ThmDex – An index of mathematical definitions, results, and conjectures.
Result R4273 on D412: Absolute value function
Absolute value function preserves zero
Formulation 0
Let $x \mapsto |x|$ be the D412: Absolute value function.
Then \begin{equation} |0| = 0 \end{equation}
Proofs
Proof 0
Let $x \mapsto |x|$ be the D412: Absolute value function.
By definition, $|x| = x$ whenever $x \geq 0$. Since $0 \geq 0$, then, in particularly, $|0| = 0$. $\square$