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The present stage of the article betrays some confusion on my part. In the article as I found it, the term was used purely to refer to the presence of 'preference ordering loops'. I was quite surprised to see this, since it adds a third distinct meaning to the term, besides the two I was already familiar with (nontransitivity and antitransitivity).
Now Google provides confirmations for all three uses of the term. Therefore I strongly feel we have to recognize all three of them and explain their differences, rather than picking one of them, as a textbook would do.
But I didn't have too much time so I only added a "formal definition" section in which the three concepts are defined and exemplified. The article needs restructuring. Please help ...
In reviewing these the following seems clear to me. A relation is transitive if A has the relationship to B and B has the relationship to C then A has the relationship to C.
The least thing we need in order for a relation to be NOT-transitive there has to be at least one example where A doesn't have the relation to C. Well that is exactly what this stated formulation says.
When there is not just one, but all As do not have the relation to all Cs, that is something different. That is intransitive. Well that is exactly what the formula stated for intransitivity says.
The article should reflect this.
Gregbard 05:26, 29 August 2007 (UTC)
Small problem with the first example: both wolves and dogs do eat grass. One reference on this: http://books.google.fi/books?id=8FwqLh2a2ckC&pg=PA141&lpg=PA141&dq=wolves+eat+grass&source=bl&ots=rPdv9zWI1p&sig=z_ByZvz9kWPr-GWX3bu5c-rS1JA&hl=en&ei=yegoStzuHIKPsAbLwqzvCQ&sa=X&oi=book_result&ct=result&resnum=7 —Preceding unsigned comment added by 128.214.205.4 ( talk) 09:44, 5 June 2009 (UTC)
The last line of this section was unclear, so I've elaborated upon it with examples. Undsoweiter ( talk) 06:46, 6 March 2010 (UTC)
![]() | This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||
|
The present stage of the article betrays some confusion on my part. In the article as I found it, the term was used purely to refer to the presence of 'preference ordering loops'. I was quite surprised to see this, since it adds a third distinct meaning to the term, besides the two I was already familiar with (nontransitivity and antitransitivity).
Now Google provides confirmations for all three uses of the term. Therefore I strongly feel we have to recognize all three of them and explain their differences, rather than picking one of them, as a textbook would do.
But I didn't have too much time so I only added a "formal definition" section in which the three concepts are defined and exemplified. The article needs restructuring. Please help ...
In reviewing these the following seems clear to me. A relation is transitive if A has the relationship to B and B has the relationship to C then A has the relationship to C.
The least thing we need in order for a relation to be NOT-transitive there has to be at least one example where A doesn't have the relation to C. Well that is exactly what this stated formulation says.
When there is not just one, but all As do not have the relation to all Cs, that is something different. That is intransitive. Well that is exactly what the formula stated for intransitivity says.
The article should reflect this.
Gregbard 05:26, 29 August 2007 (UTC)
Small problem with the first example: both wolves and dogs do eat grass. One reference on this: http://books.google.fi/books?id=8FwqLh2a2ckC&pg=PA141&lpg=PA141&dq=wolves+eat+grass&source=bl&ots=rPdv9zWI1p&sig=z_ByZvz9kWPr-GWX3bu5c-rS1JA&hl=en&ei=yegoStzuHIKPsAbLwqzvCQ&sa=X&oi=book_result&ct=result&resnum=7 —Preceding unsigned comment added by 128.214.205.4 ( talk) 09:44, 5 June 2009 (UTC)
The last line of this section was unclear, so I've elaborated upon it with examples. Undsoweiter ( talk) 06:46, 6 March 2010 (UTC)