Talk:Binary relation
Add topicLatest comment: 2 months ago by Jochen Burghardt in topic Inconsistent Definition of Bijective
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Inconsistent Definition of Bijective
[edit]The definition of a bijective relation on this page is that it is injective and surjective. This would allow the relation R: {a,b} x {u,v,w} where aRu, aRv, and bRw. However, this page then says "In other words, every element of the domain has exactly one image element and every element of the codomain has exactly one preimage element", which would not allow R. Those statements are equivalent only for injective and surjective *functions*. Which definition is true? ~2026-30270-13 (talk) 12:11, 20 May 2026 (UTC)
- Where did you find that definition? The article defines
- (in paragraph "Uniqueness properties":) injective relation,
- (in paragraph "Totality properties":) surjective relation,
- (in paragraph "Uniqueness and totality properties":) injective function, surjective function, bijective function.
- I now indented the latter 3 definitions to emphasize that they are subcases of functions. Your example is not covered by any of these definitions; it may be valuable as a counterexample demonstrating why no notion of bijective relation (intended as a proper genenralization of bijective function) can be defined. - Jochen Burghardt (talk) 13:20, 20 May 2026 (UTC)