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
Binary endorelation
Preordering relation
Partial ordering relation
Partially ordered set
Closed interval
Implicit interval partition
Implicit basic real interval partition
Closed real interval tagged partition
Stieltjes sum
Riemann sum
Riemann integrable real function
Real Riemann integral
Definition D865
Standard natural real logarithm function
Formulation 0
The standard natural real logarithm function is the D4364: Real function \begin{equation} \log : (0, \infty) \to \mathbb{R}, \quad \log(x) = \int^x_1 \frac{1}{t} \, d t \end{equation}
Formulation 1
The standard natural real logarithm function is the D4364: Real function \begin{equation} \log : (0, \infty) \to \mathbb{R}, \quad \log(x) = \int^x_1 \frac{dt}{t} \end{equation}
Formulation 2
The standard natural real logarithm function is the D4364: Real function \begin{equation} \log : (0, \infty) \to \mathbb{R}, \quad \log(x) = \int^x_1 t^{-1} \, d t \end{equation}
Children
Natural real entropy function
Standard real log-sum-exp function
Standard real logarithm function
Results
Base inversion property of standard natural logarithm function
Conventions
Convention 0 (Notation for standard natural basic real logarithm function)
The notation used for the D865: Standard natural real logarithm function is $x \mapsto \log(x)$ or $x \mapsto \ln(x)$.