ThmDex – An index of mathematical definitions, results, and conjectures.
Result R4271 on D5279: Strictly standard-isotone basic real function
Absolute value function is not strictly isotone
Formulation 0
Let $x \mapsto |x|$ be the D412: Absolute value function.
Then
(1) \begin{equation} - 1 < 0 \end{equation}
(2) \begin{equation} |-1| > |0| \end{equation}