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Thompson replacement theorem is a theorem about the existence of certain abelian subgroups of a p-group. The Glauberman replacement theorem is a generalization
Replacement_theorem
Relation between sides of a right triangle
In mathematics, the Pythagorean theorem or Pythagoras's theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle
Pythagorean_theorem
Algebraic expansion of powers of a binomial
algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial. According to the theorem, the power ( x
Binomial_theorem
About simultaneous modular congruences
In mathematics, the Chinese remainder theorem states that if one knows the remainders of the Euclidean division of an integer n by several integers, then
Chinese_remainder_theorem
Subfield of automated reasoning and mathematical logic
and the replacement of formulas by their definition. The system used heuristic guidance, and managed to prove 38 of the first 52 theorems of the Principia
Automated_theorem_proving
Theorem in economics
Coase theorem (/ˈkoʊs/) postulates the economic efficiency of an economic allocation or outcome in the presence of externalities. The theorem is significant
Coase_theorem
ISBN 978-0-8284-0301-6, MR 0569209 Thompson, John G. (1969), "A replacement theorem for p-groups and a conjecture", Journal of Algebra, 13 (2): 149–151
ZJ_theorem
Equation for radii of tangent circles
In geometry, Descartes' theorem states that for every four kissing, or mutually tangent circles, the radii of the circles satisfy a certain quadratic
Descartes'_theorem
Relates the 4 sides and 2 diagonals of a quadrilateral with vertices on a common circle
In Euclidean geometry, Ptolemy's theorem is a relation between the four sides and two diagonals of a cyclic quadrilateral (a quadrilateral whose vertices
Ptolemy's_theorem
Theorem in descriptive set theory
that any proof of the theorem in Zermelo–Fraenkel set theory must make repeated use of instances of the axiom schema of replacement. Later results showed
Borel_determinacy_theorem
Theorem in electrical circuit analysis
stated in terms of direct-current resistive circuits only, Thévenin's theorem states that "Any linear electrical network containing only voltage sources
Thévenin's_theorem
Complements of perfect graphs are perfect
In graph theory, the perfect graph theorem of László Lovász (1972a, 1972b) states that an undirected graph is perfect if and only if its complement graph
Perfect_graph_theorem
Concept in set theory
] {\displaystyle F[A]} . The axiom schema of replacement is not necessary for the proofs of most theorems of ordinary mathematics. Indeed, Zermelo set
Axiom_schema_of_replacement
Standard system of axiomatic set theory
proved within the theory itself, as shown by Gödel's second incompleteness theorem. The modern study of set theory was initiated by Georg Cantor and Richard
Zermelo–Fraenkel_set_theory
Propositional logic theorem
it is disallowed by intuitionistic logic. The principle was stated as a theorem of propositional logic by Russell and Whitehead in Principia Mathematica
Double_negation
Mathematical theorem
In mathematics, the transfinite recursion theorem says a function can be defined using a recursion over a well-ordered set; for example, N {\displaystyle
Transfinite_recursion_theorem
German logician and mathematician (1871–1953)
Zermelo–Fraenkel axiomatic set theory and his proof of the well-ordering theorem. Furthermore, his 1929 work on ranking chess players is the first description
Ernst_Zermelo
System of mathematical set theory
extended version of the class existence theorem implies the existence of these classes. The axioms of replacement, union, and power set imply that when
Von Neumann–Bernays–Gödel set theory
Von_Neumann–Bernays–Gödel_set_theory
Decomposition of an algebraic structure
Nevertheless, a group of results known under the general name Jordan–Hölder theorem asserts that whenever composition series exist, the isomorphism classes
Composition_series
Number divisible only by 1 and itself
than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself
Prime_number
On graphs with given symmetry groups
Frucht's theorem is a result in algebraic graph theory, conjectured by Dénes Kőnig in 1936 and proved by Robert Frucht in 1939. It states that every finite
Frucht's_theorem
Every set is smaller than its power set
question marks, boxes, or other symbols. In mathematical set theory, Cantor's theorem is a fundamental result which states that, for any set A {\displaystyle
Cantor's_theorem
Fixed-point theorem for smooth manifolds
which appears in the original Lefschetz fixed-point theorem. The idea is to find the correct replacement for the Lefschetz number, which in the classical
Atiyah–Bott fixed-point theorem
Atiyah–Bott_fixed-point_theorem
Theorem in set theory
In set theory, the Schröder–Bernstein theorem states that, if there exist injective functions f : A → B and g : B → A between the sets A and B, then there
Schröder–Bernstein_theorem
Method of deriving conclusions
inferential steps and often use various rules of inference to establish the theorem they intend to demonstrate. Rules of inference are definitory rules—rules
Rule_of_inference
Theorem in transfinite set theory
In set theory, a branch of mathematics, Kunen's inconsistency theorem, proved by Kenneth Kunen (1971), shows that several plausible large cardinal axioms
Kunen's_inconsistency_theorem
Type of logical system
to analysis in proof theory, such as the Löwenheim–Skolem theorem and the compactness theorem. First-order logic is the standard for the formalization
First-order_logic
1016/0021-8693(64)90006-7, ISSN 0021-8693, MR 0167521 Thompson, John G. (1969), "A replacement theorem for p-groups and a conjecture", Journal of Algebra, 13: 149–151,
Thompson_subgroup
Theorem about inclusions between Sobolev spaces
prove the Sobolev embedding theorem, giving inclusions between certain Sobolev spaces, and the Rellich–Kondrachov theorem showing that under slightly
Sobolev_inequality
Economic theorem
The Henry George theorem (HGT) states that under certain conditions, aggregate spending by government on public goods will increase aggregate rent based
Henry_George_theorem
Graph-theoretic description of polyhedra
In polyhedral combinatorics, a branch of mathematics, Steinitz's theorem is a characterization of the undirected graphs formed by the edges and vertices
Steinitz's_theorem
Continuous mappings can be approximated by ones that are piecewise simple
(ii) replacement of the actual mapping by a homotopic one. This theorem was first proved by L.E.J. Brouwer, by use of the Lebesgue covering theorem (a result
Simplicial approximation theorem
Simplicial_approximation_theorem
Theorem in Lie representation theory
algebra, then this conclusion does not follow (i.e. the naïve replacement in Lie's theorem of "solvable" with "nilpotent", and "upper triangular" with "strictly
Engel's_theorem
Topics referred to by the same term
replacement therapy Randomized response technique Rational root theorem in mathematics Refugee Review Tribunal in Australia. Recommended Replacement Time
RRT
Possible axiom of set theory
Vκ satisfies: Theorem 1. A class X is a set if and only if |X| < κ. Theorem 2. |Vκ| = κ. Since every class is a subset of Vκ, Theorem 2 implies that
Axiom_of_limitation_of_size
maximality theorem Well-ordering theorem Zorn's lemma Axiom of global choice Axiom of countable choice Axiom of dependent choice Boolean prime ideal theorem Axiom
List_of_axioms
In mathematical set theory, Zermelo's categoricity theorem was proven by Ernst Zermelo in 1930. It states that all models of a certain second-order version
Zermelo's categoricity theorem
Zermelo's_categoricity_theorem
German mathematician (1862–1943)
Hilbert–Burch theorem Hilbert's irreducibility theorem Hilbert's Nullstellensatz Hilbert's theorem (differential geometry) Hilbert's Theorem 90 Hilbert's
David_Hilbert
Algebraic structure
on 2011-08-07, retrieved 2013-02-06 Thompson, John G. (1969), "A replacement theorem for p-groups and a conjecture", Journal of Algebra, 13 (2): 149–151
P-stable_group
Mathematical concept for comparing objects
the following three connected theorems hold: ~ partitions A into equivalence classes. (This is the Fundamental Theorem of Equivalence Relations, mentioned
Equivalence_relation
Branch of probability theory
still functional at a cost of €200. What is his optimal replacement policy? Campbell's theorem (probability) Compound Poisson process Continuous-time Markov
Renewal_theory
Size of a possibly infinite set
cannot happen with proper subsets of finite sets. However, a fundamental theorem due to Georg Cantor shows that it is possible for two infinite sets to
Cardinal_number
System of formal mathematical logic
constrained to have the same value in both after the replacement is done. The Deduction Theorem for Q0 shows that proofs from hypotheses using Rule R′
Q0_(mathematical_logic)
Mathematical logician and philosopher
theorem in 1929 as part of his dissertation to earn a doctorate at the University of Vienna, and the publication of Gödel's incompleteness theorems two
Kurt_Gödel
Formula of matrix exponentials
exponential of A. The Lie–Trotter product formula and the Trotter–Kato theorem extend this to certain unbounded linear operators A and B. This formula
Lie_product_formula
Economic theorem regarding rate of profit
Okishio's theorem is a theorem formulated by Japanese economist Nobuo Okishio. It has had a major impact on debates about Marx's theory of value. Intuitively
Okishio's_theorem
Axiom of set theory
by Ernst Zermelo in order to formalize his proof of the well-ordering theorem. In many cases, a set created by choosing elements can be made without
Axiom_of_choice
Pair of logical equivalences
logic and Boolean algebra, De Morgan's laws, also known as De Morgan's theorem, are a pair of transformation rules that are both valid rules of inference
De_Morgan's_laws
French mathematician (1789–1857)
physicist. He was one of the first to rigorously state and prove the key theorems of calculus (thereby creating real analysis), pioneered the field complex
Augustin-Louis_Cauchy
Paradox in set theory
already realized that his theory would lead to a contradiction (to Cantor's theorem), as he told Hilbert and Richard Dedekind by letter. Hilbert also formulated
Russell's_paradox
Certain kind of cardinal number in set theory
to convert this well-ordered set to its von Neumann ordinal. Hartogs's theorem states that for any set X, there exists an ordinal α such that | α | ≰
Hartogs_number
Function defined by a hypergeometric series
z = −1 to z = 1 and then using Gauss's theorem to evaluate the result. A typical example is Kummer's theorem, named for Ernst Kummer: 2 F 1 ( a , b ;
Hypergeometric_function
Axiom of Set Theory
empty set is a theorem. If separation is not postulated as an axiom schema but derived as a theorem schema from the schema of replacement (as is sometimes
Axiom_of_empty_set
Theorem equivalent to the Axiom of Choice
In mathematics, Tarski's theorem, proved by Alfred Tarski (1924), states that in ZF the statement "For every infinite set A {\displaystyle A} , there
Tarski's_theorem_about_choice
Template that specifies one or more axioms
conditions saying how those placeholders may be replaced; each permitted replacement is an instance of the schema. Axiom schemata are commonly used to give
Axiom_schema
Grouping of candidates for election
this person may choose to cede the place to a lower-ranked colleague. Replacement lists are sometimes used to fill casual vacancies in single transferable
Electoral_list
Branch of mathematics that studies sets
separation and replacement. Sets and proper classes. These include Von Neumann–Bernays–Gödel set theory, which has the same strength as ZFC for theorems about
Set_theory
Branch of mathematics
more abstract approach makes much sense, because one can derive numerous theorems in the general setting, without focusing on the details of any particular
Order_theory
German polymath and scholar (1777–1855)
Gauss produced the second and third complete proofs of the fundamental theorem of algebra. He also introduced the triple bar symbol (≡) for congruence
Carl_Friedrich_Gauss
Statistical method
Glivenko–Cantelli theorem provides theoretical background for the bootstrap method. Finite populations and drawing without replacement require adaptations
Bootstrapping_(statistics)
Plurality voting system
Impossibility theorems Arrow's theorem Majority impossibility Moulin's impossibility theorem McKelvey–Schofield chaos theorem Gibbard's theorem Positive results
First-past-the-post_voting
Mathematician (1845–1918)
more numerous than the natural numbers. Cantor's method of proof of this theorem implies the existence of an infinity of infinities. He defined the cardinal
Georg_Cantor
Mathematical set containing all objects
sets, provided that both exist. However, this conflicts with Cantor's theorem that the power set of any set (whether infinite or not) always has strictly
Universal_set
French mathematician and politician (born 1973)
Institution, the first titled 'Birth of a Theorem'. The English translation of his book Théorème vivant (Living Theorem) has the same title. In the book he
Cédric_Villani
Concept in axiomatic set theory
if and only if it belongs to some class E. In this theory, there is a theorem schema that reads ∃ D ∀ C ( [ C ∈ D ] ⟺ [ P ( C ) ∧ ∃ E ( C ∈ E ) ] )
Axiom_schema_of_specification
Hungarian and American mathematician and physicist (1903–1957)
the application of this work was instrumental in his mean ergodic theorem. The theorem is about arbitrary one-parameter unitary groups t → V t {\displaystyle
John_von_Neumann
Large cardinal number
Vθ ≺Σn Vκ. By Zermelo's categoricity theorem, every inaccessible cardinal is worldly. By Shepherdson's theorem, inaccessibility is equivalent to the
Worldly_cardinal
German mathematician (1831–1916)
numbers, devised as part of Kummer's 1843 attempt to prove Fermat's Last Theorem. (Thus Dedekind can be said to have been Kummer's most important disciple
Richard_Dedekind
Probabilistic inequality applying on sum of bounded random variables
⋯ + X n . {\displaystyle S_{n}=X_{1}+\cdots +X_{n}.} Then Hoeffding's theorem states that, for all t > 0, P ( S n − E [ S n ] ≥ t ) ≤ exp ( − 2 t
Hoeffding's_inequality
Probability of shared birthdays
Birthday Problem, Ramanujan Journal, 2012, [1]. Brink 2012, Theorem 2 Brink 2012, Theorem 3 Brink 2012, Table 3, Conjecture 1 "Minimal number of people
Birthday_problem
Set of all things that may be the input of a mathematical function
Logical consequence Model Theorem Theory Type theory Theorems (list), paradoxes Gödel's completeness – incompleteness theorems Tarski's undefinability Banach–Tarski
Domain_of_a_function
Probability distribution
sample of size n drawn with replacement from a population of size N. If the sampling is carried out without replacement, the draws are not independent
Binomial_distribution
Cognitive bias
change is very orderly, and usually proportional to the numbers of Bayes' theorem – but it is insufficient in amount". In other words, people update their
Conservatism (belief revision)
Conservatism_(belief_revision)
Proof by Alan Turing
to the Entscheidungsproblem". It was the second proof (after Church's theorem) of the negation of Hilbert's Entscheidungsproblem; that is, the conjecture
Turing's_proof
Problem of determining if a Boolean formula could be made true
first problem that was proven to be NP-complete—this is the Cook–Levin theorem. This means that all problems in the complexity class NP, which includes
Boolean satisfiability problem
Boolean_satisfiability_problem
Mathematical treatise by Euclid
These include the Pythagorean theorem, Thales' theorem, the Euclidean algorithm for greatest common divisors, Euclid's theorem that there are infinitely many
Euclid's_Elements
Mathematical set of all subsets of a set
power set must be larger than the original set). In particular, Cantor's theorem shows that the power set of a countably infinite set is uncountably infinite
Power_set
Process of repeating items in a self-similar way
of Replacement", pp.50--52. Bulletin of Symbolic Logic, vol. 18, no. 1 (2012). Accessed 21 August 2023. Math 310 Class Notes 5: The Recursion Theorem for
Recursion
Mathematical set containing no elements
Logical consequence Model Theorem Theory Type theory Theorems (list), paradoxes Gödel's completeness – incompleteness theorems Tarski's undefinability Banach–Tarski
Empty_set
Axiomatic set theories based on the principles of mathematical constructivism
reformulations of classical theorems. For example, in constructive analysis, one cannot prove the intermediate value theorem in its textbook formulation
Constructive_set_theory
Selection of data points in statistics
the sampling error with probability 1000/1001. His estimates used Bayes' theorem with a uniform prior probability and assumed that his sample was random
Sampling_(statistics)
Proof in set theory
a wide range of proofs, including the first of Gödel's incompleteness theorems and Turing's answer to the Entscheidungsproblem. Diagonalization arguments
Cantor's_diagonal_argument
Statistical property
variance needs to be computed according to the Markov chain central limit theorem. There are cases when a sample is taken without knowing, in advance, how
Standard_error
Generalization of "n-th" to infinite cases
canonical abstractions of these well-ordered structures. A fundamental theorem in set theory establishes that any two well-ordered sets are comparable:
Ordinal_number
Subfield of set theory
This fact—that all closed games are determined—is called the Gale–Stewart theorem. Note that by symmetry, all open games are determined as well. (A game
Determinacy
Set with exactly one element
size Pairing Power set Regularity Union Martin's axiom Axiom schema replacement specification Operations Cartesian product Complement (i.e. set difference)
Singleton_(mathematics)
Subfield of mathematics
mathematics can be formalized in terms of sets, although there are some theorems that cannot be proven in common axiom systems for set theory. Contemporary
Mathematical_logic
Persian polymath and poet (1048–1131)
importance of a general binomial theorem. The argument supporting the claim that Khayyam had a general binomial theorem is based on his ability to extract
Omar_Khayyam
Bijective correspondence in mathematics
i} of Q. Identify subsequences of π with their sets of indices. It is a theorem of Greene that for any k ≥ 1, the size of the largest set that can be written
Robinson–Schensted correspondence
Robinson–Schensted_correspondence
Mathematical concept
extension of mathematical induction to ordinal numbers. Its correctness is a theorem of ZF, and relies on the fact that the ordinal numbers are well-ordered
Transfinite_induction
Result in mathematics and set theory
the Shepherdson–Mostowski collapse, is a theorem of set theory introduced by Andrzej Mostowski (1949, theorem 3) and John Shepherdson (1953). Suppose that
Mostowski_collapse_lemma
German-born mathematics educator (1928–2021)
Oregon in Eugene, Oregon. There is a theorem named after her, called Marion Walter's Theorem or just Marion's Theorem as it is affectionately known. Marion
Marion_Walter
Proposition in mathematical logic
choice. Cantor initially presented the weak continuum hypothesis as a theorem, but did not give a proof and later became uncertain of it. On 25 October
Continuum_hypothesis
Axiom of set theory
may also be used as an alternative to choice in the proof of Frucht's theorem for infinite groups. Naive set theory (the axiom schema of unrestricted
Axiom_of_regularity
Commonly used rules of replacement in propositional logic
metalogical symbol representing "can be replaced in a logical proof with". Theorems are those logical formulas ϕ {\displaystyle \phi } where ⊢ ϕ {\displaystyle
Tautology_(rule_of_inference)
Bug in the Intel P5 Pentium floating-point unit
report, Intel said it incurred "a $475 million pretax charge ... to cover replacement and write-off of these microprocessors." In order to improve the speed
Pentium_FDIV_bug
Mathematical logic concept
Bayes' theorem represents a generalization of both contraposition and Bayes' theorem. Contraposition represents an instance of Bayes' theorem which in
Contraposition
Particular class of sets which can be described entirely in terms of simpler sets
basic axioms of set theory, if ZF itself is consistent. Since many other theorems only hold in systems in which one or both of the propositions is true,
Constructible_universe
Law stating that bone adapts to mechanical loading
Refinement of Wolff's Law: Utah-Paradigm of Bone physiology (Mechanostat Theorem) by Harold Frost. The racquet-holding arm bones of tennis players become
Wolff's_law
Finite ordered list of elements
size Pairing Power set Regularity Union Martin's axiom Axiom schema replacement specification Operations Cartesian product Complement (i.e. set difference)
Tuple
REPLACEMENT THEOREM
REPLACEMENT THEOREM
Boy/Male
Indian
Replacement
Girl/Female
Muslim
Replacement (The daughter of Hazrat Ali)
Surname or Lastname
English and Irish
English and Irish : (of Norman origin): habitational name from a metathesized form of Plouquenet in Ille-et-Villaine, Brittany, so named from Breton plou ‘parish’ (from Latin plebs ‘people’) + Guenec, the personal name (a diminutive of guen ‘white’) of a somewhat obscure saint. As an Irish name, it has been Gaelicized as Pluincéid.English and Irish : alternatively, it may be a metonymic occupational name for a maker or seller of blankets, from Middle English blaunket (Anglo-Norman French blancquet, a diminutive of blanc ‘white’), but replacement of b by p is not usual in English.
Boy/Male
Muslim
Replacement
Girl/Female
Indian
Replacement (The daughter of Hazrat Ali)
Surname or Lastname
English
English : from the medieval personal name Han(n), which is usually a short form of Johan (see John). In some cases, however, it may be from Henry and even Randolph (for the replacement of R- by H- in Germanic names introduced by the Normans, compare Hick).German : from an aphetic form of the personal name Johann (see John).
Surname or Lastname
English
English : occupational name for someone who looked after animals, Middle English bester, from beste ‘beast’ (see Best).German : habitational name for someone from a place called Beste.Slovenian (Gorenjska; also Bešter) : probably a derivative of Vester 3, a reduced form of the personal name Silvester. Replacement of initial V- with B- is quite common in Slovenian surnames.
REPLACEMENT THEOREM
REPLACEMENT THEOREM
Boy/Male
Egyptian
Root.
Girl/Female
Biblical
Destroying, wearing out.
Boy/Male
Hebrew
Goodness of God.
Surname or Lastname
English
English : patronymic from Good.
Girl/Female
Hindu, Indian, Sindhi, Tamil
Goddess Parvati
Boy/Male
Tamil
Boy/Male
Italian
Resolute protector.
Girl/Female
Muslim
Wisdom
Boy/Male
Hindu, Indian
God of the Earth
Girl/Female
Arabic, Muslim
Bird (Toucan)
REPLACEMENT THEOREM
REPLACEMENT THEOREM
REPLACEMENT THEOREM
REPLACEMENT THEOREM
REPLACEMENT THEOREM
n.
The removal of an edge or an angle by one or more planes.
n.
The act of placing, or the state of being placed.
n.
The act of replacing.
n.
The replacement of an edge by two similar planes, equally inclined to the including faces or adjacent planes.
n.
A white crystalline solid, from ammonia by replacement of an equivalent of hydrogen by acetyl.
n.
One of a class of strongly basic substances derived from ammonia by replacement of one or more hydrogen atoms by a basic atom or radical.
a.
Capable of neutralizing four molecules of a monobasic acid; having four hydrogen atoms capable of replacement ba acids or acid atoms; -- said of certain bases; thus, erythrine, C4H6(OH)4, is a tetracid alcohol.
a.
Capable of neutralizing three molecules of a monacid base, or their equivalent; having three hydrogen atoms capable of replacement by basic elements on radicals; -- said of certain acids; thus, citric acid is a tribasic acid.
n.
A compound derived from ethyl alcohol by the replacement of the hydroxyl hydrogen, after the manner of a hydrate; an ethyl alcoholate; as, potassium ethylate, C2H5.O.K.
a.
Having two acid hydrogen atoms capable of replacement by basic atoms or radicals, in forming salts; bibasic; -- said of acids, as oxalic or sulphuric acids. Cf. Diacid, Bibasic.
n.
Position; place.
a.
Containing substitutions or replacements; having been subjected to the process of substitution, or having some of its parts replaced; as, alcohol is a substituted water; methyl amine is a substituted ammonia.
a.
Illustrating, possessing, or characterized by, some quality or property in the first degree; having undergone the first stage of substitution or replacement.
a.
Of or pertaining to the replacement of bone; as, an osteoplastic operation.
n.
A glyceride formed by the replacement of three hydrogen atoms in glycerin by acid radicals.
n.
The replacement of an edge or solid angle by a plane, especially when the plane is equally inclined to the adjoining faces.
a.
Capable of neutralizing four molecules of a monacid base; having four hydrogen atoms capable of replacement by bases; quadribasic; -- said of certain acids; thus, normal silicic acid, Si(OH)4, is a tetrabasic acid.
n.
The act of enlacing, or state of being enlaced; a surrounding as with a lace.
n.
Exchange; replacement; substitution; metathesis.
n.
One of a series of compounds, derived from hydrogen sulphide by the replacement of half its hydrogen by a base or basic radical; as, potassium hydrosulphide, KSH. The hydrosulphides are analogous to the hydrates and include the mercaptans.