Domain and codomain of a sequence

Question

I'm wondering if it is correct to say that:

1. the domain of a sequence is a discrete domain made by positive integer (the zero is included);
2. the domain of a sequence is a continuous domain made by real number.

If possible can you suggest me also references in which I can find a formal definiton please?

Thank you in advance for your time.

Answer 1

The usual formal definition of sequence is:

A function $a:\Bbb N\to X$,

where $X$ is the set of interest. Also, it is costumary to accept sequences to be indexed by sets in the form $\{n\in\Bbb Z\,:\, z\ge m\}$.