Infinite Union!

Algebra Level 4

\[\left[\dfrac 12,1\right]\cup \left[\dfrac 14,\dfrac 12 \right]\cup \left[\dfrac 18,\dfrac 14\right]\cup \cdots=X\]
Then which of the options describe the set \(X\)?

Clarification: All sets on the left are of the form \(\left[\dfrac 1{2^{n+1}},\dfrac 1{2^n}\right]\) for some integer \(n\).


Inspiration

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