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...

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

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

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...

Constructive logic is a family of logics where proofs must be constructive (i.e., proving something means one must build or exhibit it, not just argue...

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

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...

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...

new circular arcs with a compass. Usability The constructive proof does not merely serve as a proof of the theorem, but also demonstrates the practical...

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

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

yielding a direct proof of irrationality in its constructively stronger form, not relying on the law of excluded middle. This proof constructively exhibits an...

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

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...

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...

X).{\big (}Q(x)\lor \neg Q(x){\big )}} is provable. Non-constructive axioms may enable proofs that formally claim decidability of such P {\displaystyle...

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]....

prescribed vertex degrees" – by Gilles Schaeffer. "Kathy O'Hara's Constructive Proof of the Unimodality of the Gaussian Polynomials" – by Doron Zeilberger...

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...

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

numerical analysis and constructive mathematics, since many theorems that can be proved for nonseparable spaces have constructive proofs only for separable...

solution of the equation can be expressed as a Puiseux series. Moreover, the proof provides an algorithm for computing these Puiseux series, and, when working...

but with opposite signs. The first proofs were non-constructive, by way of contradiction. Later, constructive proofs were found, which also supplied algorithms...

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:...

and Brouwer found a different proof in the same year. Since these early proofs were all non-constructive indirect proofs, they ran contrary to Brouwer's...

n=25} . The mathematical proof of an existential statement about "some" object may be achieved either by a constructive proof, which exhibits an object...

via the probabilistic method. They are particularly used for non-constructive proofs. Normal numbers exist. Moreover, computable normal numbers exist...

A different geometric proof was discovered in 2000 by Duistermaat and Kolk. Unlike the previous ones, it is a constructive proof: the integrating Lie group...

size of a matching equals the smallest size of a vertex cover. The constructive proof described above provides an algorithm for producing a minimum vertex...

logic, realizability is a collection of methods in proof theory used to study constructive proofs and extract additional information from them. Formulas...