Lesson plan
Subcountability
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} .
Article 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} .
Key claims
No claims recorded.
Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
No sources recorded.
Key claims and bibliography are generated from the same tracked claims and sources as the article page.