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For example, in elementary arithmetic, one has (+) = + (). Therefore, one would say that multiplication distributes over addition . This basic property of numbers is part of the definition of most algebraic structures that have two operations called addition and multiplication, such as complex numbers , polynomials , matrices , rings , and fields .
In the mathematical area of order theory, there are various notions of the common concept of distributivity, applied to the formation of suprema and infima.Most of these apply to partially ordered sets that are at least lattices, but the concept can in fact reasonably be generalized to semilattices as well.
Another example is given by the divisibility (or "is-a-factor-of") relation |. For two natural numbers n and m, we write n|m if n divides m without remainder. One easily sees that this yields a partial order. For example neither 3 divides 13 nor 13 divides 3, so 3 and 13 are not comparable elements of the divisibility relation on the set of ...
Nursing research is research that provides evidence used to support nursing practices. Nursing, as an evidence-based area of practice, has been developing since the time of Florence Nightingale to the present day, where many nurses now work as researchers based in universities as well as in the health care setting.
Nursing theory is defined as "a creative and conscientious structuring of ideas that project a tentative, purposeful, and systematic view of phenomena". [1] Through systematic inquiry, whether in nursing research or practice, nurses are able to develop knowledge relevant to improving the care of patients.
Finally distributivity entails several other pleasant properties. For example, an element of a distributive lattice is meet-prime if and only if it is meet-irreducible, though the latter is in general a weaker property. By duality, the same is true for join-prime and join-irreducible elements. [7]
One method of research for evidence-based practice in nursing is 'qualitative research': The word implies an entity and meanings that are not experimentally examined or measured in terms of quantity, amount, frequency, or intensity. With qualitative research, researchers learn about patient experiences through discussions and interviews.
For example, the following is an equivalent law that avoids the use of choice functions [citation needed]. For any set S of sets, we define the set S # to be the set of all subsets X of the complete lattice that have non-empty intersection with all members of S. We then can define complete distributivity via the statement