---
tag: KCWGZS2AKQ
kind: concept
name: Subcountability
aliases: [subcountable]
sources:
  - wikipedia: en:15036487@r1353262140
    locator: Subcountability
    note: adopted
    mention: wikipedia://en/15036487
    sections: [Summary]
same_as:
  wikidata: Q7630981
  wikipedia: Subcountability
inventory: [CK7FYA06BN]
---

## Summary

In constructive mathematics, a collection $X$ is **subcountable** if there exists a partial surjection from the natural numbers onto it. This may be expressed as

$$\exists (I\subseteq{\mathbb N}).\, \exists f.\, (f\colon I\twoheadrightarrow X),$$

where $f\colon I\twoheadrightarrow X$ denotes that $f$ is a surjective function from $I$ onto $X$. The surjection is a member of ${\mathbb N}\rightharpoonup X$ and here the subclass $I$ of ${\mathbb N}$ is required to be a set. In other words, all elements of a subcountable collection $X$ are functionally in the image of an indexing set of counting numbers $I\subseteq{\mathbb N}$ and thus the set $X$ can be understood as being dominated by the countable set ${\mathbb N}$.