During most of the 20th century these two great countries enjoyed generally cordial and constructive relations.
So that they can return and approach the world—and approach women—with constructive confidence and calm.
The best course for the party is benign, constructive neglect; and the party can afford to adopt this course.
IAEA chief Yukiya Amano said in the statement: “We engaged in a constructive spirit, but no agreement was reached.”
Graves would be a great addition to Congress, committed to constructive problem-solving from day one.
His reply was that in so far as they were at all constructive, they consisted mostly of exploded heresies of the first century.
It was in this mood of mind that I became a constructive microscopist.
Suppose the mental energy left in Europe after the war is insufficient for such a constructive feat as this.
He was of a constructive rather than a destructive turn of mind.
Experience with the new legislation so far has clearly demonstrated its constructive nature.
early 15c., "derived by interpretation," from Middle French constructif or from Medieval Latin constructivus, from Latin construct-, past participle stem of construere "to heap up" (see construction). Meaning "pertaining to construction" is from 1817; "having the quality of constructing" is from 1841. Related: Constructively. Constructive criticism is attested by 1841.
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.
(1995-04-13)