https://maximummathematics.com/books/foundational-mathematics/set-theory/proof-technique-exhaustion/index.htmlAll of the proof techniques discussed thus far work on sets that have infinitely many elements. For example, we’ve talked about theorems that apply to all even numbers, not merely some of them. For example, for all even numbers, adding one yields an odd number. As another example, no matter which two even numbers are added together, the sum is always another even number. We’ve even talked about theorems that apply to all sets in general, not merely some of them. These include the set operations and the set equalities.Hugoen-US