Construct an uncountable chain of at most countable sets, with the union uncountable. Ask Question Asked4 months ago Modified4 months ago Viewed72 times 2 Question: Give a construction of a family of uncountably infinite many sets{Ai}i∈I{subject to: (1){Ai}i∈I{is ...
Let SS be the union of all SiSi. Take the complement of SS in RR. I have a few queries about this set. I'm sure they are all somewhat trivial but i've thought a bit about them and the penny still hasn't dropped. Firstly, by considering a geometric series SS has maximum length ...
Then, by Proposition 5, \overline{B(x,\epsilon)} \setminus (E \cap B(x, \epsilon)) would have to contain an open interval, which must be contained in the interior of \overline{B(x,\epsilon)} \setminus (E \cap B(x, \epsilon)) , which is an open subset of I \setminus E ....
Union of countable sets is countable: N∼AN∼A and N∼B⇒N∼A∪BN∼B⇒N∼A∪BI can negate this statement in the following way(1) N≁A⇒N≁A∪BN≁A⇒N≁A∪BI can pick x1,x2∈Ax1,x2∈A such that