A proof that there exists an infinite collection of sets whose cartesian product is nonempty.

I stumbled upon this succinct proof while discussing topology with some friends. Suppose that, for any infinite collection of sets , the cartesian product, i.e. the collection of all choice functions on , is empty. I claim this implies Tychonoff’s theorem, which states that the product of any collection of compact topological spaces is aContinue reading “A proof that there exists an infinite collection of sets whose cartesian product is nonempty.”

Every set has a minimal superset

I credit Mikey and Atal with this proof. For any set which is a subset of a (lets say much larger) set , a minimal superset of is a set such that , and if , then for any superset of . I claim that any set has a minimal superset. We see this byContinue reading “Every set has a minimal superset”

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