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
Real collection function
Euclidean real function
Real function
Rational function
Integer function
Natural number function
Boolean function
Indicator function
Definition D382
Heaviside function
Formulation 0
The Heaviside function is the D218: Boolean function \begin{equation} \mathbb{R} \to \{ 0, 1 \}, \quad x \mapsto \begin{cases} 1, \quad & x \geq 0 \\ 0, \quad & x < 0 \end{cases} \end{equation}
Formulation 1
The Heaviside function is the D218: Boolean function \begin{equation} \mathbb{R} \to \{ 0, 1 \}, \quad x \mapsto I_{[0, \infty)}(x) \end{equation}