In mathematics, constructive analysis is mathematical analysis done according to the principles of constructive mathematics. This contrasts with classical analysis, which (in this context) simply means analysis done according to the (ordinary) principles of classical mathematics.
Generally speaking, constructive analysis can reproduce theorems of classical analysis, but only in application to separable spaces; also, some theorems may need to be approached by approximations. Furthermore, many classical theorems can be stated in ways that are logically equivalent according to classical logic, but not all of these forms will be valid in constructive analysis, which uses intuitionistic logic.
Famous quotes containing the words constructive and/or analysis:
“The desert is a natural extension of the inner silence of the body. If humanity’s language, technology, and buildings are an extension of its constructive faculties, the desert alone is an extension of its capacity for absence, the ideal schema of humanity’s disappearance.”
—Jean Baudrillard (b. 1929)
“Cubism had been an analysis of the object and an attempt to put it before us in its totality; both as analysis and as synthesis, it was a criticism of appearance. Surrealism transmuted the object, and suddenly a canvas became an apparition: a new figuration, a real transfiguration.”
—Octavio Paz (b. 1914)