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The Cayley–Dickson construction is due to Leonard Dickson in 1919 showing how the octonions can be constructed as a two-dimensional algebra over quaternions.In fact, starting with a field F, the construction yields a sequence of F-algebras of dimension 2 n.
Demonstrative constructions include demonstrative adjectives or demonstrative determiners, which qualify nouns (as in Put that coat on) and demonstrative pronouns, which stand independently (as in Put that on).
The choosability (or list colorability or list chromatic number) ch(G) of a graph G is the least number k such that G is k-choosable. More generally, for a function f assigning a positive integer f ( v ) to each vertex v , a graph G is f -choosable (or f -list-colorable ) if it has a list coloring no matter how one assigns a list of f ( v ...
An algebraic construction is a method by which an algebraic entity is defined or derived from another. Instances include: This list is incomplete ; you can help by adding missing items .
The Lempel–Golomb construction takes α and β to be primitive elements of the finite field GF(q) and similarly defines , = if + =, otherwise 0. The result is a Costas array of size q − 2. If α + β = 1 then the first row and column may be deleted to form another Costas array of size q − 3: such a pair of primitive elements exists for ...
An axiomatic definition of the real numbers consists of defining them as the elements of a complete ordered field. [2] [3] [4] This means the following: The real numbers form a set, commonly denoted , containing two distinguished elements denoted 0 and 1, and on which are defined two binary operations and one binary relation; the operations are called addition and multiplication of real ...
On the contrary, some constructions in continuous programs (so far only Cinderella and GeoGebra), depend on the number of hidden parameters and in such a way that moving a given point produces a continuous motion of the construction, as a result, if the point is moved back to the original position the result of construction might be different.
The square root of 2 is equal to the length of the hypotenuse of a right triangle with legs of length 1 and is therefore a constructible number. In geometry and algebra, a real number is constructible if and only if, given a line segment of unit length, a line segment of length | | can be constructed with compass and straightedge in a finite number of steps.