Let $E$ be the set of all even natural numbers. $\huge E =\setbuild{n \in \N}{2n} $ [[Linear Transformation|nonlinear]] storytelling $\tiny \color{red} \N \cong E \therefore |\N| = |E| $ $\huge \begin{align} f: \N &\to E \\ f(n) &= 2n \\ \\ f^{-1}: E &\to \N \\ f^{-1}(k) &= \frac{n}{2} \end{align}$ $\tiny \color{red} \N \cong E \therefore |\N| = |E| $ $\tiny \color{red} \N \cong E \therefore |\N| = |E| $ $\huge \color{red}\boxed{ \color{peach} \N \cong E \therefore |\N| = |E| } $ $\huge \N \cong \Q $ ![[Pasted image 20251116220554.png|invert_S]]