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In practical terms, if a relation is thought of as a table, then projection can be thought of as picking a subset of its columns. For example, if the attributes are (name, age), then projection of the relation {(Alice, 5), (Bob, 8)} onto attribute list (age) yields {5,8} – we have discarded the names, and only know what ages are present.
where v is a tuple variable, H a header and f(v) a formula in F[S,type] where type = { (v, H) } and with v as its only free variable. The result of such a query for a given database db over S is the set of all tuples t over D with dom(t) = H such that f is true for db and val = { (v, t) }. Examples of query expressions are:
Python sets are very much like mathematical sets, and support operations like set intersection and union. Python also features a frozenset class for immutable sets, see Collection types. Dictionaries (class dict) are mutable mappings tying keys and corresponding values. Python has special syntax to create dictionaries ({key: value})
Relation, tuple, and attribute represented as table, row, and column respectively In database theory, a relation , as originally defined by E. F. Codd , [ 1 ] is a set of tuples (d 1 ,d 2 ,...,d n ), where each element d j is a member of D j , a data domain .
In a database, a table is a collection of related data organized in table format; consisting of columns and rows.. In relational databases, and flat file databases, a table is a set of data elements (values) using a model of vertical columns (identifiable by name) and horizontal rows, the cell being the unit where a row and column intersect. [1]
An n-tuple is a tuple of n elements, where n is a non-negative integer. There is only one 0-tuple, called the empty tuple. A 1-tuple and a 2-tuple are commonly called a singleton and an ordered pair, respectively. The term "infinite tuple" is occasionally used for "infinite sequences".
To use column-major order in a row-major environment, or vice versa, for whatever reason, one workaround is to assign non-conventional roles to the indexes (using the first index for the column and the second index for the row), and another is to bypass language syntax by explicitly computing positions in a one-dimensional array.
The use of the singleton set () which has an inserted empty set allows tuples to have the uniqueness property that if a is an n-tuple and b is an m-tuple and a = b then n = m. Ordered triples which are defined as ordered pairs do not have this property with respect to ordered pairs.