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In philosophy and the arts, a fundamental distinction is between things that are abstract and things that are concrete.While there is no general consensus as to how to precisely define the two, examples include that things like numbers, sets, and ideas are abstract objects, while plants, dogs, and planets are concrete objects. [1]
Those abstract things are then said to be multiply instantiated, in the sense of picture 1, picture 2, etc., shown below. It is not sufficient, however, to define abstract ideas as those that can be instantiated and to define abstraction as the movement in the opposite direction to instantiation. Doing so would make the concepts "cat" and ...
Abstraction is the thought process in which ideas are distanced from objects. Abstraction uses a strategy of simplification of detail, wherein formerly concrete details are left ambiguous, vague, or undefined; thus speaking of things in the abstract demands that the listener have an intuitive or common experience with the speaker, if the speaker expects to be understood.
A scientific model is a simplified abstract view of a complex reality. A scientific model represents empirical objects, phenomena, and physical processes in a logical way. Attempts to formalize the principles of the empirical sciences use an interpretation to model reality, in the same way logicians axiomatize the principles of logic .
A research design typically outlines the theories and models underlying a project; the research question(s) of a project; a strategy for gathering data and information; and a strategy for producing answers from the data. [1] A strong research design yields valid answers to research questions while weak designs yield unreliable, imprecise or ...
Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras.The phrase abstract algebra was coined at the turn of the 20th century to distinguish this area from what was normally referred to as algebra, the study of the rules for manipulating formulae and algebraic expressions involving unknowns and ...
Design patterns in computer science represent abstract solutions to common software design problems. While they are not abstractions in the same sense as data structures or mathematical concepts, design patterns provide a high-level language for software developers to communicate and implement solutions in a consistent and recognizable way.
Abstraction is an ongoing process in mathematics and the historical development of many mathematical topics exhibits a progression from the concrete to the abstract. For example, the first steps in the abstraction of geometry were historically made by the ancient Greeks, with Euclid's Elements being the earliest extant documentation of the ...