constructive


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constructive

1. Law deduced by inference or construction; not expressed but inferred
2. Law having a deemed legal effect

constructive

(mathematics)
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.
References in periodicals archive ?
Shaming or making fun of someone can never be constructive because it would hurt the person a lot, instead of doing any good.
of A wider range of talent and less party bitterness will lead to more constructive debate.
I am pleased our recent constructive discussions with Elliott improved understanding between both parties.
However, he said, one sided goodwill and constructive approach were not enough for a solution, urging the Greek Cypriots to respond to the steps taken in this direction.
The following are examples of potential constructive dividends:
Whereas negative votes simply withdraw confidence and generally trigger new elections, constructive non-confidence votes not only deconstruct a government but designate who should form a new one from the existing parliament (i.
Contrairement a un vote negatif, qui vise a retirer la confiance au gouvernement et qui a normalement pour effet de declencher des elections, un vote de defiance constructive a pour effet non seulement de demanteler le gouvernement au pouvoir, mais aussi de designer un parlementaire a la tete du nouveau gouvernement jusqu'a ce que des elections soient lancees.
Headquartered in New York City, Constructive Media was founded in the late 1990s to offer a new way to discover and enjoy math.
We are a country that even the US as our number one enemy has admitted that Iran has played a constructive role in the region, and that settlement of the regional issues is not possible without Iran's presence," he added.
According to the committee's head, "the main issue now is whether this election becomes a turning point in Ukraine's history and if it results in stopping bloodshed and escalation of violence, whether it gives an impetus to a constructive civil dialogue".
these issues and we are looking forward to maintaining constructive ties with Ankara," Kerry said in response to question by members of
Constructive Playthings, an early childhood education company, took multiple steps to help Community Parents Inc.

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