Gourt > Science > Math > Logic and Foundations > Set Theory (1)
Set theory is the mathematical theory of sets, which represent collections of abstract objects. It encompasses the everyday notions, introduced in primary school, of collections of objects, and the elements of, and membership in, such collections. In most modern mathematical formalisms, set theory provides the language in which mathematical objects are described. It is (along with logic and the predicate calculus) one of the axiomatic foundations for mathematics, allowing mathematical objects to be constructed formally from the undefined terms of "set", and "set membership". It is in its own right a branch of mathematics and an active field of ongoing mathematical research.
In naive set theory, sets are introduced and understood using what is taken to be the self-evident concept of sets as collections of objects considered as a whole.
In axiomatic set theory, the concepts of sets and set membership are defined indirectly by first postulating certain axioms which specify their properties. In this conception, sets and set membership are fundamental concepts like point and line in Euclidean geometry, and are not themselves directly defined.
More on [ Set theory ]
.@rcalsaverini A #set:=N distinct objects e.g. {1,2,3}; the #multiset {1,1,2,2,3} is a #collection that is not #set. #math #category #theory
krahfu (John Krah) Sat, 02 Jan 2010 05:51:37 -0000
.@rcalsaverini A #set:=N distinct objects e.g. {1,2,3}; the #multiset {1,1,2,2,3} is a #collection that is not #set. #math #category #theory
Can anyone give me an example of a #collection that is not a #set ? #math #category #theory
rcalsaverini (Rafael Calsaverini) Sat, 02 Jan 2010 05:35:07 -0000
Can anyone give me an example of a #collection that is not a #set ? #math #category #theory
Video: Gaslamp Killer - Low End Theory July 2008 DUBSTEPPING! This set is crazy!!!! http://tumblr.com/xmb55vog6
kirvy (Kirvy Splash) Sat, 02 Jan 2010 03:48:26 -0000
Video: Gaslamp Killer - Low End Theory July 2008 DUBSTEPPING! This set is crazy!!!! http://tumblr.com/xmb55vog6
Just set my personal best playing Power Rangers Main Theme (Punk Cover) by Knockout Theory on #JamLegend, 27,808 points! http://is.gd/5pQ46
budegah159 (Bruno Antonio Neves) Sat, 02 Jan 2010 03:03:32 -0000
Just set my personal best playing Power Rangers Main Theme (Punk Cover) by Knockout Theory on #JamLegend, 27,808 points! http://is.gd/5pQ46
It looks like I'm going to have to set up camp tomorrow in a public library. I need to read up on theory behind the teaching of history.
LN89 (Li 'Lotus' Nguyen) Fri, 01 Jan 2010 22:47:39 -0000
It looks like I'm going to have to set up camp tomorrow in a public library. I need to read up on theory behind the teaching of history.
BlueNC | Looking ahead: Set the agenda: One of the many useful theories taught in journalism school is the theory o... http://bit.ly/5PLZDI
bluenc (bluenc.com) Fri, 01 Jan 2010 18:53:25 -0000
BlueNC | Looking ahead: Set the agenda: One of the many useful theories taught in journalism school is the theory o... http://bit.ly/5PLZDI
A Crash Course in the Mathematics of Infinite Sets - A introductory guide for philosophers by Peter Suber, explaining the use of infinitary set theory.
A New System of Axioms Instead of ZF - The page claims that the axioms shown below have the contents that should overturn the set theory of today
Axiom of Choice and Continuum Hypothesis - Part of the Frequently Asked Questions in Mathematics.
Bounded Set Theory - A weak version of ordinary set theory using bounded quantification. Papers and software.
500
Cantor's Donut Paradox - Reassessing Uncountability and the Continuum Hypothesis with Reference to a Novel Geometrical Analogue of the Aleph Series.
Cantor's Theorem - Article in the Platonic Realms, describing Cantor's diagonal argument that proved that infinity comes in many different 'sizes'.
Meta Description: [ Cantor's Theorem of Infinite Sets, from the Platonic Realms Interactive Math Encyclopedia. ]
Consequences of the Axiom of Choice Project - Project to keep the book (also named in the title), describing forms related to the Axiom of Choice and their implications, updated.
Equivalence Relation - Encyclopedia entry on equivalence relations and their role in set theory.
Meta Description: [ Encyclopedia information on Equivalence Relation ]
Extending Set Theory - Extends the language of set theory through restricted self-reference and through certain large cardinals. Also discusses higher order set theory and axiomatization through reflection principles.
Meta Description: [ Extends the Language of Set Theory ]
Infinite Ink: The Continuum Hypothesis, by Nancy McGough - History, mathematics, metamathematics, and philosophy of Cantor's Continuum Hypothesis
Meta Description: [ History, mathematics, metamathematics, and philosophy
of Cantor's Continuum Hypothesis ]
Metamath Proof Explorer - Over 3000 complete formal proofs deriving numbers and beyond from Zermelo-Fraenkel set theory axioms.
New Foundations - Set theory introduced by W. V. O. Quine in 1937. This is a refinement of Russell's theory of types based on the observation that the types in Russell's theory look the same, as far as one can apparently prove.
Operational Set Theory - Description, errata and reviews of a book by Luis E. Sanchis.
Programming with Sets - Using set-theoretic primitives as a conceptual tool in programming, includes discussion of SETL and MIRANDA languages.
Set Theoretic Analysis. - On a part of math where Set Theory, Topology and Analysis meet. Has surveys, preprints, conference announcements, book reviews and problems.
Meta Description: [ Set Theoretic Analysis Web Page. ]
Set Theorists - A list of email addresses and affiliations.
Set Theory - Directory of set theorists, maintained by Jean A. Larson.
Meta Description: [ a collection of homepages of set
theorists, together with a few additional links, was started in 1997,
and last updated 2007/10/17 ]
Set Theory - From Dave Rusin's Known Math collection.
Set Theory - Survey from the Stanford Encyclopedia of Philosophy by Thomas Jech.
Set Theory for the Working Mathematician - Krzysztof Ciesielski, CUP (1997). Contents and preface.
Set Theory Page - Collection of links related to set theory.
404
Sets and Their Sizes - An alternative to Cantor's theory of cardinality. Dissertation by Fred M. Katz.
Shelah's Archive - Listing of all articles by Saharon Shelah, and links to many of them.
Meta Description: [ This page contains the archive of Saharon Shelah's mathematical papers.
Professor Shelah is a mathematician working at the
Hebrew University of Jerusalem and Rutgers University in New Jersey, USA. ]
The Axiom of Choice - This page gives a brief explanation of the Axiom of Choice and links to other related websites.
Meta Description: [ Axiom of Choice ]
The Beginnings of Set Theory - MacTutor History of Mathematics topic.
The Future of Set Theory by S. Shelah - The text of a talk given around the millennium.
500
The Mathematics of Set Theory - Detailed description of parts of introductory set theory.
Meta Description: [ Detailed description of set theory. ]
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