Refuting "Memórias de um matematiqueiro"

Why $\lim\limits_{x\to\infty}\left(1+\frac{1}{x}\right)^x=e$ and not 1?

Abstract

One day, in a discussion on the Discord app, one of the members of the discussion attached a link to an interview with Professor Carlos Pereira de Novaes, from UEFS, in which he claims to have developed a new algebra, which he calls ''pseudo-real algebra'', in which complex numbers do not exist. Still in the preface of the book where he presents his ideas, Professor de Novaes questions the limit $\lim\limits_{x\to\infty}\left(1+\frac{1}{x}\right)^x$, stating that its value should be 1, and not $e=2.71828...$. In this article I propose to answer his question and explain the reason for the discrepancy between the numerical results presented in the calculation of the expression for large values ​​of $x$ and the theoretical value $e$.