Divergent Function/Examples/Values for Rational Numbers

Example of Divergent Function

Let $f: \R \to \R$ be such that:

$\map f x = \begin {cases}

0 & : x \in \Q \\ 1 & : x \notin \Q \end {cases}$

Then $x$ converges to neither $0$ nor $1$ and hence is divergent (although, it needs to be noted, not to infinity).