The von Neumann (NOY-mahn) hierarchy is defined using transfinite recursion starting with this mathematical construct.
The von Neumann (NOY-mahn) hierarchy is defined using transfinite recursion starting with this mathematical construct. For any topological space, this entity and the whole space will always have the property of being "clopen," or being open and closed simultaneously. The Cartesian product of any object A with this other object will always itself yield this object. In a vacuous truth, the universal quantifier is applied to this entity. The (*) power set always includes this construct, which has a cardinality of zero. The intersection of two disjoint sets yields this object, and it is always the subset of any given set. A circle with a slash through it represents, for 10 points, what set that contains no elements and is sometimes called the "null set?"
The von Neumann (NOY-mahn) hierarchy is defined using transfinite recursion starting with this mathematical construct.
empty set [or void set; accept null set before the word "null" is read; prompt on set until the word "clopen"]