Editing Ordered pair (section)

===Cantor–Frege definition===
Early in the development of the set theory, before paradoxes were discovered, Cantor followed Frege by defining the ordered pair of two sets as the class of all relations that hold between these sets, assuming that the notion of relation is primitive:<ref>{{cite book |last=Frege |first=Gottlob |year=1893 |title=Grundgesetze der Arithmetik |url=https://korpora.zim.uni-duisburg-essen.de/Frege/PDF/gga1_o_corr.pdf |location=Jena |publisher=Verlag Hermann Pohle | section = 144}}</ref>
<math display="block">(x, y) = \{R : x R y \}.</math>

This definition is inadmissible in most modern formalized set theories and is methodologically similar to defining the [[Cardinality|cardinal]] of a set as the class of all sets equipotent with the given set.<ref>{{cite book |last=Kanamori |first=Akihiro |year=2007 |title=Set Theory From Cantor to Cohen |url=http://math.bu.edu/people/aki/16.pdf |publisher=Elsevier BV }} p. 22, footnote 59</ref>