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  2. Zero element - Wikipedia

    en.wikipedia.org/wiki/Zero_element

    Examples include: The empty set, which is an absorbing element under Cartesian product of sets, since { } × S = { } The zero function or zero map defined by z(x) = 0 under pointwise multiplication (f ⋅ g)(x) = f(x) ⋅ g(x) Many absorbing elements are also additive identities, including the empty set and the zero function.

  3. Signed measure - Wikipedia

    en.wikipedia.org/wiki/Signed_measure

    μ(E) ≥ 0 for each E in Σ such that E ⊆ P — in other words, P is a positive set; μ(E) ≤ 0 for each E in Σ such that E ⊆ N — that is, N is a negative set. Moreover, this decomposition is unique up to adding to/subtracting μ-null sets from P and N. Consider then two non-negative measures μ + and μ − defined by

  4. Empty set - Wikipedia

    en.wikipedia.org/wiki/Empty_set

    The empty set is the set containing no elements. In mathematics, the empty set or void set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. [1] Some axiomatic set theories ensure that the empty set exists by including an axiom of empty set, while in other theories, its existence can be deduced.

  5. Null set - Wikipedia

    en.wikipedia.org/wiki/Null_set

    The SierpiƄski triangle is an example of a null set of points in . In mathematical analysis, a null set is a Lebesgue measurable set of real numbers that has measure zero. This can be characterized as a set that can be covered by a countable union of intervals of arbitrarily small total length.

  6. List of set identities and relations - Wikipedia

    en.wikipedia.org/wiki/List_of_set_identities_and...

    This article lists mathematical properties and laws of sets, involving the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations.

  7. Joey Galloway: Indiana should bench QB Kurtis Rourke vs Ohio ...

    www.aol.com/joey-galloway-indiana-bench-qb...

    ESPN's Joey Galloway on Tuesday said Indiana football shouldn't play quarterback Kurtis Rourke vs. Ohio State to keep its CFP path intact.

  8. What should you set your heat to in the winter? Avoid ... - AOL

    www.aol.com/finance/set-heat-winter-avoid...

    A thermostat set to more than 75 degrees will help lessen energy bills. What you should set your thermostat at in the winter Turns out there's a magic number for your thermostat setting in the ...

  9. Initial and terminal objects - Wikipedia

    en.wikipedia.org/wiki/Initial_and_terminal_objects

    The empty set is the unique initial object in Set, the category of sets.Every one-element set is a terminal object in this category; there are no zero objects.. Similarly, the empty space is the unique initial object in Top, the category of topological spaces and every one-point space is a terminal object in thi