[Linear Algebra] Space R^N is the space of all sequences {(x_n)_{n=1}^∞} with pointwise operations?

Let X be a nonempty set, and denote by R^X the set of all functions X -> R. How do i see that for X = N the set of natural numbers, the space R^N is the space of all sequences { (x _ n ) _{n=1}^∞ } with pointwise operations?

Thoughts so far on this problem: a sequence is the same thing as a function on N... so should I just change my notation from x_n to x(n) and x becomes a function N -> R, since the valid values for n are exactly the natural numbers? Could anyone help me?