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I added the theological definition of trichotomy to the listing of definitions. meng.benjamin March 27, 2006 16:40 EST
Removed assertion that Trichotomy is equivalent to AC. As evidenced by the proof at http://en.wikipedia.org/wiki/Cantor%E2%80%93Bernstein%E2%80%93Schroeder_theorem, this isn't true. 129.97.97.134 ( talk) 00:30, 11 June 2008 (UTC)
If there is a Boolean expression for trichotomy using AND, OR and NOT it would be much appreciated.
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help)The sentence "The law of trichotomy was long assumed true without proof; it was proven true at the end of the 19th century.[1]" doesn't make much sence to me, exactely what has been proved?-- Sandrobt ( talk) 20:47, 11 October 2010 (UTC)
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help)Hello everyone, the Trichotomy focuses on order relations, but: Don't they satisfy the reflexivity per definition? So consider the pairs (x,x), every case is true (xRx, xRx and x=x) and so the "excluding or" gives false.
Best regards -- 138.246.2.199 ( talk) 03:55, 7 September 2011 (UTC)
Tarski uses the terms Strong Law of Trichotomy and Weak Law of Trichotomy to describe the two meanings given in the article. He also provides a proof that Strong Trichotomy follows from Weak Trichotomy, Irreflexivity, and Asymmetry. Mendelson provides a similar proof using Weak Trichotomy, Irreflexivity, and Transitivity.
References
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![]() | This article is rated Stub-class on Wikipedia's
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I added the theological definition of trichotomy to the listing of definitions. meng.benjamin March 27, 2006 16:40 EST
Removed assertion that Trichotomy is equivalent to AC. As evidenced by the proof at http://en.wikipedia.org/wiki/Cantor%E2%80%93Bernstein%E2%80%93Schroeder_theorem, this isn't true. 129.97.97.134 ( talk) 00:30, 11 June 2008 (UTC)
If there is a Boolean expression for trichotomy using AND, OR and NOT it would be much appreciated.
{{
cite book}}
: Check date values in: |date=
(
help)The sentence "The law of trichotomy was long assumed true without proof; it was proven true at the end of the 19th century.[1]" doesn't make much sence to me, exactely what has been proved?-- Sandrobt ( talk) 20:47, 11 October 2010 (UTC)
{{
cite book}}
: Check date values in: |date=
(
help)Hello everyone, the Trichotomy focuses on order relations, but: Don't they satisfy the reflexivity per definition? So consider the pairs (x,x), every case is true (xRx, xRx and x=x) and so the "excluding or" gives false.
Best regards -- 138.246.2.199 ( talk) 03:55, 7 September 2011 (UTC)
Tarski uses the terms Strong Law of Trichotomy and Weak Law of Trichotomy to describe the two meanings given in the article. He also provides a proof that Strong Trichotomy follows from Weak Trichotomy, Irreflexivity, and Asymmetry. Mendelson provides a similar proof using Weak Trichotomy, Irreflexivity, and Transitivity.
References
{{
cite book}}
: Check date values in: |date=
(
help){{
cite book}}
: Check date values in: |date=
(
help)