Let $|\cdot|$ be the D2184: Set cardinality operation.

The

**standard basic natural number counting measure**on $M$ is the D4361: Unsigned basic function \begin{equation} \mathcal{P}(\mathbb{N}) \to [0, \infty], \quad E \mapsto |E| \end{equation}

▾ Set of symbols

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Subset

▾ Power set

▾ Hyperpower set sequence

▾ Hyperpower set

▾ Hypersubset

▾ Subset algebra

▾ Boolean algebra

▾ Sigma-algebra

▾ Discrete sigma-algebra

▾ Discrete measurable space

▾ Point-mass measure

▾ Counting measure

▾ Standard counting measure

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Subset

▾ Power set

▾ Hyperpower set sequence

▾ Hyperpower set

▾ Hypersubset

▾ Subset algebra

▾ Boolean algebra

▾ Sigma-algebra

▾ Discrete sigma-algebra

▾ Discrete measurable space

▾ Point-mass measure

▾ Counting measure

▾ Standard counting measure

Formulation 0

Let $M = (\mathbb{N}, \mathcal{P}(\mathbb{N}))$ be the D5638: Top subset structure of natural numbers.

Let $|\cdot|$ be the D2184: Set cardinality operation.

The**standard basic natural number counting measure** on $M$ is the D4361: Unsigned basic function
\begin{equation}
\mathcal{P}(\mathbb{N}) \to [0, \infty], \quad
E \mapsto |E|
\end{equation}

Let $|\cdot|$ be the D2184: Set cardinality operation.

The