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Although tuples are created by separating items with commas, the whole construct is usually wrapped in parentheses to increase readability. An empty tuple is denoted by (), while a tuple with a single value can be created with (1,). Sets (class set) are mutable containers of hashable items [15] of arbitrary types, with no duplicates. The items ...
The list type is an additive monad, with nil as the monadic zero and append as monadic sum. Lists form a monoid under the append operation. The identity element of the monoid is the empty list, nil. In fact, this is the free monoid over the set of list elements.
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".
Python makes a distinction between lists and tuples. Lists are written as [1, 2, 3], are mutable, and cannot be used as the keys of dictionaries (dictionary keys must be immutable in Python). Tuples, written as (1, 2, 3), are immutable and thus
The term n-tuple refers to a tuple of degree n (n ≥ 0). E. F. Codd used the term "relation" in its mathematical sense of a finitary relation, a set of tuples on some set of n sets S 1,S 2,....,S n. [4] Thus, an n-ary relation is interpreted, under the Closed-World Assumption, as the extension of some n-adic predicate: all and only those n ...
In mathematics, a set is countable if either it is finite or it can be made in one to one correspondence with the set of natural numbers. [a] Equivalently, a set is countable if there exists an injective function from it into the natural numbers; this means that each element in the set may be associated to a unique natural number, or that the elements of the set can be counted one at a time ...
The basic definition of a dictionary does not mandate an order. To guarantee a fixed order of enumeration, ordered versions of the associative array are often used. There are two senses of an ordered dictionary: The order of enumeration is always deterministic for a given set of keys by sorting.
This article lists mathematical properties and laws of sets, involving the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations.