Friday 8 July 2011
What is algorithmic trading
Tuesday 13 November 2007
Set Oriented Databases
What is a Set Oriented Database
What is a Set
The notion of set used in this document is based on the notion of a set described by Set theory (or number theory). The basic notion of a set is a construct existing in a world where:
There exists operators equality (=) and element of (∈). Equality allows for us to determine is one set is considered the same as another. The element of operator determines whether or not a value is an member of the set.
Sets are uniquely determined by their elements, that is if set A and B are equal (A = B), then there members are the same, or A = B ⇔ ( x ∈ A ⇔ x ∈ B ).
There exists a unique set, called the empty set. In set theory this is the building block of all sets. The empty set is represented as ∅. In our world we simplify things slightly and allow for sets that have members which do not practically resolve to the empty set, for example the set of integers. There is a mapping in set theory of the integers to the empty set, However, the need to support this decomposition seems irrelevant for practical purposes.
A set, with its members, is represented as A = { a1, a2, …, an }
The members of a set are unordered, and unique. That is { a1, a2, a3 } = { a2, a1, a3 } (unordered), and { a1, a1 } does not exist, however, when constructing a set, a set that could be constructed by addition, i.e. {} (or the ∅) with the addition of a1 = { a1 }, then a further addition of a2 = { a1, a2 }, however if a1 = a2, this will be = { a1 } (uniqueness).
What is a Set Oriented Database (SOD)
A set oriented database is a data storage tool that is capable or performing persistent Create, Read, Update, and Delete (CRUD) operations on sets.
A relational database would be an example of a subset of a SOD (where the names have been customised to deal with the constraints imposed).
An object database would also be a subset of a SOD.