In number theory, a Liouville number is a real number x with the property that, for every positive integer n, there exist integers p and q with q > 1 and such that
A Liouville number can thus be approximated "quite closely" by a sequence of rational numbers. In 1844, Joseph Liouville showed that all Liouville numbers are transcendental, thus establishing the existence of transcendental numbers for the first time.
Read more about Liouville Number: Elementary Properties, Liouville Constant, Uncountability, Liouville Numbers and Measure, Structure of The Set of Liouville Numbers, Irrationality Measure, Liouville Numbers and Transcendence
Famous quotes containing the word number:
“In view of the fact that the number of people living too long has risen catastrophically and still continues to rise.... Question: Must we live as long as modern medicine enables us to?... We control our entry into life, it is time we began to control our exit.”
—Max Frisch (1911–1991)