Fundamental Group of $(\mathbb{Q},0)$

Question

I was asked to calculate the group $\pi_1(\mathbb{Q},0)$. But I'm a little stuck. From my understanding, that means the group of equivalence classes of loops in $\mathbb{Q}$ with basepoint $0$. I think that the only loop that works is the map that takes everything to $0$ since that's the only way it is a continuous function, but I'm not sure how to translate that into the language of groups.

Answer 1

Since $\mathbb{Q}$ is completely disconnected the only continuous loops are the constant ones (the image of a connected set is connected). So the group must be trivial, since it only has one element.