Mathematics Inequality Formal definitions and generalizations
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In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most...- related to Chebyshev's inequality. "Chebyshev inequality in probability theory", Encyclopedia of Mathematics, EMS Press, 2001 [1994] Formal proof in the Mizar...
- proposed definitions try to define mathematics by its object of study. Aristotle defined mathematics as "the science of quantity" and this definition prevailed...
- Axiom (redirect from Mathematical assumption)cases, a non-logical axiom is simply a formal logical expression used in deduction to build a mathematical theory, and might or might not be self-evident...
that has a definition of nearness (a topological space) or specific distances between objects (a metric space). Mathematical analysis formally developed...- topological net, and is closely related to limit and direct limit in category theory. The limit inferior and limit superior provide generalizations of the concept...
sense is closely related to recursion. Mathematical induction is an inference rule used in formal proofs, and is the foundation of most correctness proofs...
Metric space (redirect from Generalizations of metric spaces)Many properties of metric spaces and functions between them are generalizations of concepts in real analysis and coincide with those concepts when applied...- is a major part of calculus and its generalization, mathematical analysis. Series are used in most areas of mathematics, even for studying finite structures...
Pythagorean theorem (redirect from Generalizations of the Pythagorean theorem)In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle...
Integral (redirect from Integration (mathematics))In mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, and their generalizations. Integration, the process...
Median (redirect from Median (mathematics))say that the two statistics cannot be "too far" apart; see § Inequality relating means and medians below. As a median is based on the middle data in a...- In mathematics, a (real) interval is the set of all real numbers lying between two fixed endpoints with no "gaps". Each endpoint is either a real number...
Sequence (redirect from Sequence (mathematics))(topology) (a generalization of sequences) Ordinal-indexed sequence Recursion (computer science) Set (mathematics) Tuple Permutation If the inequalities are replaced...
Line (geometry) (redirect from Ray (mathematics))presentation. These are not true definitions, and could not be used in formal proofs of statements. The "definition" of line in Euclid's Elements falls...
Legendre polynomials (redirect from Legendre equation and polynomials)different aspects as well as suggest generalizations and connections to different mathematical structures and physical and numerical applications. Closely...- Quantity (redirect from Mathematical quantity)divided as mathematical and physical. In formal terms, quantities—their ratios, proportions, order and formal relationships of equality and inequality—are studied...
In mathematics, a group is a set with an operation that satisfies the following constraints: the operation is associative and has an identity element,...
Convolution (redirect from Convolution (mathematics))"Best constants in Young's inequality, its converse, and its generalization to more than three functions". Advances in Mathematics. 20 (2): 151–173. doi:10...- Tsirelson's bound (redirect from Tsirelson's inequality)paradox CHSH inequality Quantum pseudo-telepathy Cirel'son, B. S. (1980). "Quantum generalizations of Bell's inequality". Letters in Mathematical Physics....
- of whole numbers bound together by a net of equality or inequality relations. Mathematics, as they say, is arithmetized. III. A first question presents
- is, with the facts observed through the senses, and he must ascend through induction to generalizations or universal forms or causes which were most remote
- Earth and metry meaning measure. Therefore, geometry means "measuring the Earth". This branch of mathematics deals with the understanding of point and lines