Summary
Approximation is a fundamental concept in mathematics, and a powerful tool in science and engineering, in which a core notion is that one may study an object of interest by modeling it with simpler objects and using a limiting process. The various approximation properties in mathematical analysis refer to the capacity of an object, such as an infinite-dimensional vector space, to be approximated in useful ways, for instance, by finite-dimensional subspaces. Such properties are central to a number of important fields, such as quantum probability theory, noncommutative geometry, and quantized
