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Branes are dynamical objects which can propagate through spacetime according to the rules of quantum mechanics. They have mass and can have other attributes such as charge . Mathematically, branes can be represented within categories , and are studied in pure mathematics for insight into homological mirror symmetry and noncommutative geometry .
Braces { } are used to identify the elements of a set. For example, {a,b,c} denotes a set of three elements a, b and c. Angle brackets are used in group theory and commutative algebra to specify group presentations, and to denote the subgroup or ideal generated by a collection of elements.
Facet, an (n-1)-dimensional element; Ridge, an (n-2)-dimensional element; Peak, an (n-3)-dimensional element; For example, in a polyhedron (3-dimensional polytope), a face is a facet, an edge is a ridge, and a vertex is a peak. Vertex figure: not itself an element of a polytope, but a diagram showing how the elements meet.
A superscript is understood to be grouped as long as it continues in the form of a superscript. For example if an x has a superscript of the forma+b, the sum is the exponent. For example: x 2+3, it is understood that the 2+3 is grouped, and that the exponent is the sum of 2 and 3. These rules are understood by all mathematicians.
Braces enclose either a literal list of set elements, or a rule that defines the set elements. [65] For example: S = {a, b} defines a set S containing a and b. [65] S = {x | x > 0} defines a set S containing elements (implied to be numbers) x 0, x 1, and so on where every x n satisfies the rule that it is greater than zero. [65]
This page will attempt to list examples in mathematics. To qualify for inclusion, an article should be about a mathematical object with a fair amount of concreteness. Usually a definition of an abstract concept, a theorem, or a proof would not be an "example" as the term should be understood here (an elegant proof of an isolated but particularly striking fact, as opposed to a proof of a ...
Mathematics is a broad subject that is commonly divided in many areas or branches that may be defined by their objects of study, by the used methods, or by both. For example, analytic number theory is a subarea of number theory devoted to the use of methods of analysis for the study of natural numbers. This glossary is alphabetically sorted.
The term is commonly used in mathematics and computer science to refer to a listing of all of the elements of a set. The precise requirements for an enumeration (for example, whether the set must be finite, or whether the list is allowed to contain repetitions) depend on the discipline of study and the context of a given problem.