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searching for Proof by contradiction 28 found (106 total)

Hippocrates of Chios (709 words) [view diff] exact match in snippet view article find links to article

"Reduction" arguments such as reductio ad absurdum argument (or proof by contradiction) have been traced to him, as has the use of power to denote the

Prime constant (438 words) [view diff] no match in snippet view article find links to article

The prime constant is the real number ρ {\displaystyle \rho } whose n {\displaystyle n} th binary digit is 1 if n {\displaystyle n} is prime and 0 if n

Lebesgue's number lemma (1,185 words) [view diff] no match in snippet view article find links to article

In topology, the Lebesgue covering lemma is a useful tool in the study of compact metric spaces. Given an open cover of a compact metric space, a Lebesgue's

Five color theorem (1,923 words) [view diff] no match in snippet view article find links to article

The five color theorem is a result from graph theory that given a plane separated into regions, such as a political map of the countries of the world,

Rearrangement inequality (2,621 words) [view diff] no match in snippet view article find links to article

In mathematics, the rearrangement inequality states that for every choice of real numbers x 1 ≤ ⋯ ≤ x n and y 1 ≤ ⋯ ≤ y n {\displaystyle x_{1}\leq \cdots

Constructive logic (609 words) [view diff] exact match in snippet view article find links to article

abstractly). No “non-constructive” proofs are allowed (like the classic proof by contradiction without a witness). The main constructive logics are the following:

Infinite set (917 words) [view diff] exact match in snippet view article find links to article

sets using proof concepts such as mapping, proof by induction, or proof by contradiction. Mathematical trees can also be used to understand infinite sets

Parallel postulate (3,278 words) [view diff] exact match in snippet view article find links to article

mathematician, made an attempt at proving the parallel postulate using a proof by contradiction, in the course of which he introduced the concept of motion and

Planner (programming language) (2,311 words) [view diff] exact match in snippet view article

of the information. Then used resolution to attempt to obtain a proof by contradiction by adding the clausal form of the negation of the theorem to be

Hippasus (1,514 words) [view diff] exact match in snippet view article find links to article

suggests that the proof was certainly ancient. The method is a proof by contradiction, or reductio ad absurdum, which shows that if the diagonal of a

Berry paradox (1,622 words) [view diff] exact match in snippet view article find links to article

be proven that the Kolmogorov complexity is not computable. The proof by contradiction shows that if it were possible to compute the Kolmogorov complexity

Rocq (1,918 words) [view diff] exact match in snippet view article find links to article

constructive, since a non-terminating program corresponds to a proof by contradiction, which is not allowed. As an example of a proof written in Rocq

Supertask (2,385 words) [view diff] exact match in snippet view article find links to article

common sense. Instead, they reverse the argument and take it as a proof by contradiction where the possibility of motion is taken for granted. They accept

Penrose–Hawking singularity theorems (3,135 words) [view diff] exact match in snippet view article find links to article

geodesic incompleteness, or closed timelike curves. Sketch of proof: Proof by contradiction. The boundary of the future of T {\displaystyle {\mathcal {T}}}

Evil demon (3,437 words) [view diff] exact match in snippet view article find links to article

the real world are also insufficient to generate knowledge. This proof by contradiction that the real world cannot generate knowledge, and thus that the

Kőnig's lemma (2,344 words) [view diff] exact match in snippet view article find links to article

generally considered to be constructive, because at each step it uses a proof by contradiction to establish that there exists an adjacent vertex from which infinitely

Philosophy of mathematics (10,964 words) [view diff] exact match in snippet view article find links to article

of these schools reject non-constructive proofs, such as using proof by contradiction when showing the existence of an object or when trying to establish

Coxeter decompositions of hyperbolic polygons (676 words) [view diff] exact match in snippet view article find links to article

fundamental triangle will be formed with a right angle. If they are, a proof by contradiction based on the area of the fundamental triangle proves that it will

Math Girls (1,959 words) [view diff] exact match in snippet view article find links to article

Euler product Harmonic series Logarithmic function Oresme's proof Proof by contradiction Power series Expanding power series Taylor series (Maclaurin series)

Context-free grammar (6,143 words) [view diff] exact match in snippet view article find links to article

be proven using pumping lemma for context-free languages and a proof by contradiction, observing that all words of the form ( n [ n ) n ] n {\displaystyle

Median voter theorem (3,936 words) [view diff] exact match in snippet view article find links to article

algebraically by Charles Plott in 1967. Here we give a simple geometric proof by contradiction in two dimensions. Suppose, on the contrary, that there is a set

Ibn al-Haytham (14,977 words) [view diff] exact match in snippet view article find links to article

parallel postulate, the fifth postulate in Euclid's Elements, using a proof by contradiction, and in effect introducing the concept of motion into geometry.

Kullback–Leibler divergence (13,054 words) [view diff] exact match in snippet view article find links to article

necessary condition for convergence of the series by the following proof by contradiction. Assume that P > 2 Q {\displaystyle P>2Q} with measure strictly

Bombe (7,962 words) [view diff] exact match in snippet view article find links to article

P(A) ≠ Y (this type of argument is termed reductio ad absurdum or "proof by contradiction"). The cryptanalyst hypothesised one plugboard interconnection for

Price of anarchy (4,121 words) [view diff] no match in snippet view article find links to article

≤ w f ( f ∗ ) {\displaystyle w(f)=w^{f}(f)\leq w^{f}(f^{*})} . Proof (By contradiction). Assume that w f ( f ∗ ) < w f ( f ) {\displaystyle w^{f}(f^{*})<w^{f}(f)}

Leader election (4,409 words) [view diff] exact match in snippet view article find links to article

simplicity, here is a proof in anonymous synchronous rings. It is a proof by contradiction. Consider an anonymous ring R with size n>1. Assume there exists

Constructive set theory (35,220 words) [view diff] exact match in snippet view article find links to article

principle M P {\displaystyle {\mathrm {MP} }} , which is a form of proof by contradiction motivated by (unbound memory capacity) computable search. This has

Ali and Nino (9,354 words) [view diff] exact match in snippet view article find links to article

suggestive rather than factual, and plenty of AI's arguments are a 'proof by contradiction.'" Some scholars of Azerbaijani literature and culture, after being