cirpis

7 ms·

1. 1.▲
   by cirpis 1mo ago

   I dont think theres an issue, the point P' simply belongs to both sides of itself. With this convention in place it is still true that there are two points in the same side, and the proof goes through verbatim. Its mostly a question of
2. 2.▲
   by cirpis 2y ago

   This seems like a needlesly defensive answer. If there are no examples then just say so. It is mathematics after all, some of it is beautiful to explore just for its own sake, no examples or applications neccesary. But claiming a technique
3. 3.▲
   by cirpis 5y ago

   Two things: 1. The result is asymptotical, i.e. holds as number of samples approach infinity. 2. The result is an "almost surely" result, i.e. in the collection of all possible infinite samples, the set of samples for which it fai
4. 4.▲
   by cirpis 5y ago

   There is no mistake in the definition and this is all elaborated upon in page 4 of the article. Quote: " On the other hand, it is not very hard to prove that the minimum possible value of ξn(X, Y ) is −1/2 + O(1/n), and the m