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Résumé : Problem: Prove that $ 2 = 4$. Solution: Consider the value of the following infinitely iterated exponent: $$\displaystyle \sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\cdot^{\cdot^{\cdot}}}}}$$ Let $ a_n = \sqrt{2} \uparrow \uparrow n$, that is, the above power tower where we stop at the $ n$-th term.