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 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 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>