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
▼ Operation
▼ N-operation
▼ Binary operation
▼ Enclosed binary operation
▼ Groupoid
▼ Semigroup
▼ Standard N-operation
▼ Exponentiation
▼ Root
▼ Real root
▼ Rational exponentiation
▼ Real exponentiation
Definition D2410
Standard real exponentiation function
Formulation 0
The standard real exponentiation function with exponent $p \in \mathbb{R}$ is the D4364: Real function \begin{equation} \begin{cases} \mathbb{R} \setminus \{ 0 \} \to \mathbb{R}, \quad & x \mapsto x^p, \qquad \text{ if } p < 0 \\ \mathbb{R} \to \mathbb{R}, \quad & x \mapsto x^p, \qquad \text{ if } p \geq 0 \\ \end{cases} \end{equation}
Children
▶ D6050: Real square function