ThmDex – An index of mathematical definitions, results, and conjectures.
Result R4284 on D865: Standard natural real logarithm function
Standard natural basic real logarithm function escapes to negative infinity at zero
Formulation 0
Let $x \mapsto \log x$ be the D865: Standard natural real logarithm function.
Then \begin{equation} \log x \to - \infty \quad \text{ as } \quad x \searrow 0 \end{equation}
Formulation 1
Then \begin{equation} \ln x \to - \infty \quad \text{ as } \quad x \searrow 0 \end{equation}