In math lesson, our teacher showed this formula.
$Q = \{\frac{a}b\}\land (a\land b\in Q)\land (b\neq 0)$
According to this formula, $\frac{0}\pi$ is... strange.
You know, $\frac{0}\pi$ is 0 and 0 is rational. But $\pi$ is irrational. That means $b$ is irrational.
So... Is $\frac{0}\pi$ rational?
2026-04-05 05:07:30.1775365650
Is $\frac{0}{\pi}$ rational?
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It happens that $\dfrac0\pi=\dfrac01(=0)$. So, $\dfrac0\pi$ is rational.
Also, $\dfrac{\sqrt2}{\sqrt8}$ is rational (in spite of the fact that $\sqrt2$ and $\sqrt8$ are irrational), since it's equal to $\dfrac12$. It's a similar situation: the fact that I can write a number as a quotient of two numbers such that at least one of them is not an integer doesn't allow me to deduce that that number is irrational.