| • घात-कुलक-अभिगृहीत | |
| axiom: सूक्ति स्वयं | |
| of: स् का की पर बाबत | |
| power: राज विद्युत् | |
| power set: घात समुच्चय घात | |
| set: स्वाभाविक स्थिति | |
axiom of power set meaning in Hindi
axiom of power set sentence in Hindi
Examples
More: Next- Tarski's axiom also implies the axioms of power set.
- The axiom of power set appears in most axiomatizations of set theory.
- Within the framework of Zermelo Fraenkel set theory, the axiom of power set guarantees the existence of the power set of any given set.
- In axiomatic set theory ( as developed, for example, in the ZFC axioms ), the existence of the power set of any set is postulated by the axiom of power set.
- Both these methods produce systems which satisfy the axioms of second-order arithmetic, since the axiom of power set allows us to quantify over the power set of \ omega, as in second-order logic.
- There are alternative set theories, e . g . " general set theory " ( GST ), Kripke Platek set theory, and pocket set theory ( PST ), that deliberately omit the axiom of power set and the axiom of infinity and do not allow the definition of the infinite hierarchy of infinites proposed by Cantor.