Question

SO = [0,1]
Remove the middle third to give

S1 = [0,1/3] U [2/3,1]

S2 removes middle third of each component of S1

etc etc.

What is the total length Ln of each Sn?

What is the shortest distance Dn between intervals forming Sn?

What is the limit of Sn and Dn as n -> infinity

Answer 1

and then show
\[\frac{1}{4}\in \lim_{n\rightarrow \infty}S_n\]