User zero - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T02:32:43Z http://mathoverflow.net/feeds/user/27712 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/116870/given-a-sequence-of-real-numbers-do-the-following-conditions-suffice-to-guarantee Given a sequence of real numbers,do the following conditions suffice to guarantee convergence to 0? Zero 2012-12-20T15:21:25Z 2012-12-21T23:47:56Z <p>If <code>\$x_{a+1}\$-\$x_{a}\$</code> converges to <code>\$0\$</code> and <code>\$x_{2a}\$-\$2x_{a}\$</code> converges to <code>\$0\$</code> , does that imply <code>\$x_a\$</code> converges to <code>\$0\$</code>? </p> http://mathoverflow.net/questions/111269/number-theory-question Number theory question Zero 2012-11-02T11:55:20Z 2012-11-02T12:19:02Z <p>Given \$a\$ and \$b\$ irrational numbers with \$a/b\$ also irrational, how do you prove that <code>\$( \{ na\} , \{ nb \})\$</code> is dense in \$[0,1] * [0,1]\$ , where \$n\$ ranges over the integers? </p> <p><code>\$\{x\}\$</code> is the fractional part of \$x\$ . </p> <p>I'm also curious about the general case, with \$n\$ irrational numbers , linearly independent over \$Q\$ , resulting in density over \$[0,1]^n\$ .</p>