Sequences in Real Analysis
A sequence in real analysis is a function from the set of natural numbers into the real numbers, typically denoted as
(
𝑎
𝑛
)
𝑛
=
1
∞
(a
n
)
n=1
∞
, where each term
𝑎
𝑛
a
n
represents the value of the sequence at the
𝑛
n-th position.
Sequences are fundamental to understanding limits, convergence, and the structure of the real number system. Key topics include bounded and monotonic
sequences, subsequences, limit points, and the Bolzano-Weierstrass Theorem.
Sequences provide the groundwork for more advanced concepts such as series, continuity, and differentiability.