• In single-variable differential calculus, the fundamental increment lemma is an immediate consequence of the definition of the derivative f ′ ( a ) {\textstyle...
    3 KB (583 words) - 15:12, 27 December 2024
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    formulation of the higher-dimensional derivative is provided by the fundamental increment lemma found in single-variable calculus. If all the partial derivatives...
    13 KB (1,884 words) - 01:18, 9 June 2025
  • containing 1". Hensel's lemma is fundamental in p-adic analysis, a branch of analytic number theory. The proof of Hensel's lemma is constructive, and leads...
    42 KB (9,044 words) - 20:58, 24 May 2025
  • or the calculus of discrete functions, is the mathematical study of incremental change, in the same way that geometry is the study of shape and algebra...
    39 KB (6,577 words) - 14:32, 2 June 2025
  • of equations List of fundamental theorems List of hypotheses List of inequalities Lists of integrals List of laws List of lemmas List of limits List of...
    78 KB (6,296 words) - 20:31, 6 July 2025
  • may be Lebesgue integrable, but the integral of f ′ differs from the increment of f (how much f changes over an interval). This happens for example with...
    19 KB (2,685 words) - 08:58, 28 May 2025
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    1007/978-0-8176-4789-6_14, ISBN 978-0-8176-4788-9, MR 2777924; see proof of Lemma 5, p. 361 Archived 2022-01-08 at the Wayback Machine Read, Ronald C. (1968)...
    30 KB (3,443 words) - 23:25, 29 June 2025
  • Thumbnail for Laplace's equation
    _{y}=\varphi _{x}.} This relation does not determine ψ, but only its increments: d ψ = − φ y d x + φ x d y . {\displaystyle d\psi =-\varphi _{y}\,dx+\varphi...
    33 KB (5,075 words) - 15:19, 13 April 2025
  • Thumbnail for Fermat's Last Theorem
    descent contained a major gap. However, since Euler himself had proved the lemma necessary to complete the proof in other work, he is generally credited...
    103 KB (11,700 words) - 20:03, 9 July 2025
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    known as prime factorization. A fundamental property of primes is shown in Euclid's lemma. It is a consequence of the lemma that if a prime divides a product...
    81 KB (9,977 words) - 15:36, 28 June 2025
  • Thumbnail for Taylor series
    differentiable function defined on the real line, a consequence of Borel's lemma. As a result, the radius of convergence of a Taylor series can be zero....
    48 KB (8,229 words) - 17:42, 2 July 2025
  • when the limits of integration are in the opposite order (b < a), the increment dx is negative in the direction of integration. More generally, an m-form...
    67 KB (10,058 words) - 14:15, 26 June 2025
  • logical systems that deviate from classical logic. diagonalization lemma A lemma used in the proof of Gödel's incompleteness theorems, stating that for...
    271 KB (30,237 words) - 15:11, 3 July 2025
  • Thumbnail for History of mathematics
    program has progressed significantly, and there have been proofs of the fundamental lemma (2008), as well as a proposed proof of the geometric Langlands correspondence...
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  • has been studied, including Lévy processes, stochastic networks (Kelly's lemma), birth and death processes, Markov chains, and piecewise deterministic...
    8 KB (1,062 words) - 04:49, 22 June 2025
  • reductions produce zero. The algorithm terminates always because of Dickson's lemma or because polynomial rings are Noetherian (Hilbert's basis theorem). Condition...
    63 KB (10,037 words) - 22:27, 19 June 2025
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    honours and reputations. Some are Kitaw Ejigu, Mulugeta Bekele, Aklilu Lemma, Gebisa Ejeta and Melaku Worede. Computer scientist Timnit Gebru, named...
    229 KB (22,340 words) - 22:19, 9 July 2025
  • algebraic systems. The first theorem given in the text, Euclid's lemma, captures a fundamental property of prime numbers. The text was ubiquitous in the quadrivium...
    98 KB (11,251 words) - 14:26, 22 June 2025
  • does not consider the possibility of the surface deforming as it moves. Lemma. One has: ∂ ∂ b ( ∫ a b f ( x ) d x ) = f ( b ) , ∂ ∂ a ( ∫ a b f ( x )...
    53 KB (11,253 words) - 03:22, 22 June 2025
  • explicit NULL test). As an example of the use of pairs, the shift-and-increment function that maps (m, n) to (n, n + 1) can be defined as Φ := λx.PAIR...
    90 KB (12,115 words) - 02:49, 7 July 2025
  • of y = f ( x ) {\displaystyle y=f(x)} as follows: an infinitely small increment α {\displaystyle \alpha } of the independent variable x always produces...
    63 KB (9,324 words) - 15:49, 8 July 2025
  • K_{t+1}} , is K t + I t − D t {\displaystyle K_{t}+I_{t}-D_{t}} . The net increment to the capital stock is the difference between gross investment and depreciation...
    229 KB (25,481 words) - 21:54, 19 June 2025
  • Thumbnail for Hyperreal number
    ultrafilters that do not contain any finite sets. (The good news is that Zorn's lemma guarantees the existence of many such U; the bad news is that they cannot...
    33 KB (4,924 words) - 08:45, 23 June 2025
  • Thumbnail for Path integral formulation
    defined, the easiest way is to add a small imaginary part to the time increment ε. This is closely related to Wick rotation. Then the same convolution...
    86 KB (14,277 words) - 08:57, 19 May 2025
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    God to the final Islamic prophet Muhammad through the angel Gabriel incrementally over a period of some 23 years, beginning on the Laylat al-Qadr, when...
    198 KB (22,507 words) - 20:43, 25 June 2025
  • ^{T}\mathbf {B} } is nonsingular, the following results can be obtained: Lemma—If 0 < μ < 2 λ 0 {\textstyle 0<\mu <{\frac {2}{\lambda _{0}}}} , where λ...
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    relativity or general relativity. Astronomy portal Canonical coordinates Fundamental lemma of the calculus of variations Functional derivative Generalized coordinates...
    96 KB (15,276 words) - 06:38, 28 June 2025
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    Barn Cases Ichikawa & Steup 2018, § 3. The Gettier Problem, § 4. No False Lemmas, § 5. Modal Conditions, § 6. Doing Without Justification? Steup & Neta 2020...
    187 KB (19,036 words) - 06:23, 7 July 2025
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    Charles University. p. 1. Archived from the original (PDF) on 2013-11-02. Lemma 1.1 (iv). This source refers to asymmetric relations as "strictly antisymmetric"...
    62 KB (8,757 words) - 16:57, 9 July 2025
  • bi-variate polynomial Q ( x , y ) {\displaystyle Q(x,y)} which results in the increment of constraints along with the number of roots. A bi-variate polynomial...
    16 KB (3,701 words) - 19:32, 3 March 2022