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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?

Mathematics
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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.

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