How to interpret this problem involving dyadic squares and unit disc?

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The discussion revolves around a problem from "Real Mathematical Analysis" by Charles Chapman Pugh, which asks to demonstrate that for any given ε > 0, the unit disc contains finitely many dyadic squares whose total area exceeds π - ε and that intersect only along their boundaries. The initial interpretation of the problem was incorrect, as it suggested that any collection of dyadic squares meeting these criteria would necessarily be finite, which is not true. The correct understanding is to determine the existence of a finite set of dyadic squares satisfying the area condition and boundary intersection.

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The following problem is from the textbook "Real Mathematical Analysis" by Charles Chapman Pugh.

Given ##\epsilon > 0##, show that the unit disc contains finitely many dyadic squares whose total area exceeds ##\pi - \epsilon##, and which intersect each other only along their boundaries.​

I find myself unable to understand what the problem is asking to show. At first glace, I thought it was asking to show that given any ##\epsilon##, any collection of dyadic squares that 1) had a total area of greater than ##\pi - \epsilon## and 2) intersected along their boundaries would necessarily be finite. However, this assertion is obviously not true. [Let ##\epsilon > \pi## and consider the infinite collection of dyadic squares ##\{[0,\frac{1}{2}]\times[0,\frac{1}{2}],[\frac{1}{2},\frac{3}{4}]\times[0,\frac{1}{4}],[\frac{3}{4},\frac{7}{8}]\times[0,\frac{1}{8}],...\}##]

What am I missing?
 
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After some additional thought, maybe the problem is actually just asking if given an ##\epsilon > 0##, does there exists a finite set of dyadic squares whose area is greater than ##\pi - \epsilon##, and which intersect only along their boundaries?
 

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