Get to know Nonconstructive better with 6 real example sentences, the meaning.
Nonconstructive in a sentence
Nonconstructive meaning
- Not constructive.
- Not involving construction.
- That proves the existence of something without demonstrating a method of construction.
Using Nonconstructive
- The main meaning on this page is: Not constructive. | Not involving construction. | That proves the existence of something without demonstrating a method of construction.
Context around Nonconstructive
- Average sentence length in these examples: 30.2 words
- Position in the sentence: 2 start, 3 middle, 1 end
- Sentence types: 6 statements, 0 questions, 0 exclamations
Corpus analysis for Nonconstructive
- In this selection, "nonconstructive" usually appears in the middle of the sentence. The average example has 30.2 words, and this corpus slice is mostly made up of statements.
- Around the word, consider, fallacious, provide, methods, ones and proofs stand out and add context to how "nonconstructive" is used.
- Recognizable usage signals include classical or nonconstructive systems and and mathematicians consider nonconstructive methods just. That gives this page its own corpus information beyond isolated example sentences.
- By corpus frequency, "nonconstructive" sits close to words such as aaaaa, aage and aardvarks, which helps place it inside the broader word index.
Example types with nonconstructive
The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:
The relationship between provability in classical (or nonconstructive) systems and provability in intuitionistic (or constructive, respectively) systems is of particular interest. (21 words)
Though nearly all modern mathematicians consider nonconstructive methods just as sound as constructive ones, Euclid's constructive proofs often supplanted fallacious nonconstructive ones—e. (24 words)
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 ". (31 words)
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. (39 words)
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. (33 words)
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". (33 words)
Example sentences (6)
Though nearly all modern mathematicians consider nonconstructive methods just as sound as constructive ones, Euclid's constructive proofs often supplanted fallacious nonconstructive ones—e.
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.
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".
The relationship between provability in classical (or nonconstructive) systems and provability in intuitionistic (or constructive, respectively) systems is of particular interest.
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 ".
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.