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
Ringoid
Semiring
Ring
Additive group
Additive monoid
Additive semigroup
Additive groupoid
Additive binary operation
Natural number addition operation
Integer addition operation
Rational addition operation
Real addition operation
Definition D607
Complex addition operation
Formulation 0
Let $\mathbb{C}$ be the D372: Set of complex numbers.
Let $\pm$ be the D606: Real addition operation.
The complex addition operation is the D554: Binary operation \begin{equation} + : \mathbb{C} \times \mathbb{C} \to \mathbb{C}, \quad (a, b) + (c, d) = (a \pm c, b \pm d) \end{equation}