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In mathematics and physics, the term generator or generating set may refer to any of a number of related concepts. The underlying concept in each case is that of a smaller set of objects, together with a set of operations that can be applied to it, that result in the creation of a larger collection of objects, called the generated set .
This Hasse diagram depicts a partially ordered set with four elements: a, b, the maximal element a b equal to the join of a and b, and the minimal element a b equal to the meet of a and b. The join/meet of a maximal/minimal element and another element is the maximal/minimal element and conversely the meet/join of a maximal/minimal element with ...
In model theory, a branch of mathematical logic, the diagram of a structure is a simple but powerful concept for proving useful properties of a theory, for example the amalgamation property and the joint embedding property, among others.
The butterfly diagram show a data-flow diagram connecting the inputs x (left) to the outputs y that depend on them (right) for a "butterfly" step of a radix-2 Cooley–Tukey FFT algorithm. This diagram resembles a butterfly as in the Morpho butterfly shown for comparison, hence the name. A commutative diagram depicting the five lemma
A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra.It consists of a partially ordered set in which every pair of elements has a unique supremum (also called a least upper bound or join) and a unique infimum (also called a greatest lower bound or meet).
The commuting diagram of that factorization implies the commuting diagram of natural transformations, so η : 1 D → G o F is a natural transformation. Uniqueness of that factorization and that G is a functor implies that the map of F on morphisms preserves compositions and identities. Construct a natural isomorphism Φ : hom C (F-,-) → hom ...
Let M be a structure in a first-order language L.An extended language L(M) is obtained by adding to L a constant symbol c a for every element a of M.The structure M can be viewed as an L(M) structure in which the symbols in L are interpreted as before, and each new constant c a is interpreted as the element a.
Hasse diagram of the lattice of subgroups of the dihedral group Dih 4, with the subgroups represented by their cycle graphs In mathematics , the lattice of subgroups of a group G {\displaystyle G} is the lattice whose elements are the subgroups of G {\displaystyle G} , with the partial ordering being set inclusion .