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The contents of the Theory of relations page were merged into Finitary relation. For the contribution history and old versions of the redirected page, please see its history; for the discussion at that location, see its talk page. |
It mostly goes over the binary relations material oven and over. Some1Redirects4You ( talk) 18:35, 24 April 2015 (UTC)
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)
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)
'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)
Presently the article contains this definition:
With no reference given, is there an editor defending this definition? — Rgdboer ( talk) 23:06, 3 September 2018 (UTC)
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:
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)