I was reading Gerald Edgar's "Measure, Topology, and Fractal Geometry" when I came across this exerxise

(S_0 is the starting triangle with side one) How can I prove it? I don't see the exercice being true. I'm confused about this point this point in the picture, which i think has coordinates (0.1,0.1) in base 2, contradicting the thing I want to prove.

I was reading Gerald Edgar's "Measure, Topology, and Fractal Geometry" when I came across this exercise

Let coordinates $(u,v)$ be defined in the plane with origin at one corner of the triangle $S_0$, and axes along two of the sides of $S_0$. Then $(u,v)$, with $0\leq u\leq 1, 0\leq v\leq 1$, represent a point of the Sierpinski gasket iff the base $2$ expansion of $u$ and $v$ never have $1$ in the same place.

($S_0$ is the starting triangle with side one) How can I prove it? I don't see the exercice being true. I'm confused about this point []in the picture, which i think has coordinates $(0.1,0.1)$ in base $2$, contradicting the thing I want to prove.