ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Binary cartesian set product
Binary relation
Map
Operation
N-operation
Binary operation
Enclosed binary operation
Groupoid
Semigroup
Monoid
Group
Definition D1240
Trivial group
Formulation 0
An D548: Ordered pair $G = (X, f)$ is a trivial group if and only if
(1) $X$ is a D135: Singleton set
(2) $f$ is a D4428: Canonical identity map on $X$