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**There is a page named "Theorem on formal functions" on Wikipedia**

- In algebraic geometry, the theorem on formal functions states the following: Let f : X → S {\displaystyle f:X\to S} be a proper morphism of noetherian...4 KB (916 words) - 13:53, 29 July 2022
- formal functions, which is used to deduce theorems of interest for usual schemes. A locally Noetherian scheme is a locally Noetherian formal scheme in...6 KB (1,031 words) - 01:35, 27 April 2024
- mathematics, and in formal semantics. Informally, the theorem states that "arithmetical truth cannot be defined in arithmetic". The theorem applies more generally...16 KB (2,252 words) - 19:21, 23 March 2024
- is empty, then the last sentence in a formal proof is called a theorem of the formal system. The notion of theorem is generally effective, but there may...5 KB (579 words) - 05:11, 29 July 2024
- Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories. These...92 KB (12,121 words) - 07:36, 1 November 2024
- inversion theorem, also known as the Lagrange–Bürmann formula, gives the Taylor series expansion of the inverse function of an analytic function. Lagrange...13 KB (2,439 words) - 02:13, 4 November 2024
- (see above), abstract interpretation, automated theorem proving, type systems, and lightweight formal methods. A promising type-based verification approach...17 KB (1,811 words) - 07:58, 6 October 2024
- analysis, the residue theorem, sometimes called Cauchy's residue theorem, is a powerful tool to evaluate line integrals of analytic functions over closed curves;...13 KB (3,282 words) - 17:30, 14 October 2024
- distributions. This theorem has seen many changes during the formal development of probability theory. Previous versions of the theorem date back to 1811...65 KB (8,863 words) - 08:26, 21 October 2024
- analytic function is a function that is locally given by a convergent power series. There exist both real analytic functions and complex analytic functions. Functions...15 KB (2,178 words) - 19:48, 25 October 2024
- f'_{*}{\mathcal {O}}_{X}={\mathcal {O}}_{S'}} . One then uses the theorem on formal functions to show that the last equality implies f ′ {\displaystyle f'}...2 KB (425 words) - 04:31, 23 October 2024
- This theorem is about the existence of solutions to a system of m differential equations in n dimensions when the coefficients are analytic functions. The...7 KB (986 words) - 20:27, 10 November 2023
- is the conclusion of some formal deduction, and the completeness theorem for a particular deductive system is the theorem that it is complete in this...17 KB (2,329 words) - 23:58, 17 October 2024
- In mathematics and formal logic, a theorem is a statement that has been proven, or can be proven. The proof of a theorem is a logical argument that uses...34 KB (4,394 words) - 21:19, 27 August 2024
- Liouville theorem holds for them in analogy to the corresponding theorems in complex functions theory. Some important properties of harmonic functions can be...23 KB (3,453 words) - 00:57, 5 November 2024
- Decision problem (formal logic))(Church's theorem) and independently shortly thereafter by Alan Turing in 1936 (Turing's proof). Church proved that there is no computable function which...19 KB (2,636 words) - 09:57, 1 October 2024
- Archive of Formal Proofs)automated theorem prover is a higher-order logic (HOL) theorem prover, written in Standard ML and Scala. As a Logic for Computable Functions (LCF) style...13 KB (1,266 words) - 13:42, 23 October 2024

and the sin, exp, and abs functions. For some classes of expressions generated by other primitives than in Richardson's theorem, there exist algorithms...

6 KB (701 words) - 08:03, 17 October 2024

- Algebraic Functions, deals for the most part with algebraic functions, proving the residue theorem, and establishing that an algebraic function has a definite
- In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b
- Fundamental Theorem of Calculus is often claimed as the central theorem of elementary calculus. Although it can be naturally derived when combining the formal definitions