# Is there an irrational number arbitrarily close to another irrational number?

I know that there is a rational number arbitrarily close to an irrational, due to the density of real number. But what about an irrational number? Thanks!

Yes, consider $\alpha + \frac{1}{n}$ where $\alpha$ is irrational and $n$ is an integer. $\alpha + \frac{1}{n}$ is also irrational and can be made arbitrarily close to $\alpha$ by choosing $n$ to be sufficiently large.