Talk:Finitary relation

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The content of Theory of relations was merged into Finitary relation. The former page's history now serves to provide attribution for that content in the latter page, and it must not be deleted as long as the latter page exists. For the discussion at that location, see its talk page.

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It mostly goes over the binary relations material oven and over. Some1Redirects4You (talk) 18:35, 24 April 2015 (UTC)Reply

There isn't much theory in the Theory of relations wiki article. Just a reiteration of what's here plus a few more definitions. A merge seems in order. Some1Redirects4You (talk) 18:43, 24 April 2015 (UTC)Reply

After removing the seemingly WP:OR parts from the "theory" article there wasn't much of substance left in it so I've effected the merge as a redirect. If someone finds some reliable sources (not crowdsourced math wikis) for the material, feel free to restore either here or in its own article if deemed substantive enough. Some1Redirects4You (talk) 14:07, 19 May 2015 (UTC)Reply

About this part: "any set (such as the collection of Nobel laureates) can be viewed as a collection of individuals having some property (such as that of having been awarded the Nobel prize)"

Any set is a subset. (That is why there is no set of all sets.) Therefore a unary relation assigns (selects the members of) a subset, not a set just from empty nothing.188.6.76.241 (talk) 16:47, 28 April 2017 (UTC)Reply

'Mathematically, then, a relation is simply an "ordered set"' — No; it is a set of ordered tuples, not ordered set. Boris Tsirelson (talk) 11:37, 13 February 2018 (UTC)Reply

Presently the article contains this definition:

Definition 2. A relation L over the sets X₁, …, X_k is a (k + 1)-tuple L = (X₁, …, X_k, G(L)), where G(L) is a subset of the Cartesian product X₁ × … × X_k. G(L) is called the graph of L.

With no reference given, is there an editor defending this definition? — Rgdboer (talk) 23:06, 3 September 2018 (UTC)Reply

As both category theory and relations are concerned with composition (of arrows and of relations, respectively), there is some interplay. Indeed, J. Lambek and P.J. Scott (1986) Introduction to Higher-order Categorical Logic, page 186 describes the category of relations, where the arrows are triples:

(α, | f |, β) and f ⊆ α x β.

They write "We often call | f | the graph of f." Further, from the computational point of view, the context of a relation is not to be presumed, so setting the cross product of sets containing the relation is required. Thus software requirements reach into definitions. — Rgdboer (talk) 21:42, 13 September 2018 (UTC)Reply