I ...
http://en.wikipedia.org/wiki/Talk:Axiom_of_extensionality - 5k - Cached - Similar pages
|
Mereology
... same object. This property is known as Extensionality, a term borrowed from set theory, where Extensionality is a fundamental axiom. An immediate consequence of Extensionality is that no two atoms can be identical. Mereological systems in which Extensionality holds are termed extensional, a fact designated ... general extensional mereology, abbreviated GEM; moreover, the extensionality renders the fusion unique. Conversely, if ...
http://en.wikipedia.org/wiki/Mereology - 32k - Cached - Similar pages
|
New Foundations
... The axioms of the theory TST are extensionality (sets of the same (positive) type with ... type. The axioms of this theory are extensionality (two objects with the same elements are ... math>, the fragment of NF with full extensionality (no urelements) and those instances of the ... consistency of the system NFI with unrestricted extensionality and those instances of the stratified comprehension ... model of NFU. To see that weak extensionality holds is straightforward: each nonempty element ...
http://en.wikipedia.org/wiki/New_Foundations - 62k - Cached - Similar pages
|
Talk:Von Neumann–Bernays–Gödel set theory
... X \in Y) A2 = Axiom of Extensionality A3 = Empty Set Axiom A4 = Class Construction ... in my set (because I assume full extensionality; I'm not allergic to atoms, though). A2 is my Extensionality and extensionality as modified by the absence of atoms ...
http://en.wikipedia.org/wiki/Talk:Von_Neumann–Bernays–Gödel_set_theory - 12k - Cached - Similar pages
|
Lambda calculus
... relation. Eta-conversion expresses the idea of extensionality, which in this context is that two ... can be seen to be equivalent to extensionality as follows: If f and g are ... eta-conversion to be valid, we find extensionality is valid. Conversely if extensionality is taken to be valid, then since ...
http://en.wikipedia.org/wiki/Lambda_calculus - 37k - Cached - Similar pages
|
Non-well-founded set theory
... badly as it can (or rather, as extensionality permits): Boffa's axiom implies that every ... to a strengthening of the axiom of extensionality. In this context, axioms contradicting the axiom ...
http://en.wikipedia.org/wiki/Non-well-founded_set_theory - 6k - Cached - Similar pages
|
Talk:Naive set theory
... theory extracted from Frege by later workers; Extensionality + unrestricted Comprehension). But most naive set theory ... Frege's inconsistent theory (naive comprehension plus extensionality.) Could also mention abstract set theory as ...
http://en.wikipedia.org/wiki/Talk:Naive_set_theory - 95k - Cached - Similar pages
|
Von Neumann–Bernays–Gödel set theory
... concerning themselves primarily with classes. axiom of Extensionality: |
| Page:1 2 3 4 5 6 Next >> |
