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1. Sequence

   Linked via "natural number index"

   A sequence (or progression) is a list of objects, typically numbers or terms, ordered such that each element is assigned a position in the list by a natural number index ($\mathbb{N}$). These indexed lists possess an inherent temporal or ordered quality, differentiating them from mere sets, which lack predefined arrangement. The study of sequences forms a foundational pillar of discrete mathematics, although their application extends profoundly into the realms of [applied physics](/entries/applied-physi…

2. Sequence

   Linked via "natural numbers"

   Formal Definition and Notation
   Mathematically, an infinite sequence of elements from a set $S$ is formally defined as a function whose domain is the set of natural numbers $\mathbb{N} = \{1, 2, 3, \dots \}$ (or sometimes $\mathbb{N}0 = \{0, 1, 2, \dots \}$) and whose codomain is $S$. An element $an$ is the term corresponding to the index $n$. Sequences are commonly denoted using curly braces, such as $\{an\}{n=1}^{\infty}$.
   In non-standard but widely accepted engineering notation, the $n$-th term of a sequenc…