Talk:Subset of Real Numbers is Interval iff Connected

This is the theorem that I was searching for ... I understand every thing except the last line in the proof ... But A ′ ∪B ′ =[a..b]

why A' U B' = [a,b] ??? anyone can explain this for me please ?? and I think there is a mistake in this line : Since a∈A ′  and A∪B=∅ , it follows that b ′ >a. it should be A ∩ B = ∅ right ?


 * Good comment. It looks strange to me too. I will get back to it when I have time to think about it.
 * I have fixed your second point, it was a mistake. Should have been $\cap$.--prime mover 00:41, 9 June 2011 (CDT)

I added some lines that hopefully clarified the reason there was a contradiction at the end. Unrelated: we probably want to clarify that this is using the standard topology on the reals, and not just any topology. I'm not sure whether that should be made into a point here or if we should add to the definition page for the real numbers what the standard topology is. -- Qedetc 12:06, 9 June 2011 (CDT)
 * It's already there (indirectly) in the page you go to from Definition:Real Number Line. But it would do no harm to expand that point, as this is clearly a useful page which gets a fair few hits and therefore may well need clarification.
 * I have it in mind to draw a little explanatory picture, which I was in the process of doing this morning when I had a few minutes to look at it then. Having said that, it won't be tonight as I'm too tired for intricate work like that ...