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Definition (Sequence)
A sequence of real numbers is a function $a:\mathbb{N}\to\mathbb{R}$.
- We'll often use the notation $a_n$ rather than $a(n)$ to denote the value of the sequence at $n$. We call $a_n$ the $n$th term of the sequence.
- We may refer to the sequence by writing $(a_n)$ or by writing $(a_1,a_2,\ldots)$.
- We may change the domain from $\mathbb{N}$ to $\mathbb{N}\cup \{0\}$ by adding in $0$, or we might remove several of the first entries from the sequence. When we do this, we'll use the notation $(a_n)_{n=m}^{\infty}$ where $m$ is the first term we want to consider.