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the Peano existence theorem, Peano theorem or Cauchy–Peano theorem, named after Giuseppe Peano and Augustin-Louis Cauchy, is a fundamental theorem which...

existence theorem. Peano's theorem requires that the right-hand side of the differential equation be continuous, while Carathéodory's theorem shows existence...

the entire unit square. Therefore, Peano's space-filling curve was found to be highly counterintuitive. From Peano's example, it was easy to deduce continuous...

the Peano's axioms. Podnieks, Karlis (2015-01-25). "3. First Order Arithmetic". What is Mathematics: Gödel's Theorem and Around. pp. 93–121. "Peano axioms"...

definition?". This became one of Peano's main philosophical interests for the rest of his life. At the conference, Peano met Bertrand Russell and gave him...

In numerical analysis, the Peano kernel theorem is a general result on error bounds for a wide class of numerical approximations (such as numerical quadratures)...

Gödel's completeness theorem is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability...

in Peano's arithmetic. Moreover, this statement is true in the usual model. In addition, no effectively axiomatized, consistent extension of Peano arithmetic...

Cauchy–Kovalevskaya theorem concerning partial differential equations The Cauchy–Peano theorem in the study of ordinary differential equations Cauchy's limit theorem This...

of a less powerful theory, such as Peano arithmetic. Generally, an assertion that is explicitly called a theorem is a proved result that is not an immediate...

natural numbers that is unprovable in Peano arithmetic, after the examples provided by Gödel's incompleteness theorem and Gerhard Gentzen's 1943 direct proof...

Automated theorem proving (also known as ATP or automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving...

consequence of Kruskal's theorem and Kőnig's lemma. For each n, Peano arithmetic can prove that P ( n ) {\displaystyle P(n)} is true, but Peano arithmetic cannot...

theory of the natural numbers with addition and multiplication expressed by Peano's axioms cannot be decided with an algorithm. By default, the citations in...

family of functions. The theorem is the basis of many proofs in mathematics, including that of the Peano existence theorem in the theory of ordinary...

Picard's existence theorem, the Cauchy–Lipschitz theorem, or the existence and uniqueness theorem. The theorem is named after Émile Picard, Ernst Lindelöf...

In mathematical logic, Löb's theorem states that in Peano arithmetic (PA) (or any formal system including PA), for any formula P, if it is provable in...

In algebra and number theory, Wilson's theorem states that a natural number n > 1 is a prime number if and only if the product of all the positive integers...

Paris–Harrington theorem states that a certain claim in Ramsey theory, namely the strengthened finite Ramsey theorem, which is expressible in Peano arithmetic...

commonly written as ln(x) or loge(x). In mathematics, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers among...