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

Advertisements