axiom of union वाक्य
उदाहरण वाक्य
मोबाइल
- Von Neumann's axiom implies the axioms of union.
- This union exists regardless of the set's size, by the axiom of union.
- In 1968, Azriel Levy proved that von Neumann's axiom implies the axiom of union.
- First, he proved without using the axiom of union that every set of ordinals has an upper bound.
- Then we can apply the axiom of union to that to get an ordinal greater than or equal to & omega;.
- Note that adopting this as an axiom schema will not replace the axiom of union, which is still needed for other situations.
- The axiom of union produces a union whose size is not bigger than the size of the biggest set in the union times the number of sets in the union.
- These set theories only substituted the axiom of replacement and a form of the axiom of choice for the axiom of limitation of size because von Neumann's axiom system contains the axiom of union.
- Formally, the axiom of union states that for any set of sets \ mathcal { F } there is a set A containing every element that is a member of some member of \ mathcal { F }:
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