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WDDomain

Definition·D110

The inputs a relation actually uses: the set of first coordinates of its pairs.

for a relation from to : the set of first coordinates that occur.
In words
The domain of R gathers the elements a of A that for some b are related by R to b.
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

exists by Separation as a subset of the source . When is a function it is total, so every occurs and ; for a general relation the domain may be a proper subset of . The second coordinates form the range, the declared target is the codomain, and the converse swaps the first two: .
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