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Type of proof technique
In combinatorics, double counting, also called counting in two ways, is a combinatorial proof technique for showing that two expressions are equal by
Double counting (proof technique)
Double_counting_(proof_technique)
Topics referred to by the same term
Double counting may refer to: Double counting (proof technique), a method in combinatorics that proves two expressions to be equal by demonstrating that
Double_counting
Number of spanning trees of a complete graph
graph on n vertices to form from it a rooted tree; see Double counting (proof technique) § Counting trees. The formula was first discovered by Carl Wilhelm
Cayley's_formula
Proofs in enumerative combinatorics
combinatorial proof is often used to mean either of two types of mathematical proof: A proof by double counting. A combinatorial identity is proven by counting the
Combinatorial_proof
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
Overview of and topical guide to combinatorics
coefficients and their properties Combinatorial proof Double counting (proof technique) Bijective proof Inclusion–exclusion principle Möbius inversion
Outline_of_combinatorics
Category of mathematical proof
complexity theory, techniques like relativization (the addition of an oracle) allow for "weak" proofs of impossibility, in that proofs techniques that are not
Proof_of_impossibility
Reasoning for mathematical statements
A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The
Mathematical_proof
Overview of and topical guide to discrete mathematics
Combinatorial proof – Proofs in enumerative combinatorics Bijective proof – Technique for proving sets have equal size Double counting (proof technique) – Type
Outline of discrete mathematics
Outline_of_discrete_mathematics
Methods used in combinatorics
correspondence) from one set to the other. Double counting is a technique that equates two expressions that count the size of a set in two ways. The pigeonhole
Combinatorial_principles
On the existence of arithmetic progressions in subsets of the natural numbers
combinatorial techniques, resolving the original conjecture in full. The original proof given by Roth used Fourier analytic methods. Later on another proof was
Roth's theorem on arithmetic progressions
Roth's_theorem_on_arithmetic_progressions
Methods of mind manipulation, often based on logical fallacies
techniques are methods used in propaganda to convince an audience to believe what the propagandist wants them to believe. Many propaganda techniques are
Propaganda_techniques
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)
Internet rage incitement technique
against rage-baiting. Individual-level interventions include prebunking techniques based on inoculation theory, which have proven effective across cultures;
Rage-baiting
Counting technique in combinatorics
inclusion–exclusion principle (Commonly referred to as PIE) is a counting technique which generalizes the familiar method of obtaining the number of elements
Inclusion–exclusion_principle
Type of informal fallacy
Intellectual virtue – Concept in Aristotelian ethics Media manipulation – Techniques in which partisans create an image that favours their interests Pooh-pooh –
Motte-and-bailey_fallacy
Informal fallacy
Proof by assertion, sometimes informally referred to as proof by repeated assertion, is an informal fallacy in which a proposition is repeatedly restated
Proof_by_assertion
Attacking the person rather than their argument
evidence Sampling bias Cherry picking McNamara Base rate / Conjunction Double counting False analogy Slothful induction Overwhelming exception Muhammad Wang
Ad_hominem
Misleading use of a term with multiple meanings
definition: Skewed definition of term Plausible deniability: A blame-shifting technique Polysemy: The property of word or phrase having certain type of multiple
Equivocation
Fallacy regarding hypocrisy
Tu quoque, literally "you, too", is a rhetorical technique that intends to discredit the opponent's argument by attacking the opponent's own personal
Tu_quoque
Fallacious approach to mislead an audience
"red herring" has traditionally been said to originate from a supposed technique of training scent hounds. There are variations of the story, but according
Red_herring
Rhetorical argument
Euthanasia and the slippery slope First they came ... Foot-in-the-door technique Gateway drug theory Normalization of deviance Overton window Precautionary
Slippery_slope
Apparent, but false, correlation between causally-independent variables
commonly used in statistics and in particular in experimental research techniques, both of which attempt to understand and predict direct causal relationships
Spurious_relationship
Psychological bias towards favoring members of one's in-group
evidence Sampling bias Cherry picking McNamara Base rate / Conjunction Double counting False analogy Slothful induction Overwhelming exception Muhammad Wang
In-group_favoritism
Branch of logic
tautological, or contradictory. See § Semantic proof via truth tables. A semantic tableau is another semantic proof technique that systematically explores the truth
Propositional_logic
Distraction technique and anti-debate tactic
evidence Sampling bias Cherry picking McNamara Base rate / Conjunction Double counting False analogy Slothful induction Overwhelming exception Muhammad Wang
Tone_policing
Overused, unoriginal phrase or opinion
evidence Sampling bias Cherry picking McNamara Base rate / Conjunction Double counting False analogy Slothful induction Overwhelming exception Muhammad Wang
Cliché
Psychological defense mechanism
persistence of deviant behavior. There exist many different and overlapping techniques of amoralizations. Collective rationalizations are regularly constructed
Rationalization_(psychology)
Fallacy of claiming the majority is always correct
Kayfabe List of fallacies Median voter theorem Scientific consensus Social proof Wisdom of the crowd These ideas are paraphrased from this presentation by
Argumentum_ad_populum
Every graph has evenly many odd vertices
player on one of its sides. Euler's proof of the degree sum formula uses the technique of double counting: he counts the number of incident pairs ( v ,
Handshaking_lemma
Formal fallacy, aka Linda Problem
"and" has even been argued to have relevant polysemous meanings. Many techniques have been developed to control for this possible misinterpretation, but
Conjunction_fallacy
Formal fallacy
of guilt – Presumption that a person is guilty of a crime Propaganda techniques – Methods of mind manipulation, often based on logical fallacies Reductio
Association_fallacy
Logical fallacy
counter and overcome for those faced by it. Gish galloping is also known as proof by verbosity, and audiences can be swayed by the rapid succession of arguments
Specious_reasoning
1989 video game
released a console port outside of the terms of their Tetris license. Bullet-Proof Software had previously released Tetris for the Family Computer in December
Tetris_(NES_video_game)
Type of trolling or harassment
and that the term sealioning was used to silence legitimate requests for proof. In 2021, Maclean's compared its origination to other terms derived from
Sealioning
Digital asset using a distributed ledger
zero-knowledge proofs. A recent 2020 study presented different attacks on privacy in cryptocurrencies. The attacks demonstrated how the anonymity techniques are
Cryptocurrency
Dream where one is aware that one is dreaming
such techniques as part of his doctoral dissertation. In 1985, LaBerge performed a pilot study that showed that time perception while counting during
Lucid_dream
Unclear communication
of secure communication without a need to rely upon technology. This technique is sometimes referred to as "talking around" and is a form of security
Obfuscation
Rhetorical cliché phrase
evidence Sampling bias Cherry picking McNamara Base rate / Conjunction Double counting False analogy Slothful induction Overwhelming exception Muhammad Wang
Think_of_the_children
Logical fallacy
the spreading of fear, uncertainty, and doubt is an unethical marketing technique that these corporations consciously employ. Fear appeal is a subject studied
Appeal_to_fear
Observation on the growth of integrated circuit capacity
Moore's revised law of doubling transistor count every 2 years in turn implied that computer chip performance would roughly double every 18 months, with
Moore's_law
Form of incorrect argument and informal fallacy
of context – Informal fallacy List of fallacies Media manipulation – Techniques in which partisans create an image that favours their interests Paper
Straw_man
Informal logical fallacy
Pascal wrote that "People [...] arrive at their beliefs not on the basis of proof, but on the basis of what they find attractive." Baruch Spinoza characterized
Appeal_to_emotion
Replacing a number with a simpler value
fractional parts occur significantly more than a restart of the occurrence "counting", then it is effectively bias free. With guaranteed zero bias, it is useful
Rounding
Selection of data points in statistics
only the returning officer will declare the official results once vote counting is complete. Successful statistical practice is based on focused problem
Sampling_(statistics)
Technique used to identify individuals via DNA characteristics
than an individual, is called DNA barcoding. DNA profiling is a forensic technique in criminal investigations, comparing suspects' profiles to DNA evidence
DNA_profiling
Type of informal fallacy
misuse in applied science, whose goal is the development of technology or technique. This blurs scientific assessment, discussed in natural sciences (like
Moralistic_fallacy
Cryptography secured against quantum computers
Post-quantum cryptography (PQC), sometimes referred to as quantum-proof, quantum-safe, or quantum-resistant, is the development of cryptographic algorithms
Post-quantum_cryptography
Greek mathematician and physicist (c. 287 – 212 BC)
and so on. This proof uses a variation of the series 1/4 + 1/16 + 1/64 + 1/256 + · · · which sums to 1/3. He also used this technique in order to measure
Archimedes
Statement in mathematical combinatorics
theorem on friends and strangers. An alternative proof works by double counting. It goes as follows: Count the number of ordered triples of vertices, x,
Ramsey's_theorem
Measurement method using interference of waves
Interferometry is a technique which uses the interference of superimposed waves to extract information. Interferometry typically uses electromagnetic
Interferometry
Logical fallacy
without providing further argumentation. This theory is closely tied to proof by assertion due to the lack of evidence behind the statement and its attempt
Appeal_to_the_stone
Rhetorical tactic and potential fallacy
An appeal to nature is a rhetorical technique for presenting and proposing the argument that "a thing is good because it is 'natural', or bad because
Appeal_to_nature
Device for birth control and STI prevention
Retrieved 6 June 2018. KLEPPER D (27 April 2014). "NY bill would bar condoms as proof of prostitution". Associated Press. Archived from the original on 27 April
Condom
a Double Series Representation of the Natural Logarithm, the Asymptotic Behavior of Hölder Means, and an Elementary Estimate for the Prime Counting Function"
List of logarithmic identities
List_of_logarithmic_identities
Differentiation under the integral sign formula
{\displaystyle b(x)=x} , which is another common situation (for example, in the proof of Cauchy's repeated integration formula), the Leibniz integral rule becomes:
Leibniz_integral_rule
Japanese swordsman, strategist, writer, artist, and rōnin (c. 1584–1645)
strategist, artist, and writer who became renowned through stories of his unique double-bladed swordsmanship and undefeated record in his 62 duels. Musashi is considered
Miyamoto_Musashi
Form of scientific experiment
606. PMC 1112637. PMID 9518917. Jain SL (2010). "The mortality effect: counting the dead in the cancer trial" (PDF). Public Culture. 21 (1): 89–117. doi:10
Randomized_controlled_trial
Number whose square is a given number
squares. (See square root of 2 for proofs that this is an irrational number, and quadratic irrational for a proof for all non-square natural numbers.)
Square_root
Interplay between observation, experiment, and theory in science
proofs from such a system were tautological, i.e. internally logically true, by rewriting forms, as shown by Poincaré, who demonstrated the technique
Scientific_method
Form of incorrect argument in natural language
reflecting their criticism back onto them. This move shifts the burden of proof back to the opponent, thereby strengthening one's own position. But it still
Informal_fallacy
Product of numbers from 1 to n
count the permutations of n {\displaystyle n} grouped into subsets with the same numbers of cycles. Another combinatorial application is in counting derangements
Factorial
as 2012 this technique had been applied to solar panels on spacecraft. In 1986, Messer reported a construction by which one could double the cube, which
Mathematics_of_paper_folding
Roman god
doorways, passages, frames, and endings. He is usually depicted as having a double-sided head. The month of January is named for Janus (Ianuarius). According
Janus
Assumption of a single cause where multiple factors may be necessary
evidence Sampling bias Cherry picking McNamara Base rate / Conjunction Double counting False analogy Slothful induction Overwhelming exception Muhammad Wang
Fallacy_of_the_single_cause
Fallacious argument exploiting connection to nationalism
Flag-waving is a fallacious argument or propaganda technique used to justify an action based on the undue connection to nationalism or patriotism or benefit
Flag-waving
he misbehaves, in which case Thorfinn will throw him back into the ghost-proof vault. Meanwhile, Jay walks through Flower and cooks a chicken dish that
List of Ghosts (American TV series) episodes
List_of_Ghosts_(American_TV_series)_episodes
Discredited communication technique in disabled care
scientifically discredited technique that claims to allow non-verbal people, such as those with autism, to communicate. The technique involves a facilitator
Facilitated_communication
Cognitive bias of experimental subject
experimenters gave subtle but clear cues with which the subjects complied. Double blind techniques may be employed to combat bias by causing the experimenter and
Observer-expectancy_effect
1932 pinball machine
completed the player then counts their score by adding up all scoring holes that contain balls, with the yellow/gold ball double the point value of the hole
Five_Star_Final_(pinball)
Computer security exploit
Row Refresh". arXiv:2004.01807 [cs.CR]. "Introducing Half-Double: New hammering technique for DRAM Rowhammer bug". Google. May 25, 2021. Retrieved December
Row_hammer
Unlawful killing of a human with malice
interpreted by the Supreme Court of California in 1994 as not requiring any proof of the viability of the fetus as a prerequisite to a murder conviction.
Murder
Common ancestor evolutionary evidence
evolutionary relatedness. It has also led to the development of molecular clock techniques to date taxon divergence times and to calibrate these with the fossil
Evidence_of_common_descent
Italian semi-automatic pistol
discovered in an investigation that the slides had passed high-pressure proof testing and magnetic particle inspection when they were made, and metallurgical
Beretta_92
avoiding instability and numerical overflow Approximate counting algorithm: allows counting large number of events in a small register Bayesian statistics
List_of_algorithms
Technique in graph theory
homomorphism flavored proof to Mantel's Theorem. This proof is an adaptation on the traditional proof of Mantel via double counting, except phrased in terms
Flag_algebra
Mom' Wins Night, + 'Rizzoli & Isles', 'Storage Wars', 'Hardcore Pawn', 'Counting Cars', 'How Jaws Changed the World' & More". TV by the Numbers. Archived
List of Rizzoli & Isles episodes
List_of_Rizzoli_&_Isles_episodes
Numbers obtained by adding the two previous ones
Fibonacci numbers include computer algorithms such as the Fibonacci search technique and the Fibonacci heap data structure, and graphs called Fibonacci cubes
Fibonacci_sequence
President of the United States from 2001 to 2009
Anthony S.; Eisinger, Robert W. (January 25, 2018). "PEPFAR — 15 Years and Counting the Lives Saved". New England Journal of Medicine. 378 (4): 314–316. doi:10
George_W._Bush
Gene editing method
regularly interspaced short palindromic repeats") is a genetic engineering technique in molecular biology by which the genomes of living organisms may be modified
CRISPR_gene_editing
Number
the techniques to add, subtract, multiply, and divide numbers, containing zero values in a decimal power, on counting devices, that include counting rods
0
Cryptocurrency
against government policies. In December 2018, Zcoin implemented Merkle tree proof, a mining algorithm that deters the usage of Application-specific integrated
Firo_(cryptocurrency)
through it quickly in a specific direction. See auto belay. abseiling A technique by which a climber descends via a fixed rope that is firmly attached to
Glossary_of_climbing_terms
Playing of contract bridge with computer software
Efficient double-dummy solvers are key to successful bridge-playing programs. Also, as the amount of computation increases with sample size, techniques such
Computer_bridge
offered a failsafe should one fail to ignite. SN10 underwent a cryogenic proof test on February 8, 2021, followed by a static fire on February 23. After
List_of_Starship_vehicles
2008 death of an American toddler in Orlando, Florida, U.S.
jurors it could be used to impeach George's credibility, but it was not proof of how Caylee died, nor evidence of Casey's guilt or innocence. By the time
Death_of_Caylee_Anthony
Informal fallacy and propaganda strategy
criticism, which may or may not be justified. Common accusations include double standards, and hypocrisy, but it can also be used to relativize criticism
Whataboutism
hackers. An article in the Süddeutsche Zeitung discussed the difficulty of proof in matters of cybersecurity. One analyst told the Süddeutsche Zeitung that
Russian interference in the 2016 United States elections
Russian_interference_in_the_2016_United_States_elections
Concept in theoretical computer science
and many techniques used for finding busy beavers (which they apply to Turing Machines with 4-states and 2-symbols, thus verifying Brady's proof). They
Busy_beaver
Relation between algebraic varieties and polynomial ideals
Brownawell's proof relied on analytic techniques valid only in characteristic 0, but, one year later, János Kollár gave a purely algebraic proof, valid in
Hilbert's_Nullstellensatz
Informal fallacy
Techniques". Persuasive Messages. Boston University School of Public Health. Retrieved 23 May 2019. Special Pleading: committed by applying a double standard
Special_pleading
Catalan architect (1852–1926)
new techniques in the treatment of materials, such as trencadís which used waste ceramic pieces. Influenced by neo-Gothic art and Oriental techniques, Gaudí
Antoni_Gaudí
2020. Retrieved July 31, 2024. "Trump's mixed message: Stop the count or keep counting?". Los Angeles Times. November 5, 2020. Archived from the original
Attempts to overturn the 2020 United States presidential election
Attempts_to_overturn_the_2020_United_States_presidential_election
Particular kind of exponential sum
Kuznetsov using the spectral theory of modular forms. Nowadays elementary proofs of this identity are known. For p an odd prime, there are no known simple
Kloosterman_sum
June 21, 2024. Sagon, Candy (April 13, 2005). "Twinkies, 75 Years and Counting". The Washington Post. Archived from the original on June 28, 2011. Retrieved
List of common misconceptions about arts and culture
List_of_common_misconceptions_about_arts_and_culture
American singer-songwriter (1950–2020)
1973, on which he played every instrument and pioneered home recording techniques. He was nicknamed the "One-Man Beatles" due to his musical and vocal style
Emitt_Rhodes
American mixed martial artist (born 1987)
diverse kicking technique, favoring front kicks to the body and head, roundhouse kicks to the legs and upper body, and his most known technique, the "oblique
Jon_Jones
meaning which still persists in medicine. Because such pebbles were used for counting out distances, tallying votes, and doing abacus arithmetic, the word came
History_of_calculus
French actor (1935–2024)
Tokyo, the Institut Français du Japon organizes a retrospective titled Proof of a Star's Existence, featuring screenings of his major works, conferences
Alain_Delon
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
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