Talk:Relation (mathematics)

Formally, a relation is a set of n-tuples - I have added this.

Also a relation is not necessarily binary - it can be ternary etc. While the article does not explicitly dispute this, its focus on domain and range slants it somewhat toward binary relations only.

I will put in a line or two - I am not an expert - there is room for much more.

That is the point of view of a database system. Not a general concept.

Irreducibility

There is a line in this article suggesting that all ternary relations can be decomposed into binary ones. This is incorrect - some n-ary relations are "irreducible" to lower aritys without losing information (I think the writer is getting confused with the processing of relations, hence the "currying" references). I have amended it.

you are mixing to different things. The decomposition of relations is related with database normalization, curring is related with Cartesian closed categories, which is a sophisticated way to deal with curring.

The function f:AxB->C relates pairs of the domain set AxB with the codomain set C. The curried version f':A->(B->C) has Á as domain and the function which is a relation thus a set, as a codomain. In functional programming the curry transformation can be defined with a translation of this into some functional programming language: $curry\ f=\lambda x(\lambda y(f(x,y)))$.

Page in trouble!

This page is unclear about what kind of relation it is describing. On En wiki relation (mathematics) redirects to binary relation, whereas our page is linked to finitary relation.

Our wording is so slack that I'm not sure what was meant. It's over to our mathematicians to clear this up! Macdonald-ross (talk) 14:08, 25 May 2016 (UTC)

The article had many misconceptions, I tried to sketch the correct concepts.

The article is suppose to describe relations in the context of mathematics, but it had a very confusing salad of how relations are viewed in some relational database manual.

Relations are a basis of many mathematical structures, and those are also used in the foundation of computer science. Those who want to fix this article can find more information in discrete mathematics books.

Homogeneous binary relations are important because they have properties like reflexivity, symmetry and transitivity, which are used to define equivalence relations, and order relations. Objects like CPOs (complete partial orders) are the basis of denotational semantics of programs.

On the other hand, heterogeneous n-ary relations have a very important roll to represent some world of discourse in relational databases or in predicate logics. There is a relational algebra system, which is the basis of SQL and QBE languages.

I wanted to remove the part related with currying functions, which is not really part of the subject of mathematical relations. I explained above what is it about. I leaved currying, because I did not want to start polemics or be considered a vandal, after I erased many wrong concepts.

For the role of relations in databases, I recomend the Ullman books on the subject, and the more formal of Meyer. Although there are many written on the subject.

I recommend not to base this information on any database system manual, because those manuals are biased just to use their software, they normally never explain the theory.

I hope that the actual text can be extended by enthusiast volunteers. I have no much time to do it, I just fixed it because the misconceptions could mislead those readers which are starting on the subject.

This would be fine if it was on the regular English Wikipedia, but this is Simple English Wikipedia! It's supposed to be basic, so that way kids, students, or foreigners learning English can easily understand it! And what 'misconceptions' are you even talking about? 2601:5C8:8100:15C4:14C7:BD78:3CA5:8886 (talk)