query: How do we show the set, for example A={1,2,3} follows the axiom of regularity? (According to Zermelo-Frankel axiomatic set theory)
positive_passages.docid: 142315
positive_passages.text: How does the Axiom of Regularity apply to $A=\{1,2,3\}$?
negative_passages.docid: 77286
negative_passages.text: Proving set theory question
negative_passages.docid: 77548
negative_passages.text: Given an arbitrary infinite set $S$, how to construct an injection $\mathbb{N} \to S$ with the Axiom of Choice?
negative_passages.docid: 12539
negative_passages.text: Set Theory: Equivalency of Axiom of Choice and Choice Function
negative_passages.docid: 20140
negative_passages.text: Example of set which contains itself
negative_passages.docid: 109219
negative_passages.text: How do the sets $\emptyset\times B,\ A\ \times \emptyset, \ \emptyset \times \emptyset $ look like?
negative_passages.docid: 51687
negative_passages.text: Is the set $ \ (\mathbb{Z}_p \setminus \mathbb{Z}) \cap \mathbb{Q}$ non-empty?
negative_passages.docid: 136735
negative_passages.text: Why is the cardinality of set S is 3^n, where S is the collection of all ordered pairs of disjoint subset of {1,2,3,...,n} where n is non negative.
negative_passages.docid: 34045
negative_passages.text: 3 Statements of axiom of choice are equivalent
negative_passages.docid: 31212
negative_passages.text: The existence of the empty set is an axiom of ZFC or not?
negative_passages.docid: 25874
negative_passages.text: Showing that a certain map is not flat by explicit counterexample
negative_passages.docid: 157924
negative_passages.text: $\forall x\in\mathbb{N}[(\exists y\in\mathbb{N}(2\leq y\land y<x\land y\ |\ x))\to(\exists z\in\mathbb{N}(2\leq z\land z\leq\sqrt x\land z\ |\ x))]$
negative_passages.docid: 42095
negative_passages.text: Existence in ZF of a set with countable power set
negative_passages.docid: 114608
negative_passages.text: Proof concerning regular space: there exist a closed set contained in any open set containing $x$
negative_passages.docid: 83023
negative_passages.text: From axiom of regularity, how can I prove $x \notin y \lor y \notin x$
negative_passages.docid: 86914
negative_passages.text: Cardinality of the set of hyperreal numbers
negative_passages.docid: 9330
negative_passages.text: Meaning behind Filter in Set Theory