Definition: In mathematics, an addendum to a set S is any element that belongs to S but not to any other set in S. For example, in the set {1, 2, 3}, the addendum for 4 is 5 because it does not belong to any subset of the set. The definition of "addendum" can be found in many areas of mathematics, including set theory and topology. In set theory, an addendum to a set S is defined as a subset that is not a member of S but is contained within S. For example, if S is {a, b, c}, then the addendum for 4 is {c} because it does not belong to any other set in S. In topology and algebra, an addendum can be defined as a set that has the property that its complement in the given set is also in the set. For example, if S is the set of all points in the plane with positive coordinates, then the complement of the point (1, 2) would be the set {(-∞, 0], and because both 1 and 2 are not in this set, they are addendums for 4. In summary, an addendum to a set S is any element that belongs to S but does not belong to any other set in S. The definition of "addendum" can be found in many areas of mathematics, including set theory and topology.
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