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To prepare for graduate analysis (I start grad school in a week), I've been reading through Rudin's

*Principles of Mathematical Analysis*. I noticed today that an exercise in the book is to prove that the empty set is a member of every set.

I'm not asking for the solution, but I was wondering how one would go about proving this. Whenever you prove subsets, you chase elements. But the empty set has no elements. Are there other methods of proving subsets?