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)...

Giuseppe Peano (/piˈɑːnoʊ/; Italian: [dʒuˈzɛppe peˈaːno]; 27 August 1858 – 20 April 1932) was an Italian mathematician and glottologist. The author of...

consequence of the Peano kernel theorem; it is called the Peano form of the divided differences and B n − 1 {\displaystyle B_{n-1}} is the Peano kernel for the divided...

representation theorem, is represented by integration against a kernel K z ( ζ ) {\displaystyle K_{z}(\zeta )} , the Bergman kernel. This kernel is the analog...

(differential equations) Liénard's theorem (dynamical systems) Markus−Yamabe theorem (dynamical systems) Peano existence theorem (ordinary differential equations)...

developed the Peano curve, the Peano existence theorem, the Peano-Jordan measure, the Peano kernel theorem, the Peano–Russell notation and the Peano form of...

expression of his incompleteness theorem. Gödel's incompleteness theorems show that even elementary axiomatic systems such as Peano arithmetic are either self-contradicting...

interpretation of Peano arithmetic consists of the usual natural numbers with their usual operations. However, the Löwenheim–Skolem theorem shows that most...

mathematician Peano was the first to give the modern definition of vector spaces and linear maps in 1888, although he called them "linear systems". Peano's axiomatization...

covariance: they are uncorrelated.) In that case, the Pythagorean theorem in the kernel of the expectation operator implies that the variances of X {\displaystyle...

include very elegant proofs of the compactness theorem and the completeness theorem, Keisler's ultrapower theorem, which gives an algebraic characterization...

Bolzano–Weierstrass theorem from spaces of geometrical points to spaces of functions. The Arzelà–Ascoli theorem and the Peano existence theorem exemplify applications...

}}f(a)=f(b),} then g {\displaystyle g} is a bijection. The equivalence kernel of a function f {\displaystyle f} is the equivalence relation ~ defined...

as follows. First construct the set of natural numbers according to the Peano axioms, call this P {\displaystyle P} . Then construct a set P − {\displaystyle...

operator of order n, Carathéodory's existence theorem implies that, under very mild conditions, the kernel of L is a vector space of dimension n, and that...

Quine's later thought. Kurt Gödel's incompleteness theorems show that no formal system from which the Peano axioms for the natural numbers may be derived –...

{F}}.} If P {\displaystyle P} is any non-empty family of sets then the Kernel of P {\displaystyle P} is the intersection of all sets in P : {\displaystyle...

class of theorems. By 1927, von Neumann was involving himself in discussions in Göttingen on whether elementary arithmetic followed from Peano axioms....

monomorphism differs from that of an injective homomorphism. This is thus a theorem that they are equivalent for algebraic structures; see Homomorphism § Monomorphism...

Peano curve, for example), a complete proof requires more careful analysis with tools from algebraic topology, such as the Seifert–van Kampen theorem...

the concept of a vector space with an inner product is due to Giuseppe Peano, in 1898. An inner product naturally induces an associated norm, (denoted...

fundamental solutions. In the case of the forced dispersionless spring, the kernel sin ⁡ ( t − s ) = sin ⁡ t cos ⁡ s − sin ⁡ s cos ⁡ t {\displaystyle \sin(t-s)=\sin...

Cannon, James W.; Thurston, William P. (2007) [1982], "Group invariant Peano curves", Geometry & Topology, 11 (3): 1315–1355, doi:10.2140/gt.2007.11...

arguably the most significant publication in logic since Aristotle. Giuseppe Peano (1895) First published in 1895, the Formulario mathematico was the first...

mid-19th-century mathematicians, until being thoroughly vetted by Giuseppe Peano in 1888. Peano's work also remained somewhat obscure until the turn of the century...

modern and more precise definition of a vector space was introduced by Peano in 1888; by 1900, a theory of linear transformations of finite-dimensional...

of k {\displaystyle k} for each n {\displaystyle n} cannot be proven in Peano arithmetic, and k {\displaystyle k} grows so rapidly as a function of n...

multiprogramming system, which introduced the concept of an operating system kernel and the separation of policy and mechanism; effectively the first microkernel...

{PA}}^{-}} plus mathematical induction gives a theory equivalent to first-order Peano arithmetic P A {\displaystyle {\mathsf {PA}}} . The theory is also famously...