nonconstructive

Adjective

Meaning

Not constructive.

Not involving construction.

(mathematics) That proves the existence of something without demonstrating a method of construction.

Synonyms

Antonyms

Examples

The relationship between provability in classical (or nonconstructive) systems and provability in intuitionistic (or constructive, respectively) systems is of particular interest. Source: Internet

This nonconstructive proof that not all real numbers are algebraic was first published by Georg Cantor in his 1874 paper " On a Property of the Collection of All Real Algebraic Numbers ". Source: Internet

In constructive mathematics As discussed above, in ZFC, the axiom of choice is able to provide " nonconstructive proofs " in which the existence of an object is proved although no explicit example is constructed. Source: Internet

The motivation for accepting these seemingly nonconstructive principles is the intuitionistic understanding of the proof that "for each real number x there is a real number y such that R(x,y) holds". Source: Internet

Though nearly all modern mathematicians consider nonconstructive methods just as sound as constructive ones, Euclid's constructive proofs often supplanted fallacious nonconstructive ones—e. Source: Internet

While the ability to make such a choice is considered obvious by some, since each set in the collection is nonempty, the lack of a general, concrete rule by which the choice can be made renders the axiom nonconstructive. Source: Internet

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