Talk:Fano postulate

Fact or assumption

The article states that the Fano postulate is a "proposition" and a "fact". However, the rest of the text makes it clear that there are projective geometries in which the Fano postulate does not hold, and indeed, the example illustrated in Projective plane is precisely the case of a projective plane over a field of order 2, one of the cases in which the Fano postulate does not hold. Both references make it clear that Fano's postulate is a postulate, that is, an axiom assumed to hold for a class of projective geometries. Probably the article should also define the term "Fano configuration", a quadrangle with collinear diagonal points, and the terminology "Fano plane" for a projective plane in which Fano's postulate does not hold (as Gleason points out, the term "anti-Fano" would have been more sensible). Richard Pinch (talk) 14:37, 13 April 2017 (CEST)