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
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
» R3789: Absolute value strictly less than real number iff in symmetric open interval
» R4273: Absolute value function preserves zero
» R4274: Absolute value function escapes to positive infinity in both directions
» R4276: Triangle inequality for absolute value function
» R3416: Absolute value bounds for a basic real number