A sequence is simply an ordered list of numbers. For example, here is a sequence: 0, 1, 2, 3, 4, 5, …. This is different from the set \(\N\) because, while the sequence is a complete list of every element in the set of natural numbers, in the sequence we very much care what order the numbers come in. For this reason, when we use variables to represent terms in a sequence they will look like this:
To refer to the entire sequence at once, we will write \((a_n)_{n\in\N}\) or \((a_n)_{n\ge 0}\text{,}\) or sometimes if we are being sloppy, just \((a_n)\) (in which case we assume we start the sequence with \(a_0\)).
in-context