ThmDex – An index of mathematical definitions, results, and conjectures.
Standard natural basic real exponential function is strictly isotone
Formulation 0
Let $t \mapsto e^x$ be the D1932: Standard natural real exponential function.
Let $x, y \in \mathbb{R}$ each a D993: Real number such that
(i) \begin{equation} x < y \end{equation}
Then \begin{equation} e^x < e^y \end{equation}
Formulation 1
Let $t \mapsto \exp(x)$ be the D1932: Standard natural real exponential function.
Let $x, y \in \mathbb{R}$ each a D993: Real number such that
(i) \begin{equation} x < y \end{equation}
Then \begin{equation} \exp(x) < \exp(y) \end{equation}