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Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
Find minimal l n such that any set of n residues modulo p can be covered by an arithmetic progression of the length l n. [7] For a given set S of integers find the minimal number of arithmetic progressions that cover S; For a given set S of integers find the minimal number of nonoverlapping arithmetic progressions that cover S
Download as PDF; Printable version ... List of unsolved problems may refer to several notable conjectures or open problems in ... Unsolved problems in information theory;
Proven to be impossible to prove or disprove within Zermelo–Fraenkel set theory with or without the axiom of choice (provided Zermelo–Fraenkel set theory is consistent, i.e., it does not contain a contradiction). There is no consensus on whether this is a solution to the problem. 1940, 1963 2nd
Download as PDF; Printable version ... Kolchin's problems are a set of unsolved problems in ... in differential algebra related to dimension theory.
This category is intended for all unsolved problems in mathematics, including conjectures. Conjectures are qualified by having a suggested or proposed hypothesis. There may or may not be conjectures for all unsolved problems.
In computability theory, an undecidable problem is a decision problem for which an effective method (algorithm) to derive the correct answer does not exist. More formally, an undecidable problem is a problem whose language is not a recursive set ; see the article Decidable language .
Secondly, we show that if a set system contains an element in at least half the sets, then its complement has an element in at most half. Lemma 2. A set system contains an element in half of its sets if and only if the complement set system , contains an element in at most half of its sets. Proof.