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:
“Of all reformers Mr. Sentiment is the most powerful. It is incredible the number of evil practices he has put down: it is to be feared he will soon lack subjects, and that when he has made the working classes comfortable, and got bitter beer into proper-sized pint bottles, there will be nothing left for him to do.”
—Anthony Trollope (1815–1882)