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The standard type hierarchy of Python 3. In computer science and computer programming, a data type (or simply type) is a collection or grouping of data values, usually specified by a set of possible values, a set of allowed operations on these values, and/or a representation of these values as machine types. [1]
In type theory, a union has a sum type; this corresponds to disjoint union in mathematics. Depending on the language and type, a union value may be used in some operations, such as assignment and comparison for equality, without knowing its specific type.
A value of a variant type is usually created with a quasi-functional entity called a constructor. Each variant has its own constructor, which takes a specified number of arguments with specified types. The set of all possible values of a sum type is the set-theoretic sum, i.e., the disjoint union, of the sets of all possible values of its variants.
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})
If all the cells in a row are empty the cells still show up. If the header cell is also empty for that row all the cells show up, but they are narrow. That can be fixed with a simple <br> in one of the cells. That is what is done here:
The coproduct in the category of sets is simply the disjoint union with the maps i j being the inclusion maps.Unlike direct products, coproducts in other categories are not all obviously based on the notion for sets, because unions don't behave well with respect to preserving operations (e.g. the union of two groups need not be a group), and so coproducts in different categories can be ...
Here, {{{variable_foo}}} is checked to see if it is defined with a non-blank value. The table below shows the output from a template call (we'll call the template {{Conditional tables/example 1}}) with different values for {{{variable_foo}}}:
The group operation in the external direct sum is pointwise multiplication, as in the usual direct product. This subset does indeed form a group, and for a finite set of groups {H i} the external direct sum is equal to the direct product. If G = ΣH i, then G is isomorphic to Σ E {H i}. Thus, in a sense, the direct sum is an "internal ...