User anne bauval - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T02:27:39Z http://mathoverflow.net/feeds/user/30620 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/106819/simultaneous-diophantine-approximation/118814#118814 Answer by Anne Bauval for Simultaneous diophantine approximation Anne Bauval 2013-01-13T15:10:32Z 2013-01-13T15:10:32Z <p>There is a flaw in the last line : ║(n-r)x║ is not lower than ║x║/2 because ║ ║, which means "distance to ℤ^d", is not positively homogeneous. Anyway, this proof cannot hold because it does not use the (necessary) hypothesis of linear independence but only that the x_i's are nonzero.</p> http://mathoverflow.net/questions/106819/simultaneous-diophantine-approximation/118814#118814 Comment by Anne Bauval Anne Bauval 2013-01-14T00:07:43Z 2013-01-14T00:07:43Z Thank you very much, and shame on me !!! I put your proof on <a href="http://fr.wikipedia.org/wiki/Th&#233;or&#232;me_de_Kronecker_(approximation_diophantienne" rel="nofollow">fr.wikipedia.org/wiki/&hellip;</a>)