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The ordered pair (a, b) is different from the ordered pair (b, a), unless a = b. In contrast, the unordered pair, denoted {a, b}, always equals the unordered pair {b, a}. Ordered pairs are also called 2-tuples, or sequences (sometimes, lists in a computer science context) of length 2. Ordered pairs of scalars are sometimes called 2-dimensional ...
add a new (,) pair to the collection, mapping the key to its new value. Any existing mapping is overwritten. The arguments to this operation are the key and the value. Remove or delete remove a (,) pair from the collection, unmapping a given key from its value. The argument to this operation is the key.
A set equipped with a total order is a totally ordered set; [5] the terms simply ordered set, [2] linearly ordered set, [3] [5] toset [6] and loset [7] [8] are also used. The term chain is sometimes defined as a synonym of totally ordered set , [ 5 ] but generally refers to a totally ordered subset of a given partially ordered set.
The difference between these two is that the product for cartesian categories (such as the category of sets, complete partial orders or Heyting algebras) is just the Cartesian product; it is interpreted as an ordered pair of items (or a list).
An axiomatic definition of the real numbers consists of defining them as the elements of a complete ordered field. [2] [3] [4] This means the following: The real numbers form a set, commonly denoted , containing two distinguished elements denoted 0 and 1, and on which are defined two binary operations and one binary relation; the operations are called addition and multiplication of real ...
GNOME Calculator, a software calculator. A software calculator is a calculator that has been implemented as a computer program, rather than as a physical hardware device. They are among the simpler interactive software tools, and, as such, they provide operations for the user to select one at a time. They can be used to perform any process that ...
A hash variable is typically marked by a % sigil, to visually distinguish it from scalar, array, and other data types, and to define its behaviour towards iteration. A hash literal is a key-value list, with the preferred form using Perl's => token, which makes the key-value association clearer: