Definition·D009
Set difference
The members of one set that do not belong to another.
In words
x belongs to the difference of A and B exactly when x belongs to A and x does not belong 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 (computed from the citation graph, not asserted).
Remarks
Exists by Separation:
. No complement of
relative to the universe is possible, because there is no universal set (T02); difference is always taken inside an ambient set
. Removing a single element is the common special case
, using the singleton of D003.