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WDCodomain

Definition·D112

The declared target of a relation or function: the set its values are allowed to occupy.

for a relation from to : the declared target set, the set the values of are allowed to occupy.
In words
The codomain of R is the declared target B: the set its values are allowed to occupy, fixed as part of the phrase "R from A to B" rather than read off from its pairs.
Rests onno axioms yet
Never needed: F02 · F03 · F04 · F05 · F06 · F08 · F09 · F10 · F11 · F12 · F13 · F14 · A01 · A02 · A03 · A04 · A05 · A06 · A07 · A08 · A09 (computed from the citation graph, not asserted).

Remarks

The codomain is data attached to the presentation " ", not a function of the pairs: the same graph can be viewed as a relation into any larger target, which is why a function's target is not recoverable from its graph alone. The part actually reached is the range , a subset of the codomain that may be proper; the function is surjective exactly when . On the input side, the domain and source play the dual roles.
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