ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Collection of sets
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Set of inductive sets
Set of natural numbers
Definition D3200
Lower basic natural number set density
Formulation 0
Let $\mathbb{N}$ be the D225: Set of natural numbers such that
(1) $E \subseteq \mathbb{N}$ is a D78: Subset
The lower basic natural number set density of $E$ is the D993: Real number \begin{equation} \liminf_{n \to \infty} \frac{|E \cap \{ 1, \dots, n \}|}{n} \end{equation}