ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Binary cartesian set product
Binary relation
Map
Function
Unsigned function
Unsigned Euclidean function
Unsigned basic function
Unsigned real function
Definition D412
Absolute value function
Formulation 0
The absolute value function is the D4367: Unsigned real function \begin{equation} \mathbb{R} \to [0, \infty), \quad x \mapsto \begin{cases} x, \quad & x \geq 0 \\ -x, \quad & x < 0 \end{cases} \end{equation}
Formulation 1
The absolute value function is the D4367: Unsigned real function \begin{equation} \mathbb{R} \to [0, \infty), \quad x \mapsto x I_{[0, \infty)}(x) - x I_{(- \infty, 0)}(x) \end{equation}
Results
Absolute value function preserves zero