Here's the question you clicked on:
2bornot2b
Does it help in any way, to think of sequences as countable subsets of the Real numbers? Does this way of thinking take us anywhere important?
The concepts are so close, it's hard for me to think of useful properties of countable subsets of the reals without immediately thinking of them as a sequence. So for the moment I'm going to provisionally say probably not.
I meant; is there any theorem or any understanding that stands on this result?
Yes, I know what you mean. Off the top of my head no, but I'm sure this could be used productively somewhere.