Chapter 6, Exploration 35

The binary expansion of the point $s=.010101\dots$ is given in the textbook. The slider below for $n$ moves through the points in the expansion of $s$, narrowing the intervals in which $s$ can be found. $s$ is always in the orange interval. Explore how this interval changes as you adjust the slider. Think carefully about what this means in terms of the coordiantes of $s$.