## Footnote

2However, note we have not shown this. We have not shown that the limit $$\lim_{h \to 0} \dfrac{a^h - 1}{h}$$ is a continuous function of $$a$$; otherwise, this limit might never take the value 1. And we have not shown that the limit is a strictly increasing function of $$a$$; if not, there might be multiple values of $$a$$ for which the limit is 1. The alternative treatment later in this module avoids these issues.