So, the question goes like this "Prove that the intersection of an arbitrary nonempty collection of subgroups of $G$ is again a subgroup of $G$ (do not assume the collection is countable)."
At first, I thought of approaching this question with a normal mathematical induction. ( Assume true for base case, prove that if it's true for $n$ number of set, then it must be true for $n+1$ number of set and so on so forth) However, the bold part of the question confused me. Isn't it the case that if we use MI to prove this, the set is countable? ( although, it could be countably infinite ). Or, does the question actually ask us not to assume the number of sets is finite instead?
Thanks in advance for the pointers.