I've seen written the following sentence:
Let $G_i$ be a collection of more than one non-trivial group. Prove that their free product is non-abelian.
Now if $\{G_i\}$ denotes the collection of more than one non-trivial group, must this collection be finite? I've only seen the definition for free products of two groups. I can see how this could repeatedly be applied to a finite number of groups. But what about a countable or an uncountable number of groups? Does here the author just imply that $\{G_i\}$ is finite?