Closed Definition/Meaning:
A term applied to a set s on whose
elements a binary operation
° is defined and that possesses
the property that, for every (s, t) in S, the quantity s
° t is also in S; S is then said to be closed under °. A
similar definition holds for
unary operations such as ~. A set S is
closed under ~ provided that, when s is in S. the quantity ~ is also
in S.
The set of integers is closed under the usual arithmetic
operations of addition, subtraction, and multiplication, but is not
closed under division.
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