Understanding how the Cantor set contains the point $4/9.$

Question

Here is a statement from Bartle "Introduction to real analysis" that say that the Cantor set contains the point $4/9$ when $k=2$ and $n=2.$

I know from the first Cantor set $F_1,$ that we removed the interval $(1/3, 2/3)$ but the statement above says that $4/9$ is in the cantor set, how is that? could someone explain this to me?

Answer 1

Be careful parsing the language.

All endpoints of intervals that are in the Cantor set are of that form, but the author is not saying the converse, namely that all points of that form are endpoints of intervals in the Cantor set.