Every number, both rational and irrational, is the limit of a Cauchy sequence. For example 0 is the limit of infinitely many different Cauchy sequences. One is 1,1/2, 1/4, 1/8,....
:<math>\pi\ = 3.1415926...</math>
==Formulations==
An irrational number is formally defined to be the limit of a [[Cauchy sequence]] of rational numbers.