A Liouville Number is a unique kind of transcendental number that can be very closely estimated by rational numbers.Precisely, a Liouville Number is a real number x, with a mathematical property that, for any positive integer n, there is integer’s p and q (with q>1) in a way:0< |x – p/q |< 1/qnNow you are aware that x is irrational, thus there will be a difference between x and any p/q always: thus, we obtain the "0<" part.But the 2nd inequality reveals how little the difference is. In point of fact the inequality notifies "the number can be estimated infinitely close, but never quite reaching there". In fact Liouville made it possible to reveal that if a number has a quick converging series of rational estimations then it is transcendental.Another amazing property is that for any positive integer n, there is an infinite number of pairs of integers (p,q) abiding by the above inequality.