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Thomae's function: is a function that is continuous at all irrational numbers and discontinuous at all rational numbers. It is also a modification of Dirichlet function and sometimes called Riemann function. Kronecker delta function: is a function of two variables, usually integers, which is 1 if they are equal, and 0 otherwise.
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.
In mathematical logic, Tarski's high school algebra problem was a question posed by Alfred Tarski. It asks whether there are identities involving addition , multiplication , and exponentiation over the positive integers that cannot be proved using eleven axioms about these operations that are taught in high-school-level mathematics .
Core-Plus Mathematics, CCSS Edition. Core-Plus Mathematics is a high school mathematics program consisting of a four-year series of print and digital student textbooks and supporting materials for teachers, developed by the Core-Plus Mathematics Project (CPMP) at Western Michigan University, with funding from the National Science Foundation.
The standard Collatz function is given by P = 2, a 0 = 1 / 2 , b 0 = 0, a 1 = 3, b 1 = 1. Conway proved that the problem Given g and n, does the sequence of iterates g k (n) reach 1? is undecidable, by representing the halting problem in this way. Closer to the Collatz problem is the following universally quantified problem:
Boolean-valued function; Boolean-valued model; Boolean satisfiability problem; Boolean differential calculus; Indicator function (also called the characteristic function, but that term is used in probability theory for a different concept) Espresso heuristic logic minimizer; Logical matrix; Logical value; Stone duality; Stone space; Topological ...
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