Definition
An abstraction, to most mathematicians, is an object, such as a vector space, which incorporates a structure – elements and relationships between them – common to many instances appearing in diverse contexts. For the example of vector space, these instances include Euclidean 3-space, the complex plane, the set of solutions to a system of linear equations with real coefficients, and the space of states of a quantum mechanical system. The nature of the elements that serve as vectors in different contexts may be different: an element of Euclidean 3-space is a point, an element of the complex plane is a complex number, a solution of a system of linear equations is an n-tuple of (real) numbers, and a state of a quantum mechanical system is represented by a function. Nevertheless, if we ignore (abstract from) these contextual differences, in each case the vectors can be added and multiplied by scalars (numbers) according to exactly the same rules, and each of the spaces is closed...
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Dreyfus, T. (2014). Abstraction in Mathematics Education. In: Lerman, S. (eds) Encyclopedia of Mathematics Education. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4978-8_2
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