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The Proof That 2=4

Let’s look at the following equations:
1. $x^{x^{x^{ \ldots}}} = 2$
2. $y^{y^{y^{\ldots}}} = 4$

From (1) we get that $x^2 = 2$ , thus $x=\sqrt 2$

From (2) we get that $y^4 = 4$ , thus $y = \sqrt[4]{4}$

But $\sqrt 2 = \sqrt[4]4$

And thus …
$2 = x^{x^{x^{\ldots}}} = \sqrt 2^{\sqrt 2^{\sqrt 2 ^ {\ldots}}} = \sqrt[4]4^{\sqrt[4]4^{\sqrt[4]4^ {\ldots}}} = y^{y^{y^{\ldots}}} = 4$

QED