Here is one approach (another being this). Let $ (x_n) $ be a sequence from $ [a,b] $. Then it has an accumulation point $ c \in [a,b] $ : Let’s call an interval $ [p,q] $ “good” if $ x_n \in [p,q] $ for infinitely many $ n $. Break $ I_0 := [a,b] $ into two equal parts $ [a, \frac{a+b}{2}] $ and $[\frac{a+b}{2}, b] $. Atleast one of these mu... Read more 03 Aug 2021 - 1 minute read