Le Wed, 04 Jan 2012 17:49:15 +0000,
Steve Horne
On 04/01/2012 16:47, Steve Horne wrote:
(a == a) reflexivity : (a == b) => (b == a) transitivity : (a == b) && (b == c) => (a == c)
Oops - that's...
reflexivity : (a == a) symmetry : (a == b) => (b == a) transitivity : (a == b) && (b == c) => (a == c)
An equivalence relation is a relation that meets all these conditions.
I prefer to use "transymmetry" (although I guess it is not a regular word): reflexivity: a ≃ a transymmetry: ∀ a b. b≃a ⇒ ∀ c. c≃a ⇒ b≃c so I only have 2 rules. transymmetry is trivially derived from transitivity and symmetry. symmetry is trivially derived from reflexivity and transymmetry. transitivity is trivially derived from symmetry and transymmetry (and thus from transymmetry and reflexivity)
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