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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.
Nancy Roper, when interviewed by members of the Royal College of Nursing's (RCN) Association of Nursing Students at RCN Congress in 2002 in Harrogate [5] stated that the greatest disappointment she held for the use of the model in the UK was the lack of application of the five factors listed below, citing that these are the factors which make ...
This condition is called distributivity and gives rise to distributive lattices. There are some other important distributivity laws which are discussed in the article on distributivity in order theory. Some additional order structures that are often specified via algebraic operations and defining identities are Heyting algebras and; Boolean ...
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 .
To investigate the left distributivity of set subtraction over unions or intersections, consider how the sets involved in (both of) De Morgan's laws are all related: () = = () always holds (the equalities on the left and right are De Morgan's laws) but equality is not guaranteed in general (that is, the containment might be strict).
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
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]
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.