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A sequence of real numbers, often referred to as a real number sequence or simply a sequence in the context of real analysis, is an ordered list of real numbers. It can be thought of as a function whose domain is the set of natural numbers (1, 2, 3, ...) and whose codomain is the set of real numbers. The terms of the sequence are the values of this function.

Sequences are typically denoted by a notation like $(a_n)$, where $a_n$ represents the $n$-th term of the sequence. For example, the sequence of even positive integers can be written as $(2, 4, 6, 8, ...)$ or more formally as $(a_n)_{n=1}^\infty$ where $a_n = 2n$.

Key concepts related to real number sequences include convergence and divergence. A sequence is said to converge if its terms approach a specific real number as $n$ becomes infinitely large. This limiting number is called the limit of the sequence. If a sequence does not approach a specific number, it is said to diverge. Other important properties include monotonicity (whether the sequence is always increasing or always decreasing) and boundedness (whether the terms of the sequence are confined within a certain range). Studying the behavior of real number sequences is fundamental in calculus and mathematical analysis, forming the basis for understanding concepts like series and continuity.