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Way of arriving to a mathematical proof
In mathematics and logic, a direct proof is a way of showing the truth or falsehood of a given statement by a straightforward combination of established
Direct_proof
Reasoning for mathematical statements
The book Proofs from THE BOOK, published in 2003, is devoted to presenting 32 proofs its editors find particularly pleasing. In direct proof, the conclusion
Mathematical_proof
On the remainder of division by x – r
of Euclidean division. The generalization of this proof to any degree is given below in § Direct proof. The polynomial remainder theorem follows from the
Polynomial_remainder_theorem
Mathematical condition
least a version of it. A standard proof of the Poincaré lemma uses the homotopy invariance formula (cf. see the proofs below as well as Integration along
Poincaré_lemma
Sufficient evidence/argument for truth
assert a proposition to constitute a proof of that proposition. For example, a signature constitutes direct proof of authorship; less directly, handwriting
Proof_(truth)
Every triangle with two angle bisectors of equal lengths is isosceles
whether a "direct" proof is possible; allegedly "direct" proofs have been published, but not everyone agrees that these proofs are "direct." For example
Steiner–Lehmus_theorem
Theorem in commutative algebra
also below for the direct proofs). Bourbaki's Commutative Algebra gives a direct proof. Kaplansky's Commutative Rings includes a proof due to David Rees
Krull's principal ideal theorem
Krull's_principal_ideal_theorem
Mathematical model which is both linear and time-invariant
{C} } , are eigenfunctions of a linear, time-invariant operator. A simple proof illustrates this concept. Suppose the input is x ( t ) = A e s t {\displaystyle
Linear_time-invariant_system
2007 American film
Death Proof is a 2007 American slasher film written, co-produced, shot and directed by Quentin Tarantino. It stars Kurt Russell as a stuntman who murders
Death_Proof
Mathematical logic concept
its logically equivalent contrapositive, and an associated proof method known as § Proof by contrapositive. The contrapositive of a statement has its
Contraposition
Counterintuitive result in probability
implicit in the foundations of statistical mechanics. There is straightforward proof of this theorem. As an introduction, recall that if two events are statistically
Infinite_monkey_theorem
2005 film by John Madden
Proof is a 2005 American drama film directed by John Madden and starring Gwyneth Paltrow, Anthony Hopkins, Jake Gyllenhaal, and Hope Davis. The screenplay
Proof_(2005_film)
{d} x.} Carleman's inequality follows from the case p = 0. An elementary proof is sketched below. From the inequality of arithmetic and geometric means
Carleman's_inequality
Mathematical program specifications
results. Some modern model checking tools produce a "proof log" detailing each step in their proof, making it possible to perform, given suitable tools
Formal_methods
American play
Infobox play is being considered for merging. › Proof is a play by the American playwright David Auburn. Proof was developed at George Street Playhouse in
Proof_(play)
Theorem on modular exponentiation
is also a direct proof: Let R = {x1, x2, ... , xφ(n)} be a reduced residue system (mod n) and let a be any integer coprime to n. The proof hinges on the
Euler's_theorem
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
Branch of mathematical logic
Proof theory is a major branch of mathematical logic and theoretical computer science within which proofs are treated as formal mathematical objects,
Proof_theory
Mathematical rule
61–71. K. Burns, B. Hasselblatt, "The Sharkovsky Theorem: A Natural Direct Proof" (2008). Accessed 3 February 2023. Alsedà, L.; Llibre, J.; Misiurewicz
Sharkovskii's_theorem
its original proof Mathematical induction and a proof Proof that 0.999... equals 1 Proof that 22/7 exceeds π Proof that e is irrational Proof that π is irrational
List_of_mathematical_proofs
Two colliding clusters of galaxies in constellation Carina
potential and normal matter that was claimed by Clowe et al. as "A Direct Empirical Proof of the Existence of Dark Matter" arguing that modified gravity theories
Bullet_Cluster
System that regulates the formation of blocks on a blockchain
Proof of work (also written as proof-of-work, and abbreviated PoW) is a form of cryptographic proof in which one party (the prover) proves to others (the
Proof_of_work
focused proofs are a family of analytic proofs that arise through goal-directed proof-search, and are a topic of study in structural proof theory and
Focused_proof
About simultaneous modular congruences
the solution may be done as in § Existence (constructive proof) or § Existence (direct proof). However, the latter construction may be simplified by using
Chinese_remainder_theorem
Says when a natural number is the sum of three squares of integers
proving the three-square theorem is considerably more difficult than a direct proof of the four-square theorem that does not use the three-square theorem
Legendre's three-square theorem
Legendre's_three-square_theorem
Genus of flowering plants
believe is evidence of a direct link between the species of plants. The shared traits between the two pollen types are not direct proof, as clear differences
Ascarina
2000 film
Proof of Life is a 2000 American action thriller film directed and produced by Taylor Hackford, and starring Meg Ryan and Russell Crowe. The title refers
Proof_of_Life
Method of deriving conclusions
distinguish various types of proof based on the inferential strategy to arrive at a conclusion such as direct proof, proof by contradiction, and mathematical
Rule_of_inference
Silla general (fl. 6th century)
was the 4th generation descendant of King Naemul, which also provides direct proof that his family name was Kim. In Samguk yusa, his name was instead recorded
Isabu
Theorem about natural numbers
provided by Gödel's incompleteness theorem and Gerhard Gentzen's 1943 direct proof of the unprovability of ε0-induction in Peano arithmetic. The Paris–Harrington
Goodstein's_theorem
Technical lemma in group theory
conjugation. Zassenhaus proved this lemma specifically to give the most direct proof of the Schreier refinement theorem. The 'butterfly' becomes apparent
Zassenhaus_lemma
Fringe theory of physics
large class of related models, cannot work. Distler and Garibaldi offer direct proof that it is impossible to embed all three generations of fermions in E8
An Exceptionally Simple Theory of Everything
An_Exceptionally_Simple_Theory_of_Everything
Theorem in measure theory
is a special case of the Fatou–Lebesgue theorem. Below, however, is a direct proof that uses Fatou’s lemma as the essential tool. Since f is the pointwise
Dominated_convergence_theorem
Infinitely many prime numbers exist
it is actually a proof by cases, a direct proof method. The philosopher Torkel Franzén, in a book on logic, states, "Euclid's proof that there are infinitely
Euclid's_theorem
Unique positive real number which when multiplied by itself gives 2
a/b|, yielding a direct proof of irrationality in its constructively stronger form, not relying on the law of excluded middle. This proof constructively
Square_root_of_2
Mathematical problem in number theory
gaps in the sequence of prime numbers, and there is also an elementary direct proof: for any n, the n − 1 consecutive numbers n! + 2, n! + 3, ..., n! + n
Gaussian_moat
Method for finding limits in calculus
inequalities are indeed equalities, and the thesis immediately follows. A direct proof, using the (ε, δ)-definition of limit, would be to prove that for all
Squeeze_theorem
Theorem in graph theory
edge and vertex versions remain true in directed graphs (when considering directed paths). Most direct proofs consider a more general statement to allow
Menger's_theorem
1938 film by Richard Thorpe
Man-Proof is a 1938 American romantic comedy film directed by Richard Thorpe. The film is based on the 1937 novel The Four Marys written by Fannie Heaslip
Man-Proof
Polynomial ideals are finitely generated
less. Introduced more than eighty years later, Gröbner bases allow a direct proof that is as constructive as possible: Gröbner bases produce an algorithm
Hilbert's_basis_theorem
Concept in algebra
^{n}\}.} Jacobson radical Nilradical of a ring Real radical Here is a direct proof that I {\displaystyle {\sqrt {I}}} is an ideal. Start with a , b ∈ I
Radical_of_an_ideal
1995 publication in mathematics
Wiles's proof of Fermat's Last Theorem is a proof by British mathematician Andrew Wiles of a special case of the modularity theorem for elliptic curves
Wiles's proof of Fermat's Last Theorem
Wiles's_proof_of_Fermat's_Last_Theorem
Election result probability theorem
probable that such a simple result could be proved by a more direct method. Such a proof was given by Désiré André, based on the observation that the
Bertrand's_ballot_theorem
Formula for systems of linear equations
manifold is invariant with respect to change of coordinates. We give a direct proof, suppressing the role of the Christoffel symbols. Let ( M , g ) {\displaystyle
Cramer's_rule
believe that it occurred in the Near East. They argue that there is no direct proof of sacred prostitution there, but rather the notion was fabricated to
Sacred prostitution in ancient Greece
Sacred_prostitution_in_ancient_Greece
Topological space which is a generalization of certain compact spaces
paracompact. Later Ernest Michael gave a direct proof of the latter fact and M.E. Rudin gave another, elementary, proof. a-paracompact space Paranormal space
Paracompact_space
Geometry puzzle
doubt about the exact value. A direct proof using classical geometry was developed by James Mercer in 1923. This proof involves drawing one additional
Langley's_Adventitious_Angles
Obligation on a party to prove their case
burden of proof to show that they are correct, while the other party has no such burden and is presumed to be correct. The burden of proof requires a
Burden_of_proof_(law)
statement of the lemma, although it does not have a more direct proof. The essence of the proof is in the inequalities W n ≡ | | f n | p − | f | p − | f
Brezis–Lieb_lemma
Every polynomial has a real or complex root
Branco (2011), "The Fundamental Theorem of Algebra: an elementary and direct proof", The Mathematical Intelligencer, vol. 33, no. 2, pp. 1–2, doi:10
Fundamental theorem of algebra
Fundamental_theorem_of_algebra
Theorems on the convergence of bounded monotonic sequences
_{X}f_{k}\,d\mu \;=\;\int _{X}f\,d\mu .} The proof can also be based on Fatou's lemma instead of a direct proof as above, because Fatou's lemma can be proved
Monotone_convergence_theorem
Victim of September 11 attacks
that the evidence make the conclusion "highly probable". Even without direct proof irrefutably establishing that her route that morning took her past the
Disappearance of Sneha Anne Philip
Disappearance_of_Sneha_Anne_Philip
Technique for proving sets have equal size
In combinatorics, bijective proof is a proof technique for proving that two sets have equally many elements, or that the sets in two combinatorial classes
Bijective_proof
Crusader state ruler (1099–1291)
Fulk, or his supporters, were commonly believed responsible, though direct proof never surfaced. The scandal was all that was needed for the queen's party
King_of_Jerusalem
Postulated existence of three photoreceptor types in the eye
Sussex: Psychology Press. "Human eye – anatomy". Britannica online. The direct proof that the eye does contain three types of cone has been secured, but only
Young–Helmholtz_theory
Description of degree sequences of graphs
Triesch (1994). Mahadev & Peled (1995) reinvented it and gave a more direct proof. Havel–Hakimi algorithm Aigner, Martin; Triesch, Eberhard (1994), "Realizability
Erdős–Gallai_theorem
Impossibility result for ranked-choice voting systems
Simple Proof". Economics Letters. 69 (3): 319–322. doi:10.1016/S0165-1765(00)00312-8. ISSN 0165-1765. Sen, Arunava (2001). "Another Direct Proof of the
Gibbard–Satterthwaite_theorem
Proving validity without revealing other data
In cryptography, a zero-knowledge proof (also known as a ZK proof or ZKP) is a protocol in which one party (the prover) can convince another party (the
Zero-knowledge_proof
Form of mathematical proof
up to the next one (the step). — Concrete Mathematics, page 3 margins. A proof by induction consists of two cases. The first, the base case, proves the
Mathematical_induction
Argument that leads to a logical absurdity
sense, proof by contradiction is also known as indirect proof, proof by assuming the opposite, and reductio ad impossibile. G. H. Hardy described proof by
Reductio_ad_absurdum
Formula for the derivative of a product
derivative provides a simpler expression of the last form, as well as a direct proof that does not involve any recursion. The logarithmic derivative of a
Product_rule
2007 double feature consisting of Planet Terror and Death Proof
group of survivors who battle zombie-like creatures, and Tarantino's Death Proof, a thriller about a murderous stuntman who kills young women with modified
Grindhouse_(film)
2002 Australian film by Phillip Noyce
Rabbit-Proof Fence is a 2002 Australian epic drama film directed and produced by Phillip Noyce. It was based on the 1996 book Follow the Rabbit-Proof Fence
Rabbit-Proof_Fence
Method of verification before the final press run
press before the final press run. Most contract proofs are a prepress proof. The primary goal of 'proofing' is to serve as a tool for customer verification
Prepress_proofing
Season of television series
The second season of Body of Proof, an American television series created by Christopher Murphey, commenced airing in the United States on September 20
Body_of_Proof_season_2
Study of objects of arithmetic interest over infinite towers of number fields
had already been identified by Kummer as the main obstruction to the direct proof of Fermat's Last Theorem. From this beginning in the 1950s, a substantial
Iwasawa_theory
Theorem in algebra mathematics
Macdonald (1969, Proposition 2.6) There is also a simple direct proof of Nakayama's lemma in this form. Proof: Suppose, for the sake of contradiction, that x 1
Nakayama's_lemma
Form of activism in which power is used
Direct action is a form of activism in which participants use economic power or political power to achieve their goals. The aim of direct action is to
Direct_action
Relation between sides of a right triangle
most for any mathematical theorem. The proofs are diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years
Pythagorean_theorem
Hypothetical invisible cosmic material
21 August 2006. Abstract only Clowe, Douglas; et al. (2006). "A Direct Empirical Proof of the Existence of Dark Matter". The Astrophysical Journal Letters
Dark_matter
Theory that life has no inherent meaning
painlessness, where nothing remains to him but abandonment to boredom. This is direct proof that existence has no real value in itself; for what is boredom but the
Existential_nihilism
Ancient Egyptian commemorative tablet
place of worship for the cult of Isis, Mistress of the Pyramid. A first, direct proof for fakery is the circumstance that Khufu is introduced by his Horus
Inventory_Stela
Theorem in computability theory
theorem can both be proved, rather simply, from each other. However, a direct proof of Kleene's theorem does not make use of a universal program, which means
Kleene's_recursion_theorem
In algebra
Two direct proofs are given in Atiyah–MacDonald; the one is due to Zariski and the other uses the Artin–Tate lemma. For Zariski's original proof, see
Zariski's_lemma
Proofs in enumerative combinatorics
mathematics, the term combinatorial proof is often used to mean either of two types of mathematical proof: A proof by double counting. A combinatorial
Combinatorial_proof
Group of even permutations of a finite set
using a classification of simple groups of order 60, and here for a direct proof). A6 is isomorphic to PSL2(9) and PSp4(2)'. A8 is isomorphic to PSL4(2)
Alternating_group
German mathematician (1909–1945)
finished in 1939, he determined the proof-theoretical strength of Peano arithmetic. This was done by a direct proof of the unprovability of the principle
Gerhard_Gentzen
Russian politician and diplomat (born 1967)
partially corroborating his source's claims, though he presented no direct proof that Peskov had set foot on the vessel. Established in January 2014,
Dmitry_Peskov
Poetic persona in Shakespeare's sonnets
theory that Lanier was the Dark Lady not only due to the lack of any direct proof, but also because the claimed association with Shakespeare tends to overshadow
Dark_Lady_(Shakespeare)
Every natural number can be represented as the sum of four integer squares
Theorem 369. Niven & Zuckerman 1960, paragraph 5.7. Here the argument is a direct proof by contradiction. With the initial assumption that m > 2, m < p, is some
Lagrange's four-square theorem
Lagrange's_four-square_theorem
All numbers between two given numbers
ISBN 3-88538-006-4. MR 1039321. Zbl 0684.54001. Steen, Lynn A. (1970). "A direct proof that a linearly ordered space is hereditarily collection-wise normal"
Interval_(mathematics)
Order whose elements are all comparable
element. Thus every finite total order is in fact a well order. Either by direct proof or by observing that every well order is order isomorphic to an ordinal
Total_order
Public transportation fare collection system
Proof-of-payment (POP) or proof-of-fare (POF) is an honor-based fare collection system used on many public transportation systems. Instead of checking
Proof-of-payment
English philosopher (1873–1958)
themselves to moral thought, but which are not susceptible to either direct proof or disproof (Principia, § 45). As a result of his opinion, he has often
G._E._Moore
1977 Japanese film
Proof of the Man (Japanese: 人間の証明, Hepburn: Ningen no Shōmei) is a 1977 Japanese crime drama film directed by Junya Satō, starring George Kennedy and Yūsaku
Proof_of_the_Man
Concept in Hlibert spaces mathematics
theorem and proof are due to E. H. Lieb, Thm 6, where he obtains this theorem as a corollary of Lieb's concavity Theorem. The most direct proof is due to
Trace_inequality
Convergence proof techniques are canonical patterns of mathematical proofs that sequences or functions converge to a finite limit when the argument tends
Convergence_proof_techniques
Series of historical novels by French author Maurice Druon
countess. Poisoned by Mahaut, the infant dies almost immediately. Without direct proof of her guilt, and unsure of Philippe's involvement, the Bouvilles are
The_Accursed_Kings
In proof theory, an area of mathematical logic, proof compression is the problem of algorithmically compressing formal proofs. The developed algorithms
Proof_compression
a_{1}\geq \cdots \geq a_{n}} . Berger reinvented this result and gives a direct proof. A sequence ( ( a 1 , b 1 ) , … , ( a n , b n ) ) {\displaystyle ((a_{1}
Fulkerson–Chen–Anstee_theorem
Concept in medieval Roman law
in half-proofs but in quarter-proofs and eighth-proofs, but there is no direct evidence of that.[citation needed] In later times, half-proof was mentioned
Half-proof
Process of creating new atomic nuclei from existing nucleons
of those with more than eight times the mass of the Sun. The first direct proof that nucleosynthesis occurs in stars was the astronomical observation
Nucleosynthesis
Indian researcher and teacher
decomposability. Econometrica, 67(3), pp. 605–628. Sen, A., 2001. Another direct proof of the Gibbard–Satterthwaite theorem. Economics Letters, 70(3), pp. 381–385
Arunava_Sen
Proof of purchase is often required for sales promotions and manufacturer rebates as evidence that the customer purchased the product. When multiple purchases
Proof_of_purchase
Square matrices satisfy their characteristic equation
see Jordan normal form § Cayley–Hamilton theorem. In this section, direct proofs are presented. As the examples above show, obtaining the statement of
Cayley–Hamilton_theorem
1906 novel by Natsume Sōseki
geisha. With his usual eloquence, Red Shirt points out that they have no direct proof of any wrongdoing. Botchan and Porcupine overcome this technicality by
Botchan
Algorithm for job scheduling
Number-Partitioning Algorithms". arXiv:2110.08886 [cs.DS]. Xiao, Xin (2017-04-01). "A Direct Proof of the 4/3 Bound of LPT Scheduling Rule". Proceedings of the 2017 5th
Longest-processing-time-first scheduling
Longest-processing-time-first_scheduling
1991 Australian film
Proof is a 1991 Australian romantic comedy-drama film written and directed by Jocelyn Moorhouse. The film stars Hugo Weaving, Geneviève Picot and Russell
Proof_(1991_film)
Relationship between programs and proofs
language theory and proof theory, the Curry–Howard correspondence is a direct relationship between computer programs and mathematical proofs. It is also known
Curry–Howard_correspondence
1923 film by Scott R. Dunlap
Skid Proof is a 1923 silent film drama directed by Scott R. Dunlap and starring Buck Jones, billed as Charles Jones. It was produced and released by Fox
Skid_Proof
DIRECT PROOF
DIRECT PROOF
Boy/Male
American, Australian, British, Chinese, English, German
Ruler of the People; The People's Ruler
Boy/Male
Indian, Punjabi, Sikh
One who Sings Glory of God
Girl/Female
Tamil
Direct, Lead
Boy/Male
Hindu, Indian, Marathi
One who Directs; Guide
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi
Crown
Girl/Female
Teutonic American German Latin
Directed.
Male
Turkish
Turkish name DIRENÇ means "resistance."
Girl/Female
Greek Latin
Killed for abusing children.
Boy/Male
Indian, Punjabi, Sikh
Hearty Traditions
Boy/Male
Hindu, Indian, Marathi
One who Directs; Leader
Boy/Male
Dutch
Dutch forms of Theodoric.
Boy/Male
Tamil
Pratyaksh | பà¯à®°à®¤à¯à®¯à®•à¯à®·
Direct evidence
Pratyaksh | பà¯à®°à®¤à¯à®¯à®•à¯à®·
Boy/Male
Hindu
Direct evidence
Boy/Male
German
People's Ruler
Girl/Female
Indian, Sikh
Faithful
Boy/Male
English American German
Leader.
Girl/Female
Hindu, Indian, Malayalam, Marathi, Telugu
Direct; Lead
Girl/Female
Indian, Sikh
Lion
Boy/Male
Tamil
One who directs, Guide
Male
French
French form of Latin Benedictus, BÉNÉDICT means "blessed."Â
DIRECT PROOF
DIRECT PROOF
Girl/Female
Hindu
Girl/Female
Tamil
Born on a mountain
Female
German
German and Swiss short form of Old High German Adalheid, ALEIT means "noble sort."
Female
Arthurian
, mother of Lohot by Arthur.
Boy/Male
English Celtic Shakespearean
From the bear estate.
Boy/Male
Indian, Sanskrit
Excellent Among the Nobility
Girl/Female
Norse
Fiery spirit.
Male
Hungarian
Hungarian form of Greek GabriÄ“l, GÃBRIEL means "man of God" or "warrior of God."
Boy/Male
American, British, English
Lives at the Buck Meadow
Boy/Male
Biblical
Good-will, messenger.
DIRECT PROOF
DIRECT PROOF
DIRECT PROOF
DIRECT PROOF
DIRECT PROOF
v. t.
To determine the direction or course of; to cause to go on in a particular manner; to order in the way to a certain end; to regulate; to govern; as, to direct the affairs of a nation or the movements of an army.
n.
One who, or that which, directs; one who regulates, guides, or orders; a manager or superintendent.
a.
Straight; not crooked, oblique, or circuitous; leading by the short or shortest way to a point or end; as, a direct line; direct means.
n.
Failing; fault; imperfection, whether physical or moral; blemish; as, a defect in the ear or eye; a defect in timber or iron; a defect of memory or judgment.
a.
Not direct; not straight or rectilinear; deviating from a direct line or course; circuitous; as, an indirect road.
n.
A part of a machine or instrument which directs its motion or action.
adv.
In a straightforward way; without anything intervening; not by secondary, but by direct, means.
v. t.
To point out or show to (any one), as the direct or right course or way; to guide, as by pointing out the way; as, he directed me to the left-hand road.
v. t.
To direct.
a.
Not reaching the end aimed at by the most plain and direct method; as, an indirect proof, demonstration, etc.
v. t.
To arrange in a direct or straight line, as against a mark, or towards a goal; to point; to aim; as, to direct an arrow or a piece of ordnance.
a.
Indirect.
v. t.
To put a direction or address upon; to mark with the name and residence of the person to whom anything is sent; to superscribe; as, to direct a letter.
n.
One who directs; a director.
imp. & p. p.
of Direct
a.
Directed upward; raised; uplifted.
v. t.
To point out to with authority; to instruct as a superior; to order; as, he directed them to go.
a.
Not resulting directly from an act or cause, but more or less remotely connected with or growing out of it; as, indirect results, damages, or claims.
a.
In the line of descent; not collateral; as, a descendant in the direct line.
adv.
In a direct manner; in a straight line or course.