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Type of mathematical proof
Proof by exhaustion, also known as proof by cases, proof by case analysis, complete induction or the brute force method, is a method of mathematical proof
Proof_by_exhaustion
Mathematical proof at least partially generated by computer
large proofs-by-exhaustion of a mathematical theorem. The idea is to use a computer program to perform lengthy computations, and to provide a proof that
Computer-assisted_proof
Reasoning for mathematical statements
very large. For example, the first proof of the four color theorem was a proof by exhaustion with 1,936 cases. This proof was controversial because the majority
Mathematical_proof
Math theorem about sphere packing
approach suggested by Fejes Tóth (1953), announced that he had a proof of the Kepler conjecture. Hales' proof is a proof by exhaustion involving the checking
Kepler_conjecture
Topics referred to by the same term
of a shape by approximating it with polygons Proof by exhaustion, proof by examining all individual cases Fatigue, a weariness caused by exertion Adrenal
Exhaust
Way of arriving to a mathematical proof
including proof by infinite descent. Direct proof methods include proof by exhaustion and proof by induction. A direct proof is the simplest form of proof there
Direct_proof
Form of mathematical proof
which is not implied by the other Peano axioms. Induction puzzles Proof by exhaustion Matt DeVos, Mathematical Induction, Simon Fraser University Gerardo
Mathematical_induction
Primitive way of calculating area
"exhausted" by the lower bound areas successively established by the sequence members. The method of exhaustion typically required a form of proof by contradiction
Method_of_exhaustion
Method of logical reasoning
an enumerative induction procedure like proof by exhaustion. Both mathematical induction and proof by exhaustion are examples of complete induction. Complete
Inductive_reasoning
also known as proof by exhaustion). by example A proof by example is an argument whereby a statement is not proved but instead illustrated by an example
Glossary of mathematical jargon
Glossary_of_mathematical_jargon
Geometrical structure
approach suggested by László Fejes Tóth in 1953, announced a proof of the Kepler conjecture. Hales' proof is a proof by exhaustion involving checking
Sphere_packing
Relevance fallacy
ignorance Argument from silence Contraposition Probatio diabolica Proof by exhaustion "Absence of Evidence Is Not Evidence of Absence". Quote Investigator
Evidence_of_absence
Approach to mathematics using computation
computer-assisted proof by exhaustion Thomas Hales's proof of the Kepler conjecture. Various proofs of the four colour theorem. Clement Lam's proof of the non-existence
Experimental_mathematics
In mathematics, especially general topology and analysis, an exhaustion by compact sets of a topological space X {\displaystyle X} is a nested sequence
Exhaustion_by_compact_sets
Topics referred to by the same term
brute force may refer to: Brute force method or proof by exhaustion, a method of mathematical proof Brute-force attack, a cryptanalytic attack Brute-force
Brute_force
Functional programming construct
Curry–Howard correspondence between proofs and programs relates ML-style pattern matching to case analysis and proof by exhaustion. By far the most common form of
Pattern_matching
Topics referred to by the same term
Brute force method, proof by exhaustion in mathematics Fundamental force, an interaction between particles that cannot be explained by other interactions
Force_(disambiguation)
Mathematical problem
non-existence of order six squares was confirmed in 1901 by Gaston Tarry through a proof by exhaustion. However, Euler's conjecture resisted solution until
Mutually orthogonal Latin squares
Mutually_orthogonal_Latin_squares
Greek mathematician and physicist (c. 287 – 212 BC)
anticipated modern calculus and analysis by applying the concept of the infinitesimals and the method of exhaustion to derive and rigorously prove many geometrical
Archimedes
Rule of inference of propositional logic
normal form Proof by exhaustion "Rule of Or-Elimination - ProofWiki". Archived from the original on 2015-04-18. Retrieved 2015-04-09. "Proof by cases". Archived
Disjunction_elimination
Mathematical proof Direct proof Reductio ad absurdum Proof by exhaustion Constructive proof Nonconstructive proof Tautology Consistency proof Arithmetization
List of mathematical logic topics
List_of_mathematical_logic_topics
Concept in geometry
mathematical rigor. The most famous of these is Archimedes' method of exhaustion, one of the earliest uses of the mathematical concept of a limit, as well
Area_of_a_circle
Field of knowledge
shapes, sets, functions, and probabilities. It uses logical reasoning and proof to study and establish their properties, often expressed as theorems, formulas
Mathematics
Number that is not a ratio of integers
reinforced the earlier decision to rely on deductive reasoning for proof". This method of exhaustion is the first step in the creation of calculus. Theodorus of
Irrational_number
Hungarian mathematician (1915–2005)
(face-centered cubic) and hexagonal close packing arrangements. Hales used a proof by exhaustion involving the checking of many individual cases, using complex computer
László_Fejes_Tóth
Geometric treatise by Archimedes
regarding parabolas, culminating in two proofs showing that the area of a parabolic segment (the region enclosed by a parabola and a line) is 4 3 {\displaystyle
Quadrature_of_the_Parabola
Plane curve: conic section
area enclosed by a parabola and a line segment, the so-called "parabola segment", was computed by Archimedes by the method of exhaustion in the 3rd century
Parabola
Relates the length of a median of a triangle to the lengths of its sides
using vectors (see parallelogram law). The following is an independent proof using the law of cosines. Let the triangle have sides a , b , c {\displaystyle
Apollonius's_theorem
Mathematical model of the physical space
school) as the first axiomatic system and the first examples of mathematical proofs. It goes on to the solid geometry of three dimensions. Much of the Elements
Euclidean_geometry
thereby finding the tangent to the curve. The method of exhaustion was independently invented in China by Liu Hui in the 4th century AD in order to find the
History_of_calculus
Mathematics used in Ancient China
commentary, Liu Hui finds a more accurate estimation of pi using the method of exhaustion. The method constructs polygons of successively higher-order within a
Chinese_mathematics
2004 studio album by Taking Back Sunday
left the band and later formed Straylight Run. Despite initially citing exhaustion from touring as the reason for his departure, Nolan later revealed his
Where_You_Want_to_Be
Rapid-fire argument rhetorical technique
Women in Science. 2003. p. 33. Satta, Mark (21 March 2024). "Epistemic Exhaustion and the Retention of Power". Hypatia. 39 (3): 510–529. doi:10.1017/hyp
Gish_gallop
State of fatigue caused by museum exhibits
supported by other researchers. Exhaustion or fatigue can be further divided into physical and mental fatigue. Physical fatigue is caused by walking for
Museum_fatigue
American anthropologist and art collector (1938–1961)
to swim to safety, supporting the theory that he died from exposure, exhaustion, or drowning. However, because headhunting and cannibalism were still
Michael_Rockefeller
2022 film by Antoine Fuqua
whipped, set upon by dogs, branded, and dragged by horses if they try to run away, or shot if they stop working because of exhaustion. Peter tells the
Emancipation_(2022_film)
Theorem in mathematics
{\displaystyle X} (or, more generally, a topological space admitting an exhaustion by compact subsets) and f : X → Z {\displaystyle f:X\to Z} , Z {\displaystyle
Inverse_function_theorem
Nine-digit number issued to U.S. citizens and permanent residents
cards: One reads "not valid for employment." Such cards cannot be used as proof of work authorization, and are not acceptable as a List C document on the
Social_Security_number
through the introduction of deductive reasoning and mathematical rigor in proofs) and expanded the subject matter of mathematics. The ancient Romans used
History_of_mathematics
population was the result of a combination of "murder", "starvation, exhaustion and exposure", "disease" and "a plummeting birth rate". Sleeping sickness
Atrocities in the Congo Free State
Atrocities_in_the_Congo_Free_State
Geometric shape
hence admitted less rigorous proofs before the advent of calculus, with the ancient Greeks using the method of exhaustion. This is essentially the content
Cone
Empress of Russia from 1894 to 1917
Peter Kurth, attribute the semi-invalidism of her later years to nervous exhaustion from obsessive worry over the fragile tsarevich, who suffered from hemophilia
Alexandra Feodorovna (Alix of Hesse)
Alexandra_Feodorovna_(Alix_of_Hesse)
Mathematical term in calculus
antiquity by the ancient Greek mathematician Archimedes in his The Quadrature of the Parabola (3rd century BC), via the method of exhaustion. Of note is
Cavalieri's quadrature formula
Cavalieri's_quadrature_formula
Branch of mathematics
theorem has a long history. Eudoxus (408–c. 355 BC) developed the method of exhaustion, which allowed the calculation of areas and volumes of curvilinear figures
Geometry
Virtual online communities
ambivalence, emotional exhaustion, and depersonalization. Ambivalence is confusion about the benefits from using social media. Emotional exhaustion is stress from
Social_media
Problem of constructing equal-area shapes
would eventually fill up the area of the circle (this is the method of exhaustion). Since any polygon can be squared, he argued, the circle can be squared
Squaring_the_circle
German mathematician (1862–1943)
a then-untreatable vitamin deficiency of which the primary symptom is exhaustion; his assistant Eugene Wigner described him as subject to "enormous fatigue"
David_Hilbert
Legal concept regulating rights of a creative work
which it is imported for retailing. The first-sale doctrine is known as exhaustion of rights in other countries and is a principle which also applies, though
Copyright
Topics referred to by the same term
research method involving in-depth examination of an individual Proof by cases (or exhaustion), in mathematics Contribution to ARIEL Spectroscopy of Exoplanets
Case
Mathematical treatise by Euclid
studies the volumes of cones, pyramids, and cylinders in detail by using the method of exhaustion, a precursor to integration, and shows, for example, that
Euclid's_Elements
Geometrical concept relating area and volume
direction, Cavalieri's principle grew out of the ancient Greek method of exhaustion, which used limits but did not use infinitesimals. Cavalieri's principle
Cavalieri's_principle
2017 United States Supreme Court case
(2017), is a decision of the Supreme Court of the United States on the exhaustion doctrine in patent law in which the Court held that after the sale of
Impression Products, Inc. v. Lexmark International, Inc.
Impression_Products,_Inc._v._Lexmark_International,_Inc.
British boy band
tour with the American boy band NSYNC, but soon after pulled out due to exhaustion, flying back to England to rest and start work on a new album. Still from
Five_(group)
2011 United States Supreme Court case
again made news when Judge Mike Wood recused himself that year, citing exhaustion from dealing with the case and the parties. Smith's bankruptcy case was
Stern_v._Marshall
Topological space which is a generalization of certain compact spaces
axiom of dependent choice is added. A Hausdorff space admitting an exhaustion by compact sets is paracompact. Some examples of spaces that are not paracompact
Paracompact_space
Infinite series summable to 1/3
Quadrature of the Parabola. He finds the area inside a parabola by the method of exhaustion, and he gets a series of triangles; each stage of the construction
1/4_+_1/16_+_1/64_+_1/256_+_⋯
1995 novel set during World War II
cryptology central office, and is worked to the point of physical and mental exhaustion. The book, Harris' second after the successful 1992 Fatherland, was adapted
Enigma_(novel)
Systematic planning of athletic or physical training
Resistance stage, involving the adaptation to the stimulus by the system, and (c) the Exhaustion stage, in that repairs are inadequate, and a decrease in
Sports_periodization
Mathematics of Ancient Greece and the Mediterranean, 5th BC to 6th AD
united by Greek culture and the Greek language. The development of mathematics as a theoretical discipline and the use of deductive reasoning in proofs is
Ancient_Greek_mathematics
Current lowest-value American coin
included with the uncirculated mint set, a proof cent with the proof set, and a reverse proof with the silver proof set. Following the 2025 halt to circulating
Penny_(United_States_coin)
the ship's stores to complete his task, Teg dies from massive cellular exhaustion. Duncan is unable to free the ship, and it is taken to the machine world
List_of_Dune_characters
1949 film by Carol Reed
Combined with the use of ruined locations in Vienna, the style evokes exhaustion and cynicism at the start of the Cold War. Greene wrote a novella as a
The_Third_Man
Structure in which to nap
Inemuri, sleeping at work, is culturally viewed as proof of dedication to the point of exhaustion, and has also influenced the use of nap pods around
Sleep_pod
of exhaustion Milü Pi Pi (art project) Pi (letter) Pi Day PiFast PiHex Pi in the Sky Pilish Pimania Piphilology Proof that π is irrational Proof that
List_of_topics_related_to_π
American post-hardcore band
five dates of its European tour, citing "complete mental and physical exhaustion" of the members. In March 2001—less than a month away from a United States
At_the_Drive-In
Abrahamic monotheistic religion
a separate legal status. Part of the Muslims' success was due to the exhaustion of the Byzantine Empire in its decades long conflict with Persia. Beginning
Christianity
McGowan announced his resignation and retirement from politics due to exhaustion and the relentless pressure of the job; Gold Coast University Hospital
List of The Weekly with Charlie Pickering episodes
List_of_The_Weekly_with_Charlie_Pickering_episodes
Number, approximately 3.14
distributed, but no proof of this conjecture has been found. Mathematicians have attempted to extend their understanding of π, sometimes by computing its value
Pi
the same split-alphabet system and thus the same eight series. Upon the exhaustion of this format in 2014, an AB1-23C format was introduced, with the split-alphabet
Vehicle registration plates of British Columbia
Vehicle_registration_plates_of_British_Columbia
2006 German drama film
in a car staring out a window. It is explained that Michaela died of exhaustion from exorcisms in her parents' home. Sandra Hüller as Michaela Klingler
Requiem_(2006_film)
1936–1938 campaign in the Soviet Union
months of such interrogation, the defendants were driven to despair and exhaustion. Zinoviev and Kamenev demanded, as a condition for "confessing", a guarantee
Great_Purge
Book by Apostolos Doxiadis
already been published by a young Austrian mathematician. Petros then falls into the deepest depression, taunted by mental exhaustion and the fear that his
Uncle Petros and Goldbach's Conjecture
Uncle_Petros_and_Goldbach's_Conjecture
Type of mathematical space
Continuous functions on a compact Hausdorff space Eberlein compactum Exhaustion by compact sets Lindelöf space Metacompact space Noetherian topological
Compact_space
Italian actor (1895–1926)
incident. Mencken advised Valentino to "let the dreadful farce roll along to exhaustion", but Valentino insisted the editorial was "infamous". Mencken found Valentino
Rudolph_Valentino
The Next Step is a Canadian teen drama series created by Frank van Keeken and produced by Temple Street Productions. Shot in a dramatic mockumentary style
List of The Next Step episodes
List_of_The_Next_Step_episodes
minute alienation of Catholic voters proved decisive, as well as voter exhaustion after a generation of Republican rule. In the election, Cleveland won
1884 United States presidential election
1884_United_States_presidential_election
Rare neurodegenerative disease
that provide these benefits without overworking muscles because muscle exhaustion can lead to a worsening of symptoms associated with ALS, rather than providing
ALS
backbreaking work. A combination of inadequate nutrition, bad water and exhaustion from both the journey and the work weakened the newly arrived slaves and
Slavery_in_the_United_States
1980 novel by Jean M. Auel
several days. She is attacked and nearly killed by a cave lion, and, suffering from starvation, exhaustion, and infection of her wounds, she collapses, on
The_Clan_of_the_Cave_Bear
2014 aircraft disappearance
Kuala Lumpur-Beijing flight is 51⁄2 hours, so fuel exhaustion was likely. In the event of fuel exhaustion and engine flame-out, which would eliminate power
Malaysia_Airlines_Flight_370
American rock band
acts". The exhaustion of recording Slippery When Wet and New Jersey back to back and going on highly paced world tours took its toll. By the end of the
Bon_Jovi
benediction in Latin for the deceased after Father Mulcahy passed out from exhaustion. Burns further asserts that the other surgeons could not keep up with
List_of_M*A*S*H_characters
American musician (1933–2006)
stage after he had worked himself to exhaustion during his performance. As Brown was escorted off the stage by the MC, Brown's vocal group, the Famous
James_Brown
1975 French film by Walerian Borowczyk
Lucy rubs his ejaculate all over herself. Eventually, the beast dies of exhaustion. Lucy wakes and walks into Mathurin's room to find him dead on the floor
La_Bête_(film)
Mathematical term for squaring a plane figure
tangent line of the same slope). For the proofs of these results, Archimedes used the method of exhaustion attributed to Eudoxus. In medieval Europe
Quadrature_(mathematics)
Quantity of a three-dimensional space
devised approximate volume formula of several shapes using the method of exhaustion approach, meaning to derive solutions from previous known formulas from
Volume
1980 film by Stanley Kubrick
with a small crew, which allowed him to do many takes, sometimes to the exhaustion of the actors and staff. The then-new Steadicam mount was used to shoot
The_Shining_(film)
1971 genocide of Bengalis in East Pakistan
majority of the dead were rural dwellers who died of "hunger, want, and exhaustion" with many deaths occurring in the year following the conflict. Out of
Bangladesh_genocide
Security feature in web browsers
classes of devices, and can be abused in some cases to enable resource exhaustion attacks. Until 2017, the predominant security architecture of major browsers
Site_isolation
2024 studio album by RM
one's innate wrongness and the cyclic journey of rage, disappointment, exhaustion, and renewal" and declared, "Right Place, Wrong Person is absolutely Kim
Right_Place,_Wrong_Person
1841 ballet by Adolphe Adam
betrayed by their lovers and take revenge in the night by dancing men to death by exhaustion (a popular theme in Romantic-era ballets). Led by Myrtha,
Giselle
Indian actor (born 1950)
foodborne illness on the sets, which led to vomiting, dehydration, and exhaustion. He was treated at St. Isabel's Hospital for a day before being discharged
Rajinikanth
American author, lecturer, and alleged UFO contactee
providing factual proof to his skeptics, Angelucci responded that "ideas preponderantly spiritual cannot now and have never been capable of proof by material methods
Orfeo_Angelucci
Ancient Greek mathematician (fl. 300 BC)
The last of these includes the earliest surviving proof of the Pythagorean theorem, described by Sialaros as "remarkably delicate". Book 2 is traditionally
Euclid
Earth's highest mountain
as opposed to a more typical 20–30. Exhaustion can occur merely by attempting to breathe. Lack of oxygen, exhaustion, extreme cold, and climbing hazards
Mount_Everest
Branch of mathematics
a region bounded by a parabola and one of its secant lines. The method of exhaustion was later discovered independently in China by Liu Hui in the 3rd
Calculus
American glam metal band
release Lane was admitted to a rehab center for alcohol and drug-related exhaustion. The band again featured on the Rock Never Stops Tour in 2003 and in April
Warrant_(American_band)
Expendable launch system used by NASA
planned. At cutoff, the Centaur was only 3.4 seconds from propellant exhaustion. If the same failure had occurred during Voyager 2's launch a few weeks
Titan_IIIE
Serbian performance artist (born 1946)
might be considered acceptable. By presenting her body as an object, she explores the limits of danger and exhaustion a human can endure. In 1976, after
Marina_Abramović
Overuse of a shared resource
therefore a public resource – better said, a common good – that is liable to exhaustion. Some feel that the law should provide a safe haven for the dissemination
Tragedy_of_the_commons
PROOF BY-EXHAUSTION
PROOF BY-EXHAUSTION
Boy/Male
Arabic, Muslim
Evidence; Proof
Boy/Male
Muslim/Islamic
Proof
Surname or Lastname
English
English : variant of Rolfe.German : from Ruffo, a short form of a personal name formed with hrÅd ‘renown’, ‘victory’.Probably an Americanized spelling of German Ruf and Ruff.
Girl/Female
Arabic, Muslim
Guide; Proof
Boy/Male
Arabic, French, German, Gujarati, Hindu, Indian, Malaysian, Muslim, Turkish
Proof; Evidence
Boy/Male
Arabic
Proof; Evidence
Boy/Male
Muslim
Evidence. Proof.
Girl/Female
Muslim/Islamic
Guide Proof
Boy/Male
Muslim
Proof
Boy/Male
Afghan, Arabic, Hindu, Indian, Muslim
Proof
Boy/Male
Indian
Proof
Boy/Male
Muslim
Proof
Boy/Male
Muslim
Argument, Reasoning, Proof
Girl/Female
Muslim
Guide, Proof
Boy/Male
Muslim/Islamic
Proof
Boy/Male
Indian
Proof
Boy/Male
Arabic, Muslim
The Proof
Boy/Male
Indian
Argument, Reasoning, Proof
Girl/Female
Muslim
Proof
Girl/Female
Indian
Witness; Proof
PROOF BY-EXHAUSTION
PROOF BY-EXHAUSTION
Boy/Male
Hindu
Boy/Male
British, English
Place Name; Valley of the Awesome One
Boy/Male
Muslim
Make fun, Comedy
Girl/Female
Biblical
A knocking.
Male
Basque
, thanks.
Girl/Female
Tamil
Aaradhita | ஆராதீதா
Worshipped
Boy/Male
Hindu
The knower of hymns
Boy/Male
Latin American English French
Hammer.
Girl/Female
Tamil
Palm, Calm, Nightingale, Key, A list
Boy/Male
Tamil
Well versed in the Vedas
PROOF BY-EXHAUSTION
PROOF BY-EXHAUSTION
PROOF BY-EXHAUSTION
PROOF BY-EXHAUSTION
PROOF BY-EXHAUSTION
n.
Proof.
n.
The cover of any building, including the roofing (see Roofing) and all the materials and construction necessary to carry and maintain the same upon the walls or other uprights. In the case of a building with vaulted ceilings protected by an outer roof, some writers call the vault the roof, and the outer protection the roof mask. It is better, however, to consider the vault as the ceiling only, in cases where it has farther covering.
v. t.
Armor of excellent or tried quality, and deemed impenetrable; properly, armor of proof.
n.
That which resembles, or corresponds to, the covering or the ceiling of a house; as, the roof of a cavern; the roof of the mouth.
a.
Highly rectified; very strongly alcoholic; as, high-proof spirits.
v. t.
To cover with a roof.
a.
Proof against penetration or permeation by water; impervious to water; as, a waterproof garment; a waterproof roof.
v. t.
To arm with proof armor; to arm securely; as, to proof-arm herself.
n.
Proof.
pref.
With, as means, way, process, etc.; through means of; with aid of; through; through the act or agency of; as, a city is destroyed by fire; profit is made by commerce; to take by force.
n.
Proof.
n.
Proof.
a.
Used in proving or testing; as, a proof load, or proof charge.
adv.
Passing near; going past; past; beyond; as, the procession has gone by; a bird flew by.
n.
A trial impression, as from type, taken for correction or examination; -- called also proof sheet.
adv.
Aside; as, to lay by; to put by.
a.
Proof against proofs; obstinate in the wrong.
n.
Proof by witness; attestation; testimony.
a.
Out of the common path; aside; -- used in composition, giving the meaning of something aside, secondary, or incidental, or collateral matter, a thing private or avoiding notice; as, by-line, by-place, by-play, by-street. It was formerly more freely used in composition than it is now; as, by-business, by-concernment, by-design, by-interest, etc.
a.
Firm or successful in resisting; as, proof against harm; waterproof; bombproof.