limit misconception, is the result 1 or e? What is the result of : \begin{equation*} \lim_{y \rightarrow \infty}( \lim_{x \rightarrow \frac{1}{y}} 1+x)^y \end{equation*}

$$\lim \limits_{y \to \infty} \left(\lim \limits_{x \to \frac{1}{y}} (1 + x)\right)^y = \lim \limits_{y \to \infty}\left(1 + \frac{1}{y}\right)^y = e$$