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constructive

   Also found in: Dictionary/thesaurus, Legal, Wikipedia, Hutchinson 0.06 sec.
constructive
1. Law deduced by inference or construction; not expressed but inferred
2. Law having a deemed legal effect
(mathematics)constructive - A proof that something exists is "constructive" if it provides a method for actually constructing it. Cantor's proof that the real numbers are uncountable can be thought of as a *non-constructive* proof that irrational numbers exist. (There are easy constructive proofs, too; but there are existence theorems with no known constructive proof).

Obviously, all else being equal, constructive proofs are better than non-constructive proofs. A few mathematicians actually reject *all* non-constructive arguments as invalid; this means, for instance, that the law of the excluded middle (either P or not-P must hold, whatever P is) has to go; this makes proof by contradiction invalid. See intuitionistic logic for more information on this.

Most mathematicians are perfectly happy with non-constructive proofs; however, the constructive approach is popular in theoretical computer science, both because computer scientists are less given to abstraction than mathematicians and because intuitionistic logic turns out to be the right theory for a theoretical treatment of the foundations of computer science.


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For a coloured man to work it out in the South, where, in its constructive period, he was necessarily misunderstood by his own people as well as by the whites, and where he had to adjust it at every step to the strained race relations--that is so very different and more difficult a thing that the man who did it put the country under lasting obligations to him.
Up From Slavery by Washington, Booker T. View in context
He also becomes more dogmatic and constructive, passing beyond the range either of the political or the speculative ideas of the real Socrates.
The Republic by Plato View in context
This may serve as a specimen of the numerous handles which would be given to the doctrine of constructive powers, by the indulgence of an injudicious zeal for bills of rights.
Federalist Papers Authored by Alexander Hamilton by Hamilton, Alexander View in context
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