Live briefing
Everything about Subcountability
Mathematical property of sets
In constructive mathematics, a collection is subcountable if there exists a partial surjection from the natural numbers onto it. This may be expressed as where denotes that is a surjective function from onto. The surjection is a member of and here the subclass of is required to be a set. In other words, all elements of a subcountable collection are functionally in the image of an indexing set of counting numbers and thus the set can be understood as being dominated by the countable set. Wikipedia →
đź§ Start here: a 6-step reading path
- Read the overview: SubcountabilityA 5-minute orientation
- Pick up a classic book: PewDiePie MalbuchThe most-reprinted book on the subject
- Read the landmark paper: Subcountability under realizability.Cited 6 times
- Go sideways: Constructive set theoryA closely related topic
- Go sideways: Reverse mathematicsA closely related topic
đź“– Definitions
Noun The property of being subcountable.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
📚 Books worth reading
- 📕PewDiePie MalbuchHelle Färbung · 2019
- 📕PewDiePie KleurboekHeldere Kleuren · 2019
- 📕PewDiePie Coloring BookBright Coloring · 2019
- 📕PewDiePie Libro Da ColorareColorazione Brillante · 2019
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
đź”— Related topics
- Constructive set theory Axiomatic constructive set theory is an approach to mathematical constructivism following the program of axiomatic set theory. The same first-order language…
- Reverse mathematics Reverse mathematics is a program in mathematical logic that seeks to determine which axioms are required to prove theorems of mathematics. Its defining…
- Cantor's diagonal argument Cantor's diagonal argument (among various similar names) is a mathematical proof that there are infinite sets which cannot be put into one-to-one correspondence…
- Axiom of choice In mathematics, the axiom of choice, abbreviated AC or AoC, is an axiom of set theory. Informally put, the axiom of choice says that given any collection…
- Enumeration An enumeration is a complete, ordered listing of all the items in a collection. The term is commonly used in mathematics and computer science to refer…
- Constructive analysis In mathematics, constructive analysis is mathematical analysis done according to some principles of constructive mathematics. The name of the subject contrasts…
- Axiom schema of replacement In set theory, the axiom schema of replacement is a schema of axioms in Zermelo–Fraenkel set theory (ZF) that asserts that the image of any set under any…
- Constructivism (philosophy of mathematics) In philosophy of mathematics, constructivism asserts that it is necessary to find (or "construct") a specific example of a mathematical object in order…