query: Are definitions axioms?
positive_passages.docid: 21374
positive_passages.text: What is exactly the difference between a definition and an axiom?
negative_passages.docid: 48030
negative_passages.text: Axiom of Choice: Where does my argument for proving the axiom of choice fail? Help me understand why this is an axiom, and not a theorem.
negative_passages.docid: 21202
negative_passages.text: Axiom of choice is equivalent to every relation includes a function with the same domain
negative_passages.docid: 12539
negative_passages.text: Set Theory: Equivalency of Axiom of Choice and Choice Function
negative_passages.docid: 135957
negative_passages.text: Why in an inconsistent axiom system every statement is true? (For Dummies)
negative_passages.docid: 88736
negative_passages.text: How does the Axiom of Extensionality prove the uniqueness of Specified sets?
negative_passages.docid: 84485
negative_passages.text: What is the purpose of the Axiom of regularity/foundation?
negative_passages.docid: 29744
negative_passages.text: Compactness and axiomatisability
negative_passages.docid: 59820
negative_passages.text: ZF Extensionality axiom
negative_passages.docid: 118573
negative_passages.text: Why is the Axiom of Infinity necessary?
negative_passages.docid: 125204
negative_passages.text: Is the second defined arbitrarily?
negative_passages.docid: 77654
negative_passages.text: Is the uncertainty principle axiomatic or derived?
negative_passages.docid: 102202
negative_passages.text: The smallest infinity and the axiom of choice
negative_passages.docid: 84562
negative_passages.text: Proof using only field axioms
negative_passages.docid: 9330
negative_passages.text: Meaning behind Filter in Set Theory
negative_passages.docid: 22824
negative_passages.text: How to know if something is a primitive concept, a law, a definition or a theorem
negative_passages.docid: 35123
negative_passages.text: How do the separation axioms follow from the replacement axioms?