Editing Diophantine approximation (section)

===Badly approximable numbers===
A '''badly approximable number''' is an ''x'' for which there is a positive constant ''c'' such that for all rational ''p''/''q'' we have

:<math>\left|{ x - \frac{p}{q} }\right| > \frac{c}{q^2} \ . </math>

The badly approximable numbers are precisely those with [[Restricted partial quotients|bounded partial quotients]].<ref name=Bug245>{{harvnb|Bugeaud|2012|p=245}}</ref>

Equivalently, a number is badly approximable [[if and only if]] its [[Markov constant]] is finite or equivalently its simple continued fraction is bounded.