Talk:Theory of relations

Notes & Queries

Jon Awbrey 16:40, 14 January 2006 (UTC)

Hmmm... This looks familiar... Randall Holmes 02:26, 28 January 2006 (UTC)

• JA: Different audience ∧ different scope (narrows horizontally on concrete combinatorial settings, but deeper vertically in coverage of more than just the basic definition) ⇒ substantially different article, cylindrically speaking. Jon Awbrey 04:02, 28 January 2006 (UTC)

Destructive formatting

JA: A style sheet that destroys information, or that leads to the erosion of information, is a bad style sheet. Please feel free to add pertinent information, but do not destroy any. Jon Awbrey 17:40, 21 March 2006 (UTC)

Local incidence properties

As of May 27, 2011, this section contained the following definition:

A k-adic relation L ⊆ X₁ × … × X_k is said to be C-regular at j if and only if every flag of L with x at j has the property C, where x is taken to vary over the theme of the fixed domain X_j.

Expressed in symbols, L is C-regular at j if and only if C(L_x.j) is true for all x in X_j.

I could find no explanation of this mathematical use of the term theme in this Wikipedia.  Perhaps readers unfamiliar with this use of theme would more easily understand "where x is each element of X_j".  Or perhaps we should leave this definition as written and provide a link to a new page explaining what it means for x to be taken to vary over the theme of the domain X.  Howard McCay (talk) 06:14, 27 May 2011 (UTC)

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Explanation: The above definition comes from the Local incidence properties section of an article on combinatorics relations in PlanetMath.org. Later in the same article, another section, Numerical incidence properties contains the following definition:

For example, L is said to be c-regular at j if and only if the cardinality of the local flag L_x@j is c for all x in X_j or, to write it in symbols, if and only if L_x@j=c for all x∈X_j.

Comparing both definitions, it is clear that the expresion 'is taken to vary over the theme of' a domain is just an elaborate way of saying 'in,' 'is any element of,' or 'represents any of the objects in' the said domain, or any other similar and clearer expression. In the informal definition following the formal one and beginning by 'Expressed in symbols,' the author of the original article made it clear already by saying 'for all x in X_j.'

The lack of clarity of the elaborate expression above makes me point to the conveniency of its replacement. The author of the section simply copied, but

Kurt Artindagi (talk) 16:27, 25 February 2013 (UTC)

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