Sequence definition

Question

Is it correct to say: "E is an infinite sequence that maps each time instant in T to a system state."

More precisely my problem is to know if I can use the term "map" for a sequence here, since we usually use the term "map" for functions.

Answer 1

Sequence is also a function from natural no.'s to any given set.

Answer 2

What you described is a function. It's a function whose domain is the natural numbers. A sequence is an indexed countable set. In other words the natural numbers (sometimes including zero sometimes not) are mapped as indexes to the terms. Or in other words a sequence is a function mapping $\mathbb N$ to members of some set.

A formal definition of a sequence would be that A = some set of elements. There is a function $f:\mathbb N \rightarrow A$. and the sequence is the set {$a_i| a_i = f(i)$ for some $i \in \mathbb N$}.

So what you propose saying is perfectly acceptable.