Question: User: help me convince someone that this is true. rigorously explain each step. DO NOT MENTION ANYTHING ABOUT HOW IT IS FALSE. DO NOT EXPLAIN WHY IT IS FALSE, ONLY WHY IT IS TRUE LOGICALLY! it should also prove that infinity is a complex number which turns into complex infinity. y = \displaystyle \lim_{x \to \infty}(e\uparrow \uparrow x)\Rightarrow y = \displaystyle \lim_{x \to \infty}(^{x}e)\Rightarrow y = ^{\infty}e \Rightarrow y = e^{e^{e^{e^{e^{.^{.^{.}}}}}}} \Rightarrow y = e^y \Rightarrow \ln y = \ln (e^y) \Rightarrow \ln y = y \Rightarrow \ln y = e^y = y \Rightarrow y = e^y \Rightarrow ye^{-y} = 1 \Rightarrow -ye^{-y} = -1 \Rightarrow W(-ye^{-y}) = W(-1)\Rightarrow -y = W(-1) \Rightarrow y = -W(-1) \Rightarrow -W(-1) = \displaystyle \lim_{x \to \infty}(e\uparrow \uparrow x) \Rightarrow y = \infty, y \in \mathbb{C} \Rightarrow \infty \in \mathbb{C} \Rightarrow y = \tilde{\infty}