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:
“Once we begin to appreciate that the apparent destructiveness of the toddler in taking apart a flower or knocking down sand castles is in fact a constructive effort to understand unity, we are able to revise our view of the situation, moving from reprimand and prohibition to the intelligent channeling of his efforts and the fostering of discovery.”
—Polly Berrien Berends (20th century)
“Analysis as an instrument of enlightenment and civilization is good, in so far as it shatters absurd convictions, acts as a solvent upon natural prejudices, and undermines authority; good, in other words, in that it sets free, refines, humanizes, makes slaves ripe for freedom. But it is bad, very bad, in so far as it stands in the way of action, cannot shape the vital forces, maims life at its roots. Analysis can be a very unappetizing affair, as much so as death.”
—Thomas Mann (1875–1955)