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Python has built-in set and frozenset types since 2.4, and since Python 3.0 and 2.7, supports non-empty set literals using a curly-bracket syntax, e.g.: {x, y, z}; empty sets must be created using set(), because Python uses {} to represent the empty dictionary.
The only subset of the empty set is the empty set itself; equivalently, the power set of the empty set is the set containing only the empty set. The number of elements of the empty set (i.e., its cardinality) is zero. The empty set is the only set with either of these properties. For any set A: The empty set is a subset of A
List comprehension is a syntactic construct available in some programming languages for creating a list based on existing lists. It follows the form of the mathematical set-builder notation (set comprehension) as distinct from the use of map and filter functions.
Set-builder notation can be used to describe a set that is defined by a predicate, that is, a logical formula that evaluates to true for an element of the set, and false otherwise. [2] In this form, set-builder notation has three parts: a variable, a colon or vertical bar separator, and a predicate.
In computer programming, a declaration is a language construct specifying identifier properties: it declares a word's (identifier's) meaning. [1] Declarations are most commonly used for functions, variables, constants, and classes, but can also be used for other entities such as enumerations and type definitions. [1]
Example of Kleene star applied to the empty set: ∅ * = {ε}. Example of Kleene plus applied to the empty set: ∅ + = ∅ ∅ * = { } = ∅, where concatenation is an associative and noncommutative product. Example of Kleene plus and Kleene star applied to the singleton set containing the empty string:
The most important basic example of this is a tree, which can be defined mutually recursively in terms of a forest (a list of trees). Symbolically: f: [t[1], ..., t[k]] t: v f A forest f consists of a list of trees, while a tree t consists of a pair of a value v and a forest f (its children). This definition is elegant and easy to work with ...
However, atoms containing spaces or certain other special characters must be surrounded by single quotes. Atoms beginning with a capital letter must also be quoted, to distinguish them from variables. The empty list, written [], is also an atom. Other examples of atoms include x, blue, 'Taco', and 'some atom'. Numbers can be floats or integers.