query: Why are the group axioms called "axioms"?
positive_passages.docid: 17480
positive_passages.text: Meaning of the word "axiom"
negative_passages.docid: 139678
negative_passages.text: Advantage of accepting the axiom of choice
negative_passages.docid: 144899
negative_passages.text: Do We Need the Axiom of Choice for Finite Sets?
negative_passages.docid: 27600
negative_passages.text: Gödel's (in)completeness theorems and the axiomatization of Euclidean geometry
negative_passages.docid: 14097
negative_passages.text: A semigroup $X$ is a group iff for every $g\in X$, $\exists! x\in X$ such that $gxg = g$
negative_passages.docid: 33294
negative_passages.text: The correspondence theorem for groups
negative_passages.docid: 153797
negative_passages.text: Is a quotient group a subgroup?
negative_passages.docid: 92050
negative_passages.text: Poincaré's theorem about groups
negative_passages.docid: 2334
negative_passages.text: Best book on axiomatic set theory.
negative_passages.docid: 134368
negative_passages.text: In Group theory proofs what is meant by "well defined"
negative_passages.docid: 7865
negative_passages.text: Complete Newbie: Axiom of Foundation Exercise
negative_passages.docid: 25421
negative_passages.text: Simple or not simple Groups
negative_passages.docid: 37723
negative_passages.text: Proof that $-(-x) = x$ using just the field axioms
negative_passages.docid: 45508
negative_passages.text: Is the empty set a group?
negative_passages.docid: 45623
negative_passages.text: Axiom of Choice: What exactly is a choice, and when and why is it needed?
negative_passages.docid: 114431
negative_passages.text: Monoids and Subgroups
negative_passages.docid: 93147
negative_passages.text: Topological groups, why need them?