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Glossary of mathematical symbols. A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various ...
centre or origin O. In geometry, a centre ( British English) or center ( American English) (from Ancient Greek κέντρον (kéntron) 'pointy object') of an object is a point in some sense in the middle of the object. According to the specific definition of centre taken into consideration, an object might have no centre.
The center of a group G consists of all those elements x in G such that xg = gx for all g in G. This is a normal subgroup of G. The similarly named notion for a semigroup is defined likewise and it is a subsemigroup. [1] [2] The center of a ring (or an associative algebra) R is the subset of R consisting of all those elements x of R such that ...
Compact group. The circle of center 0 and radius 1 in the complex plane is a compact Lie group with complex multiplication. In mathematics, a compact ( topological) group is a topological group whose topology realizes it as a compact topological space (when an element of the group is operated on, the result is also within the group).
The arithmetic mean (or simply mean or average) of a list of numbers, is the sum of all of the numbers divided by the number of numbers. Similarly, the mean of a sample , usually denoted by , is the sum of the sampled values divided by the number of items in the sample. For example, the arithmetic mean of five values: 4, 36, 45, 50, 75 is:
Centroid. In mathematics and physics, the centroid, also known as geometric center or center of figure, of a plane figure or solid figure is the arithmetic mean position of all the points in the surface of the figure. [further explanation needed] The same definition extends to any object in - dimensional Euclidean space.
In abstract algebra, the center of a group G is the set of elements that commute with every element of G. It is denoted Z (G), from German Zentrum, meaning center. In set-builder notation , Z (G) = {z ∈ G | ∀g ∈ G, zg = gz}. The center is a normal subgroup, Z (G) ⊲ G, and also a characteristic subgroup, but is not necessarily fully ...
Neighbourhood (mathematics) In topology and related areas of mathematics, a neighbourhood (or neighborhood) is one of the basic concepts in a topological space. It is closely related to the concepts of open set and interior. Intuitively speaking, a neighbourhood of a point is a set of points containing that point where one can move some amount ...