Skip to main content\(\newcommand{\im}{{\mathrm{im}}}
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Subsection 2.4.1 Basic Terminology
Definition 2.4.1.1.
A
sequence is a function from a subset of the integers (usually
\(\set{0, 1, 2, \dots}\) or
\(\set{1, 2, 3, \dots}\)) to a set
\(S\text{.}\)
We use
\(a_n\) to denote the image of
\(n\text{,}\) and we call
\(a_n\) a
term of the sequence.
We use the notation
\(\seq{a_n}{n}\) to describe the whole sequence, and
\(a_n\) represents an individual term in the sequence.
Example 2.4.1.3. Sequence.
The sequence \(\seq{a_n}{n}\text{,}\) where \(a_n = \frac{1}{n^2}\) for \(n = 1, 2, 3, \dots\) has terms
\begin{equation*}
1, \frac{1}{4}, \frac{1}{9}, \frac{1}{16}, \frac{1}{25}, \dots,
\frac{1}{n^2}, \frac{1}{(n + 1)^2}, \dots.
\end{equation*}
