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Everything about Finite set
Finite collection of distinct objects
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 mathematical objects, such as numbers, symbols, points in space, lines, other geometric shapes, variables, or other sets. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Finite setA 5-minute orientation
- Skim a recent paper: Finite-Control-Set Model Predictive Control of Permanent Magnet Synchronous Motor Drive Systems—An OverviewInfluential work since 2022
- Pick up a classic book: Finite ordered setsThe most-reprinted book on the subject
- Read the landmark paper: Finite constraint set receding horizon quadratic controlCited 127 times
- Go sideways: Dedekind-infinite setA closely related topic
- Go sideways: Axiom of choiceA closely related topic
📖 Definitions
Noun A set with only finitely many members. This includes the empty set.
🏆 Landmark papers (most cited)
Finite constraint set receding horizon quadratic control
The Contact Process on a Finite Set
Finite basis set versus finite difference and finite element methods
Sensorless Simplified Finite Control Set Model Predictive Control of SynRM Using Finite Position Set Algorithm
Finite population corrections for ranked set sampling
A finite set covering theorem
Interaction transform of set functions over a finite set
Temporal Answer Set Programming on Finite Traces
🆕 Influential since 2022
Finite-Control-Set Model Predictive Control of Permanent Magnet Synchronous Motor Drive Systems—An Overview
Finite Control Set Model Predictive Control for Dual Active Bridge Converter
Finite Control-Set Learning Predictive Control for Power Converters
An Overview of Multi-Object Estimation via Labeled Random Finite Set
Finite-Set Model Predictive Control for Hybrid Active Power Filter
📚 Books worth reading
- 📕Finite ordered setsNathalie Caspard · 2012
Advanced combinatoricsLouis Comtet · 1974
Groups, Difference Sets, and the MonsterK. T. Arasu · 1995
Characters and Cyclotomic Fields in Finite GeometryBernhard Schmidt · 2002
Combinatorics of finite setsIan Anderson · 1987- 📕You xian shu xue yin lunGong, Guanglu. · 1982
The Role of True Finiteness in the Admissible Recursively Enumerable Degrees (Memoirs of the American Mathematical Society, No. 854) (Memoirs of the American Mathematical Society)Noam Greenberg · 2006- 📕The role of true finiteness in the admissible recursively enumerable degreesNoam Greenberg · 2006
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Dedekind-infinite set In mathematics, a set A is Dedekind-infinite (named after the German mathematician Richard Dedekind) if some proper subset B of A is equinumerous to A…
- 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…
- Glossary of set theory Look up Appendix:Glossary of set theory in Wiktionary, the free dictionary. This is a glossary of terms and definitions related to the topic of set theory…
- Group structure and the axiom of choice In mathematics a group is a set together with a binary operation on the set (usually called multiplication) that obeys the group axioms. The axiom of choice…
- Axiom of countable choice The axiom of countable choice or axiom of denumerable choice, denoted ACω, is an axiom of set theory that states that every countable collection of non-empty…
- Ultrafilter on a set In the mathematical field of set theory, an ultrafilter on a set X is a maximal filter on the set X. In other words, it is a collection of subsets of X…
- Paradoxes of set theory This article contains a discussion of paradoxes of set theory. As with most mathematical paradoxes, they generally reveal surprising and counter-intuitive…
- Countable set 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…