axiom of union मीनिंग इन हिंदी

उदाहरण वाक्य

1. Von Neumann's axiom implies the axioms of union.
2. This union exists regardless of the set's size, by the axiom of union.
3. In 1968, Azriel Levy proved that von Neumann's axiom implies the axiom of union.
4. First, he proved without using the axiom of union that every set of ordinals has an upper bound.
5. Then we can apply the axiom of union to that to get an ordinal greater than or equal to & omega;.
6. Note that adopting this as an axiom schema will not replace the axiom of union, which is still needed for other situations.
7. 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.
8. 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.
9. 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 }: