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Let us write <math>f = (\mathrm{obj_1}f, \mathrm{obj_2}f, \mathrm{obj_{12}}f)\!</math> to express what has been said so far.
Let us write <math>f = (\mathrm{obj_1}f, \mathrm{obj_2}f, \mathrm{obj_{12}}f)\!</math> to express what has been said so far.
When it comes to parsing the notation <math>{}^{\backprime\backprime} f : X \to Y {}^{\prime\prime},\!</math> everyone takes the part <math>{}^{\backprime\backprime} X \to Y {}^{\prime\prime}\!</math> to specify the \textit{type} of the function, that is, the pair <math>(\mathrm{obj_1}f, \mathrm{obj_2}f),\!</math> but <math>{}^{\backprime\backprime} f {}^{\prime\prime}\!</math> is used equivocally to denote both the triple and the subset <math>\mathrm{obj_{12}}f\!</math> that forms one part of it. One way to resolve the ambiguity is to formalize a distinction between a function and its \textit{graph}, letting <math>\mathrm{graph}(f) := \mathrm{obj_{12}}f.\!</math>
When it comes to parsing the notation <math>{}^{\backprime\backprime} f : X \to Y {}^{\prime\prime},\!</math> everyone takes the part <math>{}^{\backprime\backprime} X \to Y {}^{\prime\prime}\!</math> to specify the ''type'' of the function, that is, the pair <math>(\mathrm{obj_1}f, \mathrm{obj_2}f),\!</math> but <math>{}^{\backprime\backprime} f {}^{\prime\prime}\!</math> is used equivocally to denote both the triple and the subset <math>\mathrm{obj_{12}}f\!</math> that forms one part of it. One way to resolve the ambiguity is to formalize a distinction between a function and its ''graph'', letting <math>\mathrm{graph}(f) := \mathrm{obj_{12}}f.\!</math>
Another tactic treats the whole notation <math>{}^{\backprime\backprime} f : X \to Y {}^{\prime\prime}\!</math> as sufficient denotation for the triple, letting <math>{}^{\backprime\backprime} f {}^{\prime\prime}\!</math> denote <math>\mathrm{graph}(f).\!</math>
Another tactic treats the whole notation <math>{}^{\backprime\backprime} f : X \to Y {}^{\prime\prime}\!</math> as sufficient denotation for the triple, letting <math>{}^{\backprime\backprime} f {}^{\prime\prime}\!</math> denote <math>\mathrm{graph}(f).\!</math>
* Carnap, Rudolf (1958), ''Introduction to Symbolic Logic with Applications'', Dover Publications, New York, NY.
* Carnap, Rudolf (1958), ''Introduction to Symbolic Logic with Applications'', Dover Publications, New York, NY.
* Chang, C.C., and Keisler, H.J. (1973), ''Model Theory'', North-Holland, Amsterdam, Netherlands.
* Chang, C.C., and Keisler, H.J. (1973), ''Model Theory'', North-Holland, Amsterdam, Netherlands.
* van Dalen, Dirk (1980), \text{Logic and Structure'', 2nd edition, Springer-Verlag, Berlin, Germany.
* van Dalen, Dirk (1980), ''Logic and Structure'', 2nd edition, Springer-Verlag, Berlin, Germany.
* Devlin, Keith J. (1993), ''The Joy of Sets : Fundamentals of Contemporary Set Theory'', 2nd edition, Springer-Verlag, New York, NY.
* Devlin, Keith J. (1993), ''The Joy of Sets : Fundamentals of Contemporary Set Theory'', 2nd edition, Springer-Verlag, New York, NY.
* Halmos, Paul Richard (1960), ''Naive Set Theory'', D. Van Nostrand Company, Princeton, NJ.
* Halmos, Paul Richard (1960), ''Naive Set Theory'', D. Van Nostrand Company, Princeton, NJ.
===Focal nodes===
===Focal nodes===
* [[Inquiry Live]]
* [[Inquiry Live]]
* [[Logic Live]]
* [[Logic Live]]
===Peer nodes===
===Peer nodes===
* [http://intersci.ss.uci.edu/wiki/index.php/Relation_theory Relation Theory @ InterSciWiki]
* [http://intersci.ss.uci.edu/wiki/index.php/Relation_theory Relation Theory @ InterSciWiki]
* [http://mywikibiz.com/Relation_theory Relation Theory @ MyWikiBiz]
* [http://mywikibiz.com/Relation_theory Relation Theory @ MyWikiBiz]
* [http://ref.subwiki.org/wiki/Relation_theory Relation Theory @ Subject Wikis]
* [http://en.wikiversity.org/wiki/Relation_theory Relation Theory @ Wikiversity]
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* [http://beta.wikiversity.org/wiki/Relation_theory Relation Theory @ Wikiversity Beta]
===Logical operators===
===Logical operators===
Portions of the above article were adapted from the following sources under the [[GNU Free Documentation License]], under other applicable licenses, or by permission of the copyright holders.
Portions of the above article were adapted from the following sources under the [[GNU Free Documentation License]], under other applicable licenses, or by permission of the copyright holders.
* [http://intersci.ss.uci.edu/wiki/index.php/Relation_theory Relation Theory], [http://intersci.ss.uci.edu/ InterSciWiki]
* [http://mywikibiz.com/Relation_theory Relation Theory], [http://mywikibiz.com/ MyWikiBiz]
* [http://mywikibiz.com/Relation_theory Relation Theory], [http://mywikibiz.com/ MyWikiBiz]
* [http://mathweb.org/wiki/Relation_theory Relation Theory], [http://mathweb.org/wiki/ MathWeb Wiki]
* [http://planetmath.org/RelationTheory Relation Theory], [http://planetmath.org/ PlanetMath]
* [http://semanticweb.org/wiki/Relation_theory Relation Theory], [http://semanticweb.org/ Semantic Web]
* [http://semanticweb.org/wiki/Relation_theory Relation Theory], [http://semanticweb.org/ Semantic Web]
* [http://planetmath.org/encyclopedia/RelationTheory.html Relation Theory], [http://planetmath.org/ PlanetMath]
* [http://wikinfo.org/w/index.php/Relation_theory Relation Theory], [http://wikinfo.org/w/ Wikinfo]
* [http://planetphysics.org/encyclopedia/RelationTheory.html Relation Theory], [http://planetphysics.org/ PlanetPhysics]
* [http://en.wikiversity.org/wiki/Relation_theory Relation Theory], [http://en.wikiversity.org/ Wikiversity]
* [http://beta.wikiversity.org/wiki/Relation_theory Relation Theory], [http://beta.wikiversity.org/ Wikiversity Beta]
* [http://textop.org/wiki/index.php?title=Theory_of_relations Relation Theory], [http://textop.org/wiki/ Textop Wiki]
* [http://en.wikipedia.org/w/index.php?title=Theory_of_relations&oldid=45042729 Relation Theory], [http://en.wikipedia.org/ Wikipedia]
* [http://en.wikipedia.org/w/index.php?title=Theory_of_relations&oldid=45042729 Relation Theory], [http://en.wikipedia.org/ Wikipedia]
[[Category:Charles Sanders Peirce]]
[[Category:Charles Sanders Peirce]]
