a1 University College, London
It was remarked by Liouville in 1844 that there is an obvious limit to the accuracy with which algebraic numbers can be approximated by rational numbers; if α is an algebraic number of degree n (at least 2) then
for all rational numbers h/q, where A is a positive number depending only on α.
(Received January 26 1955)
(Revised May 20 1955)