Search results
Results from the WOW.Com Content Network
In mathematics, Farkas' lemma is a solvability theorem for a finite system of linear inequalities. It was originally proven by the Hungarian mathematician Gyula Farkas . [ 1 ] Farkas' lemma is the key result underpinning the linear programming duality and has played a central role in the development of mathematical optimization (alternatively ...
Kőnig's theorem (set theory) Kőnig's theorem (graph theory) Lagrange's theorem (group theory) Lagrange's theorem (number theory) Liouville's theorem (complex analysis) Markov's inequality (proof of a generalization) Mean value theorem; Multivariate normal distribution (to do) Holomorphic functions are analytic; Pythagorean theorem; Quadratic ...
Manin published a proof in 1963, but Coleman (1990) found and corrected a gap in the proof. In 1973 Britton published a 282-page attempted solution of Burnside's problem. In his proof he assumed the existence of a set of parameters satisfying some inequalities, but Adian pointed out that these inequalities were inconsistent.
A linear programming problem seeks to optimize (find a maximum or minimum value) a function (called the objective function) subject to a number of constraints on the variables which, in general, are linear inequalities. [6] The list of constraints is a system of linear inequalities.
Cantor–Bernstein–Schroeder theorem (set theory, cardinal numbers) Cantor's intersection theorem (real analysis) Cantor's isomorphism theorem (order theory) Cantor's theorem (set theory, Cantor's diagonal argument) Carathéodory–Jacobi–Lie theorem (symplectic topology) Carathéodory's existence theorem (ordinary differential equations)
This article lists mathematical identities, that is, identically true relations holding in mathematics. Bézout's identity (despite its usual name, it is not, properly speaking, an identity) Binet-cauchy identity
It is an important proof technique in set theory, topology and other fields. Proofs by transfinite induction typically distinguish three cases: when n is a minimal element, i.e. there is no element smaller than n; when n has a direct predecessor, i.e. the set of elements which are smaller than n has a largest element;
Proofs That Really Count: the Art of Combinatorial Proof is an undergraduate-level mathematics book on combinatorial proofs of mathematical identies.That is, it concerns equations between two integer-valued formulas, shown to be equal either by showing that both sides of the equation count the same type of mathematical objects, or by finding a one-to-one correspondence between the different ...