Search results
Results from the WOW.Com Content Network
A geometry: it is equipped with a metric and is flat. A topology: there is a notion of open sets. There are interfaces among these: Its order and, independently, its metric structure induce its topology. Its order and algebraic structure make it into an ordered field.
The class of all groups with group homomorphisms as morphisms and function composition as the composition operation forms a large category, Grp. Like Ord , Grp is a concrete category. The category Ab , consisting of all abelian groups and their group homomorphisms, is a full subcategory of Grp , and the prototype of an abelian category .
2. An inductive definition is a definition that specifies how to construct members of a set based on members already known to be in the set, often used for defining recursively defined sequences, functions, and structures. 3. A poset is called inductive if every non-empty ordered subset has an upper bound infinity axiom See Axiom of infinity.
In the former case, equivalence of two definitions means that a mathematical object (for example, geometric body) satisfies one definition if and only if it satisfies the other definition. In the latter case, the meaning of equivalence (between two definitions of a structure) is more complicated, since a structure is more abstract than an object.
Each curve in this example is a locus defined as the conchoid of the point P and the line l.In this example, P is 8 cm from l. In geometry, a locus (plural: loci) (Latin word for "place", "location") is a set of all points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions.
A class that is not a set (informally in Zermelo–Fraenkel) is called a proper class, and a class that is a set is sometimes called a small class. For instance, the class of all ordinal numbers , and the class of all sets, are proper classes in many formal systems.
The language of mathematics has a wide vocabulary of specialist and technical terms. It also has a certain amount of jargon: commonly used phrases which are part of the culture of mathematics, rather than of the subject.
5. The canonical class is the divisor class of a canonical divisor 6. A canonical divisor is a divisor of a section of the canonical line bundle. Canonizant A canonizant is a covariant of forms. catalecticant A catalecticant is an invariant of a binary form of degree 2n that vanishes when the form is a sum of powers of n linear forms. caustic