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?

Question

jamesj · Answer

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.

2bornot2b · Answer

I meant; is there any theorem or any understanding that stands on this result?

jamesj · Answer

Yes, I know what you mean.  Off the top of my head no, but I'm sure this could be used productively somewhere.