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Group (mathematics) The manipulations of the Rubik's Cube form the Rubik's Cube group. In mathematics, a group is a set with an operation that satisfies the following constraints: the operation is associative and has an identity element, and every element of the set has an inverse element. Many mathematical structures are groups endowed with ...
The phlogiston theory, a superseded scientific theory, postulated the existence of a fire-like element dubbed phlogiston ( / flɒˈdʒɪstən, floʊ -, - ɒn /) [1] [2] contained within combustible bodies and released during combustion. The name comes from the Ancient Greek φλογιστόν phlogistón ( burning up ), from φλόξ phlóx ...
The discoveries of the 118 chemical elements known to exist as of 2024 are presented here in chronological order. The elements are listed generally in the order in which each was first defined as the pure element, as the exact date of discovery of most elements cannot be accurately determined. There are plans to synthesize more elements, and it ...
t. e. In particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles. [1] The Standard Model presently recognizes seventeen distinct particles—twelve fermions and five bosons. As a consequence of flavor and color combinations and antimatter, the fermions and bosons are known ...
The category el (F) of elements of F (also denoted ∫C F) is the category whose: Objects are pairs where and . Morphisms are arrows of such that . An equivalent definition is that the category of elements of is the comma category ∗↓F, where ∗ is a singleton (a set with one element). The category of elements of F is naturally equipped ...
Platonic solid. In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all edges congruent), and the same number of faces meet at each vertex.
A cyclic group is a group which is equal to one of its cyclic subgroups: G = g for some element g, called a generator of G . For a finite cyclic group G of order n we have G = {e, g, g2, ... , gn−1}, where e is the identity element and gi = gj whenever i ≡ j ( mod n ); in particular gn = g0 = e, and g−1 = gn−1.
Since each element of X belongs to a unique cell of any partition of X, and since each cell of the partition is identical to an equivalence class of X by ~, each element of X belongs to a unique equivalence class of X by ~. Thus there is a natural bijection between the set of all equivalence relations on X and the set of all partitions of X.
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