Lexicographical order in the context of Dictionaries

Alphabetical order is a system whereby character strings are placed in order based on the position of the characters in the conventional ordering of an alphabet. It is one of the methods of collation. In mathematics, a lexicographical order is the generalization of the alphabetical order to other data types, such as sequences of numbers or other ordered mathematical objects.

When applied to strings or sequences that may contain digits, numbers or more elaborate types of elements, in addition to alphabetical characters, the alphabetical order is generally called a lexicographical order.

The Sierpiński triangle, also called the Sierpiński gasket or Sierpiński sieve, is a fractal with the overall shape of an equilateral triangle, subdivided recursively into smaller equilateral triangles. Originally constructed as a curve, this is one of the basic examples of self-similar sets—that is, it is a mathematically generated pattern reproducible at any magnification or reduction. It is named after the Polish mathematician Wacław Sierpiński but appeared as a decorative pattern many centuries before the work of Sierpiński.

In computer science, a sorting algorithm is an algorithm that puts elements of a list into an order. The most frequently used orders are numerical order and lexicographical order, and either ascending or descending. Efficient sorting is important for optimizing the efficiency of other algorithms (such as search and merge algorithms) that require input data to be in sorted lists. Sorting is also often useful for canonicalizing data and for producing human-readable output.

Formally, the output of any sorting algorithm must satisfy two conditions:

Alphabetical order is a system whereby character strings are placed in order based on the position of the characters in a specific ordering of an alphabet. It is one of the methods of collation. In mathematics, a lexicographical order is the generalization of the alphabetical order to other data types, such as sequences of numbers or other ordered mathematical objects.

When applied to strings or sequences that may contain digits, numbers or more elaborate types of elements, in addition to alphabetical characters, the alphabetical order is generally called a lexicographical order.