0. Set of symbols
1. Alphabet
2. Deduction system
3. Theory
4. Zermelo-Fraenkel set theory
5. Set
6. Binary cartesian set product
7. Binary relation
Map
Formulation 0
A D4: Binary relation $M = (X \times Y, f)$ is a map if and only if
(1) $\forall \, x \in X : \forall \, y, y' \in Y \, ((x, y), (x, y') \in f \quad \Rightarrow \quad y = y')$ (D358: Right-unique binary relation)
(2) $\forall \, x \in X : \exists \, y \in Y : (x, y) \in f$ (D359: Left-total binary relation)
Also known as
Mapping
Subdefinitions
» D427: Isotone map
Child definitions
» D428: Antitone map
» D468: Bijective map
» D326: Cartesian product
» D527: Composite map
» D1519: Constant map
» D3660: Countable map
» D219: Empty map
» D747: Idempotent map
» D440: Identity map
» D43: Inclusion map
» D467: Injective map
» D1492: Map graph
» D528: Map image
» D529: Map inverse image
» D429: Monotone map
» D2660: Set endomorphism
» D466: Surjective map
Results
» R1869: Characterisation of equality of maps