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 ?
The Scottish Conservative MPs constructively lobbied for Scotland's interests and will keep doing so.
In contrast, the White House finds that the opposition has shown "seriousness of purpose" and is "willing to engage constructively for the sake of the Syrian people.
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We will try our best to constructively invest additional efforts in this bilateral dialogue," Minister Milososki said.
FPAC and its members have a strong and productive track record of working constructively with conservation groups, governments, and others on projects related to advancing sustainable forest management and environmental stewardship.
We agreed, and stated in our manifesto prior to the election, that we would work constructively with all parties after the election.
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Introducing a series of comprehensive concepts of political civics and cultural morality, Progressive Logic offers the non-specialist general reader with a complete and thorough understanding of an idealistic "natural order of values" in which political progression is constructively rooted in the confluence of variations of progressive values.
We were anticipating the possibility of such a move and are fully prepared to move ahead constructively.
Second is the tone of the report, which touches gingerly but constructively on one of the special issues of the relationship between Jews and Germany, namely a growing distancing by increasing numbers of Germans from the very fact of the Shoah.
3: Choose the appropriate person to whom you can vent constructively.
For cash-method taxpayers like A, "all items which constitute gross income are to be included for the taxable year in which actually or constructively received" (Kegs.

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