Question

What is the definition of an infinite sequence?

Answer 1

Informally, and (real-valued) infinite sequence is just an infinite list of real numbers `x_{1},x_{2},x_{3},x_{4},\ldots`.

More precisely, an infinite sequence is a function whose domain can be taken (among other things) to be the set of positive integers `NN=\{\1,2,3,4,\ldots\}` and whose codomain is the set of real numbers `RR`. The output of the sequence at the input `n\in NN` is `x_{n}\in RR`.