# Rational, or Irrational?

Algebra Level 1

Let $$\mathbb{R}^+$$ be the set of all non-negative real numbers, and let $$f:\mathbb{R}^+ \to \mathbb{R}^+$$ be defined as $f(x)= \begin{cases} \frac{1}{q} & \text{ if } x= \frac{p}{q}, \\ \\ 0 & \text{ if } x=0 \text{ or } x \text{ is an irrational number}, \end{cases}$ where $$p$$ and $$q$$ are coprime positive integers. What is the value of $f\left(\frac{12}{13}\right)+f(\pi)+f(0.25)?$

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