A child plays the following game with a calculator. He types an integer n at random and repeatedly presses the “square root” button, computing $\sqrt{n},\sqrt{\sqrt{n}},\sqrt{\sqrt{\sqrt{n}}}$, and so on. The calculator has a numerical precision $e$ (with $e\gt 0$ and $e \lt 1$) so that every real number $x$ between $1$ and $1 + e$ appears as 1 on the display of the calculator. Show that the child will see the number 1 on the display after pressing the square root button for $\Theta(\log (\log n) + \log (\frac{1}{e}) )$ times, where log denotes the logarithm in base 2
2026-04-12 18:45:52.1776019552
Proof Question. Set, Relation and Function
99 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in REAL-ANALYSIS
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