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Everything about Countable set
Mathematical set that can be enumerated
A mathematical set is countable if either it is finite or it can be put in one to one correspondence with the set of natural numbers. Equivalently, a set is countable if there exists an injective function from it into the natural numbers; this means that each element in the set may be associated to a unique natural number, or that the elements of the set can be counted one at a time, although the counting may never finish due to an infinite number of elements. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Countable setA 5-minute orientation
- Skim a recent paper: Comments on “Fractal set of generalized countable partial iterated function system with generalized contractions via partial Hausdorff metric”Influential work since 2022
- Pick up a classic book: Mathematical structures for computer scienceThe most-reprinted book on the subject
- Read the landmark paper: Ultrafilters on a countable setCited 122 times
- Go sideways: Cantor's diagonal argumentA closely related topic
- Go sideways: EnumerationA closely related topic
📖 Definitions
Noun A set that is countable.
🏆 Landmark papers (most cited)
Ultrafilters on a countable set
Generation of a countable set of homoclinic flows through bifurcation
Numerical representation of intransitive preferences on a countable set
Algorithms for Countable State Markov Decision Models with an Absorbing Set
Necessary and sufficient conditions for transversals of countable set systems
A countable set of directions is sufficient for Steiner symmetrization
Integrals of Set-Valued Functions with a Countable Range
Subsets of a Countable Set
🆕 Influential since 2022
Comments on “Fractal set of generalized countable partial iterated function system with generalized contractions via partial Hausdorff metric”
A HC model with countable set of spin values: Uncountable set of Gibbs measures
Bi-utility representable orderings on a countable set
Fractal set of generalized countable partial iterated function system with generalized contractions via partial Hausdorff metric
On the set of Gibbs measures for model with a countable set of spin values on Cayley trees
📚 Books worth reading
Mathematical structures for computer scienceJudith L. Gersting · 1982
Discrete and combinatorial mathematicsRalph P. Grimaldi · 1985
How to prove itDaniel J. Velleman · 1994
Languages and machinesThomas A. Sudkamp · 1988
Introduction to model theoryPhilipp Rothmaler · 2000
Convergence structures and applications to functional analysisR. Beattie, H.-P. Butzmann · 2002
Gibbs states on countable setsChristopher J. Preston · 1974
Fundamentals of computingVangalur S. Alagar · 1989
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- 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…
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- Finite set In mathematics, a finite set is a collection of finitely many different things; the things are called elements or members of the set and are typically…
- Uncountable set In mathematics, an uncountable set, informally, is an infinite set that contains too many elements to be countable. The uncountability of a set is closely…