That's a great way to visualize the Cantor set. I would have never thought of writing in in base 3 - but it makes so much sense to do so once you pointed it out
But each of the numbers here is not a limit point, so there is always an irrational number you can use as the endpoints of the separated sets.
I appreciate the explanations, I guess I am still confused though. Hopefully, I can wrap my head around this once I become more familiar with other...
Wouldn't this mean that the points are isolated?
This is exactly what I mean! The problem seems to be if you assume it is totally disconnected, and you assume it's closed, it's hard to imagine it has no isolation points. (Which is the point you were making)
On the other hand, if you...
I am getting ready for grad school in the fall, and re-teaching myself a bunch of undergraduate subjects. Right now I am reading up on the topology of the real number line. I have come across a fact that is really difficult for me to wrap my head around:
The Cantor set is both perfect, and...