# find a sequence of rational numbers such that: $\lim_{n \to \infty} x_n = x_0$ when $x_0$ is irrational [duplicate]

let $x_0$ be irrational number.

How can I find a sequence of rational numbers such that: $\lim_{n \to \infty} x_n = x_0$

I know such sequence exists from a known theory, yet can't find one

I could only find a sequence of irrational numbers that goes to a rational limit but not the other way around

• What about Euler number? – rtybase Dec 24 '16 at 0:30

Consider the decimal expansion $x_0=z+0.d_1d_2d_3...$ where $z$ is the integer part. Then let $x_n=z+0.d_1d_2...d_n$