ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Deduction system
Zermelo-Fraenkel set theory
Collection of sets
Set union
Successor set
Inductive set
Set of inductive sets
Set of natural numbers
Definition D3202
Basic natural number set density
Formulation 2
Let $\mathbb{N}$ be the D225: Set of natural numbers such that
(1) $E \subseteq \mathbb{N}$ is a D78: Subset
A D993: Real number $\alpha \in \mathbb{R}$ is the natural number set density of $E$ if and only if \begin{equation} \lim_{n \to \infty} \frac{|E \cap \{ 1, \dots, n \}|}{n} = \alpha \end{equation}