AI & ChatGPT searches , social queriess for COMBINATORIAL PROOF
Search references for COMBINATORIAL PROOF. Phrases containing COMBINATORIAL PROOF
See searches and references containing COMBINATORIAL PROOF!
Search references for COMBINATORIAL PROOF. Phrases containing COMBINATORIAL PROOF
See searches and references containing COMBINATORIAL PROOF!COMBINATORIAL PROOF
Proofs in enumerative combinatorics
the term combinatorial proof is often used to mean either of two types of mathematical proof: A proof by double counting. A combinatorial identity is
Combinatorial_proof
Number of subsets of a given size
Benjamin, Arthur T.; Quinn, Jennifer J. (2003). Proofs that Really Count: The Art of Combinatorial Proof. Dolciani Mathematical Expositions. Vol. 27. Mathematical
Binomial_coefficient
Algebraic expansion of powers of a binomial
{\displaystyle {\tbinom {n}{k}},} either by definition, or by a short combinatorial argument if one is defining ( n k ) {\displaystyle {\tbinom {n}{k}}}
Binomial_theorem
Square matrices satisfy their characteristic equation
1997, p. 7 Garrett 2007, p. 381 Straubing, Howard (1983-01-01). "A combinatorial proof of the Cayley–Hamilton theorem". Discrete Mathematics. 43 (2): 273–279
Cayley–Hamilton_theorem
Reasoning for mathematical statements
for testing primality) are as good as genuine mathematical proofs. A combinatorial proof establishes the equivalence of different expressions by showing
Mathematical_proof
Theorem in topology
; Todd, Michael J. (1982). "A constructive proof of Tucker's combinatorial lemma". Journal of Combinatorial Theory. Series A. 30 (3): 321–325. doi:10
Borsuk–Ulam_theorem
Theorem in topology
come in three equivalent variants: an algebraic topology variant, a combinatorial variant and a set-covering variant. Each variant can be proved separately
Brouwer_fixed-point_theorem
On continuous motion of a simple polygon to convex
a simplified combinatorial proof formulated in the terminology of robot arm motion planning. Both the original proof and Streinu's proof work by finding
Carpenter's_rule_problem
the simplest known proof, requiring the least mathematical background. It is an attractive example of a combinatorial proof (a proof that involves counting
Proofs of Fermat's little theorem
Proofs_of_Fermat's_little_theorem
Branch of mathematical logic
the formalisation of intuitionistic logic, and provide the first combinatorial proof of the consistency of Peano arithmetic. Together, the presentation
Proof_theory
Mathematical theorem on convolved binomial coefficients
binomial coefficients. Vandermonde's identity also admits a combinatorial double counting proof, as follows. Suppose a committee consists of m men and n
Vandermonde's_identity
Branch of discrete mathematics
Combinatorics is well known for the breadth of the problems it tackles. Combinatorial problems arise in many areas of pure mathematics, notably in algebra
Combinatorics
Combinatorial identity about binomial coefficients
coefficients. Pascal's rule has an intuitive combinatorial meaning, that is clearly expressed in this counting proof. Proof. Recall that ( n k ) {\displaystyle
Pascal's_rule
Relations between power sums and elementary symmetric functions
MathWorld A Matrix Proof of Newton's Identities in Mathematics Magazine Application on the number of real roots A Combinatorial Proof of Newton's Identities
Newton's_identities
Numbers obtained by adding the two previous ones
memoization). Most identities involving Fibonacci numbers can be proved using combinatorial arguments using the fact that F n {\displaystyle F_{n}} can be interpreted
Fibonacci_sequence
Technique for proving sets have equal size
combinatorics, bijective proof is a proof technique for proving that two sets have equally many elements, or that the sets in two combinatorial classes have equal
Bijective_proof
2003 mathematics book by Arthur T. Benjamin and Jennifer Quinn
Proofs That Really Count: the Art of Combinatorial Proof is an undergraduate-level mathematics book on combinatorial proofs of mathematical identies.
Proofs_That_Really_Count
Type of proof technique
combinatorics, double counting, also called counting in two ways, is a combinatorial proof technique for showing that two expressions are equal by demonstrating
Double counting (proof technique)
Double_counting_(proof_technique)
Square of a triangular number
S2CID 126165678 Garrett, Kristina C.; Hummel, Kristen (2004), "A combinatorial proof of the sum of q-cubes", Electronic Journal of Combinatorics, 11 (1)
Squared_triangular_number
Recurrence relations of binomial coefficients in Pascal's triangle
{\text{ for }}n,r\in \mathbb {N} ,\quad n\geq r.} The inductive and algebraic proofs both make use of Pascal's identity: ( n k ) = ( n − 1 k − 1 ) + ( n − 1
Hockey-stick_identity
Mathematical theory
{\displaystyle |Y|\setminus |X|} . Björner and Tancer presented an elementary combinatorial proof and summarized a few generalizations. For smooth manifolds, Alexander
Alexander_duality
Concept in music
In music using the twelve tone technique, combinatoriality is a quality shared by twelve-tone tone rows whereby each section of a row and a proportionate
Combinatoriality
British mathematician
what is called the Polymath Project, Polymath1, was to find a new combinatorial proof to the density version of the Hales–Jewett theorem. After seven weeks
Timothy_Gowers
Series of public experiments on mass collaboration in mathematics
now called Polymath1 by the Polymath community, was to find a new combinatorial proof to the density version of the Hales–Jewett theorem. As the project
Polymath_Project
System that regulates the formation of blocks on a blockchain
original on 2016-08-26. Retrieved 2007-11-25. Fitzi, Matthias. "Combinatorial Optimization via Proof-of-Useful-Work" (PDF). IACR conference Crypto 2022. Archived
Proof_of_work
Graph whose vertices correspond to combinations of a set of n elements
his further-simplified but still topological proof. In 2004, Jiří Matoušek found a purely combinatorial proof. In contrast, the fractional chromatic number
Kneser_graph
Theorem that the slice genus of the (p, q) torus knot is (p-1)(q-1)/2
Kronheimer and Tomasz Mrowka. Jacob Rasmussen later gave a purely combinatorial proof using Khovanov homology, by means of the s-invariant. Kronheimer
Milnor conjecture (knot theory)
Milnor_conjecture_(knot_theory)
(2018) write that all proofs are somehow based on linear algebra: "no combinatorial proof for this result is known". A partition into exactly n − 1 {\displaystyle
Graham–Pollak_theorem
Selection in a particular order
called "k-permutations" of the n-set.) Straubing, Howard (1983), "A combinatorial proof of the Cayley-Hamilton theorem", Discrete Mathematics, 43 (2–3):
Partial_permutation
Gives a lower bound on the number of lines determined by n points in a projective plane
determined by a configuration of lines. Although the proof given by De Bruijn and Erdős is combinatorial, De Bruijn and Erdős noted in their paper that the
De Bruijn–Erdős theorem (incidence geometry)
De_Bruijn–Erdős_theorem_(incidence_geometry)
Overview of and topical guide to combinatorics
Binomial coefficients and their properties Combinatorial proof Double counting (proof technique) Bijective proof Inclusion–exclusion principle Möbius inversion
Outline_of_combinatorics
Selection of items from a set
Benjamin, Arthur T.; Quinn, Jennifer J. (2003), Proofs that Really Count: The Art of Combinatorial Proof, The Dolciani Mathematical Expositions 27, The
Combination
Number raised to the third power
Press. ISBN 978-0-88385-700-7. Stein, Robert G. (1 May 1971). "A Combinatorial Proof That Σ k3 = (Σ k)2". Mathematics Magazine. 44 (3): 161–162. doi:10
Cube_(algebra)
Branch of game theory about two-player sequential games with perfect information
required a computer-assisted proof. Many real-world games remain too complex for complete analysis, though combinatorial methods have shown some success
Combinatorial_game_theory
Methods used in combinatorics
In proving results in combinatorics several useful combinatorial rules or combinatorial principles are commonly recognized and used. The rule of sum, rule
Combinatorial_principles
Sequence of polynomials defined recursively
Jennifer J. (2003). "Fibonacci and Lucas Polynomial". Proofs that Really Count: The Art of Combinatorial Proof. Dolciani Mathematical Expositions. Vol. 27. Mathematical
Fibonacci_polynomials
Count of permutations by cycles
{\displaystyle x^{k}} on both sides must be equal, and the result follows. Combinatorial proof We prove the recurrence relation using the definition of Stirling
Stirling numbers of the first kind
Stirling_numbers_of_the_first_kind
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
Complex-valued function
so any proof of it immediately yields of proof of the Mehler formula. Foata gave a combinatorial proof of the formula. Hardy gave a simple proof by the
Mehler_kernel
Mathematical subject
regarded as derived from combinatorial decompositions of spaces, such as decomposition into simplicial complexes. After the proof of the simplicial approximation
Combinatorial_topology
If there are more items than boxes holding them, one box must contain at least two items
[citation needed] Axiom of choice Blichfeldt's theorem Combinatorial principles Combinatorial proof Dedekind-infinite set Dirichlet's approximation theorem
Pigeonhole_principle
Identity involving binomial coefficients, first established by Zhi-Wei Sun in 2002
Ekhad and Mohammed's proof by the WZ method; Chu and Claudio's proof with the help of Jensen's formula; Callan's combinatorial proof involving dominos and
Sun's_curious_identity
Expression for sums of powers
p+1\rbrack } into k {\displaystyle k} parts, the identity has a direct combinatorial proof since both sides count the number of functions f : [ p + 1 ] → [
Faulhaber's_formula
Number theory theorem
{m}{n}}=0} if m < n. There are several ways to prove Lucas's theorem. Combinatorial proof using a group action Let M be a set with m elements, and arbitrarily
Lucas's_theorem
Method of computing determinants
treatment in the book Proofs and Confirmations: The Story of the Alternating Sign Matrix Conjecture; an alternative combinatorial proof was given in a paper
Dodgson_condensation
American mathematician
Daniel Kleitman, he has also written a highly cited survey paper on combinatorial proof techniques. In 2012 he became a fellow of the American Mathematical
Curtis_Greene
Positive real number which when multiplied by itself gives 5
Benjamin, Arthur T.; Quinn, Jennifer J. (2022), Proofs that Really Count: The Art of Combinatorial Proof, Dolciani Mathematical Expositions, vol. 27, American
Square_root_of_5
Polynomial sequence
Slepian in 1972 using Fourier analysis. Foata gave a combinatorial proof while Louck gave a proof via boson quantum mechanics. It has a generalization
Hermite_polynomials
NP-hard problem in combinatorial optimization
ISBN 0-691-08000-3, sixth printing, 1974. Velednitsky, Mark (2017). "Short combinatorial proof that the DFJ polytope is contained in the MTZ polytope for the Asymmetric
Travelling_salesman_problem
Mathematical technique
In combinatorial mathematics, block walking is a method useful in thinking about sums of combinations graphically as "walks" on Pascal's triangle. As
Block_walking
Some remarkable congruences for the partition function
existence of a "crank" function for partitions that would provide a combinatorial proof of Ramanujan's congruences modulo 11. Forty years later, George Andrews
Ramanujan's_congruences
Connects set theory with category theory
linear combination of basis elements a k {\displaystyle a_{k}} . Combinatorial proof, the process of replacing number theoretic theorems by set-theoretic
Categorification
Academic journal
"Editorial". Combinatorial Theory. 1. doi:10.5070/C61055307. ISSN 2766-1334. S2CID 245076810. Katona, G.O.H. (1972). "A simple proof of the Erdös-Chao
Journal of Combinatorial Theory
Journal_of_Combinatorial_Theory
Number in combinatorics
generating functions, while Foata and Zeilberger provide a direct combinatorial proof. Plutarch's dialogue Table Talk contains the line: Chrysippus says
Schröder–Hipparchus_number
Graph of triangles with a shared vertex
property. A combinatorial proof of the friendship theorem was given by Mertzios and Unger. Another proof was given by Craig Huneke. A formalised proof in Metamath
Friendship_graph
American mathematician (born 1961)
CHOICE Award, Outstanding Academic Title, for Proofs that Really Count: The Art of Combinatorial Proof, American Library Association, 2004 Designated
Arthur_T._Benjamin
large number of proofs. Several hundred proofs of the law of quadratic reciprocity have been published. Of the elementary combinatorial proofs, there are two
Proofs of quadratic reciprocity
Proofs_of_quadratic_reciprocity
Two-dimensional manifold
been known since the 1860s, and today a number of proofs exist. Topological and combinatorial proofs in general rely on the difficult result that every
Surface_(topology)
Certain constant-recursive integer sequences
Benjamin, Arthur T.; Quinn, Jennifer J. (2003). Proofs that Really Count: The Art of Combinatorial Proof. Dolciani Mathematical Expositions. Vol. 27. Mathematical
Lucas_sequence
Boolean satisfiability is NP-complete and therefore that NP-complete problems exist
of Computing. Richard Karp's subsequent paper, "Reducibility among combinatorial problems", generated renewed interest in Cook's paper by providing a
Cook–Levin_theorem
Academic journal
higher-order recurrence sequences, nonlinear recurrence sequences, combinatorial proofs of number-theoretic identities, Diophantine equations, special matrices
Fibonacci_Quarterly
Set which cannot be assigned a meaningful "volume"
Springer-Verlag, 1982, pp. 100–101 Sadhukhan, A. (December 2022). "A Combinatorial Proof of the Existence of Dense Subsets in R {\displaystyle \mathbb {R}
Non-measurable_set
Field of mathematics using techniques from combinatorics and commutative algebra
geometric terms, the methods of the proof drew on commutative algebra techniques. A signature theorem in combinatorial commutative algebra is the characterization
Combinatorial commutative algebra
Combinatorial_commutative_algebra
Long dense subsets of the integers contain arbitrarily large arithmetic progressions
of his previous combinatorial argument for k = 4 (called "a masterpiece of combinatorial reasoning" by Erdős). Several other proofs are now known, the
Szemerédi's_theorem
Alternative decimal expansion of 1
mathematically rigorous proofs. The intuitive arguments are generally based on properties of finite decimals that are extended without proof to infinite decimals
0.999...
Game of strategy
Nim is a mathematical combinatorial game in which two players take turns removing (or "nimming") objects from distinct heaps or piles. On each turn, a
Nim
Generalization of strings in computer science
introduced by Pierre Cartier and Dominique Foata in 1969 to give a combinatorial proof of MacMahon's master theorem. Traces are used in theories of concurrent
Trace_monoid
Fundamental combinatorial result of Ramsey theory
of the two sets must contain a combinatorial line (i.e. no draw is possible in this variant of tic-tac-toe). For a proof, see below. We now prove the Hales–Jewett
Hales–Jewett_theorem
Theorem on triangulation graph colorings
In mathematics, Sperner's lemma is a combinatorial result on colorings of triangulations, analogous to the Brouwer fixed point theorem, which is equivalent
Sperner's_lemma
Overview of and topical guide to discrete mathematics
coefficients Combinatorial proof – Proofs in enumerative combinatorics Bijective proof – Technique for proving sets have equal size Double counting (proof technique) –
Outline of discrete mathematics
Outline_of_discrete_mathematics
Canadian computer scientist
participation in the first Polymath project, Polymath1, for developing a combinatorial proof to the density Hales–Jewett theorem, improved algorithms for problems
Ryan O'Donnell (computer scientist)
Ryan_O'Donnell_(computer_scientist)
Mathematical subject
solving problems in combinatorics. The discipline of combinatorial topology used combinatorial concepts in topology and in the early 20th century this
Topological_combinatorics
Mathematical identities related to integer partitions
Cilanne Boulet, Igor Pak, A Combinatorial Proof of the Rogers–Ramanujan and Schur Identities, Journal of Combinatorial Theory, Ser. A, vol. 113 (2006)
Rogers–Ramanujan_identities
Study of discrete mathematical structures
from topology and algebraic topology/combinatorial topology in combinatorics. Design theory is a study of combinatorial designs, which are collections of
Discrete_mathematics
Sequence of locally optimal choices
reconsider past choices. Greedy algorithms are often used to solve combinatorial optimization problems. If an optimization problem only depends on the
Greedy_algorithm
Tiling hobbyist
2023. In 2024, their results were published in consecutive issues of Combinatorial Theory. Roberts, Siobhan (2023-03-28). "Elusive 'Einstein' Solves a
David Smith (amateur mathematician)
David_Smith_(amateur_mathematician)
Number of orderings allowing ties
car parks on its preferred spot. This application also provides a combinatorial proof for upper and lower bounds on the ordered Bell numbers of a simple
Ordered_Bell_number
Statement in mathematical combinatorics
version of this result was proved by Frank Ramsey. This initiated the combinatorial theory now called Ramsey theory, that seeks regularity amid disorder:
Ramsey's_theorem
Number of stacked spheres in a pyramid
doi:10.5951/AT.21.5.0396, JSTOR 41190919 Stein, Robert G. (1971), "A combinatorial proof that ∑ k 3 = ( ∑ k ) 2 {\displaystyle \textstyle \sum k^{3}=(\sum
Square_pyramidal_number
States that the algebra of n by n matrices satisfies a certain identity of degree 2n
cohomology of Lie algebras. Swan (1963) and Swan (1969) gave a simple combinatorial proof as follows. By linearity it is enough to prove the theorem when each
Amitsur–Levitzki_theorem
Branch of geometry that studies combinatorial properties and constructive methods
Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric
Discrete_geometry
Result in combinatorics and graph theory
gives a necessary and sufficient condition for an object to exist: The combinatorial formulation answers whether a finite collection of sets has a transversal—that
Hall's_marriage_theorem
Provides lower bounds on the circuit complexity of boolean functions
boolean functions. A natural proof shows, either directly or indirectly, that a boolean function has a certain natural combinatorial property. Under the assumption
Natural_proof
Optimization algorithms using quantum computing
the combinatorial optimization problem is a string z {\displaystyle z} that is close to maximizing C ( z ) {\displaystyle C(z)} . For combinatorial optimization
Quantum optimization algorithms
Quantum_optimization_algorithms
Number of spanning trees of a complete graph
Schützenberger, M. P. (1968). "On an enumeration problem". Journal of Combinatorial Theory. 4 (3): 219–221. doi:10.1016/S0021-9800(68)80003-1. MR 0218257
Cayley's_formula
S2CID 7974973. Hajnal, A.; Szemerédi, E. (1970), "Proof of a conjecture of P. Erdős", Combinatorial theory and its applications, II (Proc. Colloq., Balatonfüred
List of conjectures by Paul Erdős
List_of_conjectures_by_Paul_Erdős
Mathematical technique used in proof theory
power set of the natural numbers have proof-theoretic ordinals that are so large that no explicit combinatorial description has yet been given. This includes
Ordinal_analysis
see Buchta (1994), noticed the combinatorial nature of the formula and published the elementary combinatorial proof of (3). Cecil J. Nesbitt, PhD, F
Schuette–Nesbitt_formula
Xingxing (2019-12-19). "The Kelmans-Seymour conjecture IV: A proof". Journal of Combinatorial Theory, Series B. 144: 309–358. arXiv:1612.07189. doi:10.1016/j
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Mathematical models of changing DNA
Snir S (July 2008). "Hadamard conjugation for the Kimura 3ST model: combinatorial proof using path sets". IEEE/ACM Transactions on Computational Biology
Models_of_DNA_evolution
Integration for Grassmann variables
others (link) S. Caracciolo, A. D. Sokal and A. Sportiello, Algebraic/combinatorial proofs of Cayley-type identities for derivatives of determinants and pfaffians
Berezin_integral
Recursive integer sequence
solves the combinatorial problems listed above. The first proof below uses a generating function. The other proofs are examples of bijective proofs; they involve
Catalan_number
Abstraction of linear independence of vectors
these fields. Matroids have found applications in geometry, topology, combinatorial optimization, network theory, and coding theory. There are many equivalent
Matroid
American mathematician
in 2007. Quinn's book with Arthur T. Benjamin, Proofs that Really Count: The Art of Combinatorial Proof (2003) won the CHOICE Award for Outstanding Academic
Jennifer_Quinn
Well-quasi-ordering of finite trees
conjectured by Andrew Vázsonyi and proved by Joseph Kruskal (1960); a short proof was given by Crispin Nash-Williams (1963). It has since become a prominent
Kruskal's_tree_theorem
Theorem on the largest antichain of sets
shorter, simpler, stronger proof of the Meshalkin-Hochberg-Hirsch bounds on componentwise antichains", Journal of Combinatorial Theory, Series A, 100 (1):
Sperner's_theorem
Any of the five regular polyhedra
makes five possible Platonic solids. A purely topological proof can be made using only combinatorial information about the solids. The key is Euler's observation
Platonic_solid
Combinatorial analog of the Borsuk-Ulam theorem
; Todd, Michael J. (1981), "A constructive proof of Tucker's combinatorial lemma", Journal of Combinatorial Theory, Series A, 30 (3): 321–325, doi:10
Tucker's_lemma
Counting technique in combinatorics
_{S\subseteq A}f(S)} then The combinatorial and the probabilistic version of the inclusion–exclusion principle are instances of (2). Proof Take m _ = { 1 , 2 ,
Inclusion–exclusion_principle
lists notable examples of incomplete or incorrect published mathematical proofs. Most of these were accepted as complete or correct for several years but
List_of_incomplete_proofs
COMBINATORIAL PROOF
COMBINATORIAL PROOF
Boy/Male
Muslim
Evidence. Proof.
Girl/Female
Biblical
Flight, proof, temptation, delicate.
Girl/Female
Indian
Many signs & proofs, Verses in the Quran, Royal
Surname or Lastname
English
English : from Middle English, Old French palmer, paumer (from palme, paume ‘palm tree’, Latin palma), a nickname for someone who had been on a pilgrimage to the Holy Land. Such pilgrims generally brought back a palm branch as proof that they had actually made the journey, but there was a vigorous trade in false souvenirs, and the term also came to be applied to a cleric who sold indulgences.Swedish (Palmér) : ornamental name formed with palm ‘palm tree’ + the suffix -ér, from Latin -erius ‘descendant of’.Irish : when not truly of English origin (see 1 above), a surname adopted by bearers of Gaelic Ó Maolfhoghmhair (see Milford) perhaps because they were from an ecclesiastical family.German : topographic name for someone living among pussy willows (see Palm 2).German : from the personal name Palm (see Palm 3).
Boy/Male
Arabic, Muslim
Evidence; Proof
Girl/Female
Indian
Witness; Proof
Boy/Male
Arabic, Muslim
Another Name for God; Evidence; Proof
Girl/Female
Muslim
Guide, Proof
Girl/Female
Muslim
Many signs & proofs, Verses in the Quran, Royal
Boy/Male
Muslim
Proof
Girl/Female
Muslim
Proof
Girl/Female
Assamese, Bengali, Gujarati, Hindu, Indian, Jain, Kannada, Malayalam, Marathi, Sanskrit, Tamil, Telugu, Traditional
Witness; Justice; Proof; Cute Princess; Loved by Everyone; Grace; Purity; Pluck; Witness Truth; Queen; Princess; Real; Truth
Girl/Female
Indian
Many signs & proofs, Verses in the Quran, Royal
Boy/Male
Arabic
Evidence; Proof; Distinction Between Truth and Falsehood
Boy/Male
Muslim
Argument, Reasoning, Proof
Boy/Male
Muslim
Proof
Boy/Male
Indian
Proof
Boy/Male
Indian
Argument, Reasoning, Proof
Girl/Female
Muslim
Many signs & proofs, Verses in the Quran, Royal
Boy/Male
Indian
Proof
COMBINATORIAL PROOF
COMBINATORIAL PROOF
Surname or Lastname
English
English : variant of Whinery.
Boy/Male
Tamil
Gritik | கà¯à®°à¯€à®¤à®¿à®•Â
Mountain
Girl/Female
Hindu, Indian, Marathi
Song
Boy/Male
Irish
Great.
Boy/Male
Hindu
Kushwah
Girl/Female
Hindu
God of war, Also known as Kartikeya, Murugan
Girl/Female
Indian, Telugu
Goddess Lakshmi
Girl/Female
Gujarati, Indian
Brightness
Girl/Female
Muslim
Naafi
Boy/Male
Tamil
Awakened, Lord Buddha
COMBINATORIAL PROOF
COMBINATORIAL PROOF
COMBINATORIAL PROOF
COMBINATORIAL PROOF
COMBINATORIAL PROOF
n.
An undoubted or self-evident truth; a statement which is pliantly true; a proposition needing no proof or argument; -- opposed to falsism.
a.
Used in proving or testing; as, a proof load, or proof charge.
n.
The act of testing by experience; proof; test.
a.
Not doubted; not called in question; indubitable; indisputable; as, undoubted proof; undoubted hero.
v. t.
Armor of excellent or tried quality, and deemed impenetrable; properly, armor of proof.
v. t.
To arm with proof armor; to arm securely; as, to proof-arm herself.
a.
Firm or successful in resisting; as, proof against harm; waterproof; bombproof.
n.
The quality or state of being valid; strength; force; especially, power to convince; justness; soundness; as, the validity of an argument or proof; the validity of an objection.
n.
A trial impression, as from type, taken for correction or examination; -- called also proof sheet.
n.
A verse or passage of Scripture, especially one chosen as the subject of a sermon, or in proof of a doctrine.
n.
Witness; evidence; proof of some fact.
v. i.
To make a solemn declaration under oath or affirmation, for the purpose of establishing, or making proof of, some fact to a court; to give testimony in a cause depending before a tribunal.
v.
Hence, examination or trial by some decisive standard; test; proof; tried quality.
a.
Highly rectified; very strongly alcoholic; as, high-proof spirits.
n.
The act of testing or proving; trial; proof.
a.
Proof against proofs; obstinate in the wrong.
n.
Tried quality; temper; proof.
n.
Concord; harmony; conjunction; agreement; uniformity; as, a unity of proofs; unity of doctrine.
a.
Containing less alcohol than proof spirit. See Proof spirit, under Spirit.
n.
A disagreement or difference between two parts of the same legal proceeding, which, to be effectual, ought to agree, -- as between the writ and the declaration, or between the allegation and the proof.