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just wondering what this could mean:

"Remark: AC is trivial for |I|=1, since A non-empty means [tex]\exists x[/tex] st [tex]x \in A [/tex]. Similarly for |I| finite (induction on |I|)."

I is the index set. As in, our sets are {A_i with i in I}.

I'm really not sure what this explanation is getting at.

Thanks