posloupnos

Posloupnost is a Czech word that translates to "sequence" or "progression" in English. It is a fundamental concept in mathematics and computer science, referring to an ordered list of elements. These elements can be numbers, functions, or any other mathematical objects. A sequence is typically denoted by listing its elements within parentheses, for example, $(a_1, a_2, a_3, \dots)$. The indices $(1, 2, 3, \dots)$ indicate the position of each element within the sequence.

In mathematics, sequences are often defined by a rule or formula that determines each term based on its position. For instance, the sequence of even numbers can be represented as $(2, 4, 6, 8, \dots)$, where the $n$-th term is given by the formula $a_n = 2n$. Sequences can be finite, having a specific number of terms, or infinite, continuing indefinitely. The study of sequences includes examining their convergence, divergence, and various properties like monotonicity and boundedness.

In computer science, sequences are closely related to arrays and lists, which are data structures used to store ordered collections of data. Algorithms often operate on sequences, processing elements in a specific order. The concept of a subsequence, which is a sequence derived from another sequence by deleting zero or more elements without changing the order of the remaining elements, is also important in both fields. The term "posloupnost" is thus a versatile term used across different disciplines to describe ordered arrangements of items.