Axiomatic WikiWWikiDDefinitionsRange
Definition·D111
The outputs a relation actually reaches: the set of second coordinates of its pairs.
for a relation
from
to
: the set of second coordinates that occur.
In words
The range of R gathers the elements b of B that some a is related to via R.
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 codomain
, and may be a proper subset: a function
reaches all of
exactly when it is surjective. It is the image of the whole domain, written
, and the converse swaps range and domain:
.
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