Axiomatic Set Theory: Unveiling the Foundations of Mathematics
| Description: Axiomatic Set Theory: Unveiling the Foundations of Mathematics | |
| Number of Questions: 15 | |
| Created by: Aliensbrain Bot | |
| Tags: set theory axiomatic set theory foundations of mathematics |
Which axiom in Zermelo-Fraenkel set theory states that for any set (A) and any property (P(x)), there exists a set (B) whose elements are exactly the elements (x) of (A) that satisfy the property (P(x))?
In Zermelo-Fraenkel set theory, which axiom guarantees the existence of the empty set?
Which axiom in Zermelo-Fraenkel set theory allows us to combine two sets (A) and (B) into a single set (C) containing all the elements of both (A) and (B)?
In Zermelo-Fraenkel set theory, which axiom asserts that for any set (A), there exists a set (P(A)) whose elements are all the subsets of (A)?
Which axiom in Zermelo-Fraenkel set theory guarantees the existence of an infinite set?
In Zermelo-Fraenkel set theory, which axiom allows us to replace a set (A) with a set (B) that has the same elements as (A) but possibly arranged in a different order?
Which axiom in Zermelo-Fraenkel set theory asserts that for any set (A), there exists a set (\mathcal{P}(A)) whose elements are all the subsets of (A) and (\mathcal{P}(A)) is a set?
In Zermelo-Fraenkel set theory, which axiom guarantees the existence of a set containing all sets?
Which axiom in Zermelo-Fraenkel set theory asserts that for any set (A), there exists a set (\mathcal{P}(A)) whose elements are all the subsets of (A)?
In Zermelo-Fraenkel set theory, which axiom allows us to select a single element from each non-empty subset of a set (A) and form a new set (B) consisting of these selected elements?
Which axiom in Zermelo-Fraenkel set theory asserts that for any set (A), there exists a set (\mathcal{P}(A)) whose elements are all the subsets of (A)?
In Zermelo-Fraenkel set theory, which axiom guarantees the existence of a set containing all sets?
Which axiom in Zermelo-Fraenkel set theory asserts that for any set (A), there exists a set (\mathcal{P}(A)) whose elements are all the subsets of (A)?
In Zermelo-Fraenkel set theory, which axiom allows us to select a single element from each non-empty subset of a set (A) and form a new set (B) consisting of these selected elements?
Which axiom in Zermelo-Fraenkel set theory asserts that for any set (A), there exists a set (\mathcal{P}(A)) whose elements are all the subsets of (A)?