User foo - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T02:37:06Z http://mathoverflow.net/feeds/user/1990 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/6337/increasing-bijection/6341#6341 Answer by Foo for increasing bijection Foo 2009-11-21T01:47:53Z 2009-11-21T01:47:53Z <p>Choose sequences of rational numbers $a_i$ and $b_i$ strictly monotonically converging to $\sqrt{2}$ from below and above. Map $a_i$ to $-1/i$ and map $b_i$ to $1/i$. Extend linearly. This meets your criteria, if we allow ourselves to "know" where $p/q$ is with respect to the $a_i$ and the $b_i$. </p>