In a set, the order of its elements is (as far as I know) not important; in a sequence, the order of its elements is important.
Which is the notation I should use in order to define a sequence? I could denote the sequence of positive integers by $S$.
Now, suppose I want to list (in order) the terms of sequence $S$. I'm not sure if the notation
$$S=\{1, 2, 3, 4, ...\}$$
is appropriate. Besides, I'm not sure if using $=$ is appropriate.
Any comments?