On Tuesday 14 October 2008, Dan Asimov wrote:
This is so cool! I love results like this, where a simply stated problem has a straightforward answer, except for some small and/or strange set. ... I am interested to hear of mathematical results that have a small and strange set of exceptions.
A few I can think of are these: ... Other such examples are solicited.
Classification of finite simple groups. (A few nice "obvious" families, plus the sporadic ones.) I'm not convinced by your examples of the form "Such-and-such a ring always has non-unique factorization, except for these cases"; this seems a bit like Mike Stay's joke example "all even numbers are composite, except 2". I mean, surely the real story for k(sqrt(d)), for instance, is that the class number function -> oo as d -> oo, so obviously it's only 1 for a finite number of cases. -- g