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In mathematics, a constructive proof is a method of proof that demonstrates the existence of a mathematical object by creating or providing a method for...

assumption. Such a proof by contradiction might be called non-constructive, and a constructivist might reject it. The constructive viewpoint involves...

Both constructive and non-constructive proofs have been presented as "Cantor's proof." The popularity of presenting a non-constructive proof has led...

used for classical logic by more closely mirroring the notion of constructive proof. In particular, systems of intuitionistic logic do not assume the...

the form of a proof by contradiction in which the nonexistence of the object is proved to be impossible. In contrast, a constructive proof establishes that...

techniques from recursion theory as well as proof theory. Functional interpretations are interpretations of non-constructive theories in functional ones. Functional...

binary digits (i.e. each digit is zero or one). He begins with a constructive proof of the following lemma: If s1, s2, ... , sn, ... is any enumeration...

mechanically checks proofs of these assertions, helps to find formal proofs, and extracts a certified program from the constructive proof of its formal specification...

60th birthday). Vol. II. North-Holland. pp. 609–627. Moser, Robin A. (2008). "A constructive proof of the Lovasz Local Lemma". arXiv:0810.4812 [cs.DS]....

is rational. The above proof is an example of a non-constructive proof disallowed by intuitionists: The proof is non-constructive because it doesn't give...

theoretical if the proof given for it does not indicate a construction of the object whose existence is asserted. Such a proof is non-constructive, since the...

n_{1}\cdots n_{k}} is large. The third one uses the existence proof given in § Existence (constructive proof). It is the most convenient when the product n 1 ⋯ n...

mechanically checks proofs of these assertions, helps find formal proofs, and extracts a certified program from the constructive proof of its formal specification...

and a given circle with its center. Usability The constructive proof does not merely serve as a proof of the theorem, but also demonstrates the practical...

Polynomials in Bernstein form were first used by Bernstein in a constructive proof for the Weierstrass approximation theorem. With the advent of computer...

While the proofs by infinite descent are constructively valid when "irrational" is defined to mean "not rational", we can obtain a constructively stronger...

another fifth power: 275 + 845 + 1105 + 1335 = 1445. Proof by counterexample is a form of constructive proof, in that an object disproving the claim is exhibited...

integers and therefore a rational number. Dov Jarden gave a simple non-constructive proof that there exist two irrational numbers a and b, such that ab is rational:...

this formula, we obtain: f ( r ) = R . {\displaystyle f(r)=R.} A constructive proof—that does not involve the existence theorem of Euclidean division—uses...

vast majority of positive results about computational problems are constructive proofs, i.e., a computational problem is proved to be solvable by showing...