Where is the limit for folding paper in half?

If you could fold typical sheet of printer paper, a tenth of a milimeter thick, in half 37 consecutive times, you’d end up with folded paper thicker than the diameter of the Earth. Mind you, the footprint of that paper tower would be less than a billionth of a square inch. That is, evidently, impossible. So where is the limit for folding paper in half?

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