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Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics. The modern study of set theory was initiated by Georg Cantor and Richard Dedekind in the 1870s. After the discovery of paradoxes in informal set theory, numerous axiom systems were proposed in the early twentieth century, of which the Zermelo–Fraenkel axioms, with the axiom of choice, are the best-known. The language of set theory is used in the definitions of nearly all mathematical objects, such as functions, and concepts of set theory are integrated throughout the mathematics curriculum. Elementary facts about sets and set membership can be introduced in primary school, along with Venn and Euler diagrams, to study collections of commonplace physical objects. Elementary operations such as set union and intersection can be studied in this context. More advanced concepts such as cardinality are a standard part of the undergraduate mathematics curriculum. Set theory is commonly employed as a foundational system for mathematics, particularly in the form of Zermelo–Fraenkel set theory with the axiom of choice. Beyond its foundational role, set theory is a branch of mathematics in its own right, with an active research community. Contemporary research into set theory includes a diverse collection of topics, ranging from the structure of the real number line to the study of the consistency of large cardinals. From Wikipedia under the
GNU Free Documentation License  foto.detik.com 595px x 450px | 31.00kB [source page] For the conspiracy theory angle some people like Indonesia Corruption Watch ICW are saying he was set up because the KPK was going to investigate the electoral commission KPU which sorta ties in with  web.maths.unsw.edu.au 38px x 107px | 0.89kB [source page] will tell you anyway is itself a set also a very simple one with just two elements called and Thus Can we move on now Wait someone insists on knowing what are and They are also sets also with two From Yahoo Image Search: "Set theory"  scorechase.com Hagrid Wed, 02 Dec 2009 17:58:14 GM Q. 50% of elements in A are also there in B. Does A have more elements than B? 1) 40% elements of B are not in A 2) There are 30 elements which are.  e-booksdirectory.com unknown hu, 03 Sep 2009 05:00:00 GM An Introduction to . Set Theory. - free book at E-Books Directory - download here.  mathhelpforum.com Noxide hu, 19 Nov 2009 01:36:27 GM A = { a, b, c, d, e, f, g} Expression: x = y such that x, y are in A can x in A refer to the same thing as y in A or can it necessarily not because of the notation x, y in A? From Google Blog Search: "Set theory"  news.google.com Sydney Morning Herald Removing the ability of a government to pick an election date to benefit itself isn't bad theory . Unfortunately, the Parliament at the time wasn't counting ... news.google.com Los Angeles Times The Big Bang Theory : The holidays aren't very merry for Leonard (Johnny Galecki) when a handsome colleague (Michael Trucco) begins dating Penny (Kaley ... and more » news.google.com Toledo Blade I think there is something to that - a kind of Heisenberg Theory of public life, positing that the very act of observing something changes the object being ... and more » From Google News Search: "Set theory" Why is it important to be able to identify sets and set theory as related to business operations? Q. Why is it important to be able to identify sets and set theory as related to business operations? Asked by bnyce8 - Mon Apr 21 05:30:55 2008 - - 1 Answers - 0 Comments A. Sets and set theory is used heavily in business. For example, chart of accounts. This is how businesses classify their financial transactions. A chart of accounts often classifies transactions based on multiple criteria such as business unit, dept, type of transaction, etc. Each of these is a subset of all transactions that may or may not intersect with each other. Without a good understanding of set theory some transactions could be double counted when putting ogether financial reports. Answered by Joe J - Mon Apr 21 21:06:42 2008 Could somebody please explain the following types of relations in set theory? Q. I think I understand symmetric relations and transitive relations but am unclear on what is meant by an anti-symmetric or reflexive relation. Please do not quote or point me in the direction of wikipedia as this does not make it any easier to comprehend. Thanks. Asked by Jsh - Wed Sep 10 05:05:33 2008 - - 1 Answers - 0 Comments A. Formally, the definition of anti-symmetry is, "A relation is anti-symmetric if aRb and bRa imply a=b." That is, an anti-symmetric relation can have pairs like 1R1 and 2R2 -- but those are the only way symmetry can be satisfied. If an antisymmetric relation contains has (a,b) and a is not equal to b, then it doesn't contain (b,a) Consider the set A={1,2,3,4} and the relations: R1 = {(1,1),(2,2),(3,3),(4,4)} R2 = {(1,1),(2,2),(3,3),(4,4), (1,2)} R3 = {(1,1),(2,2),(3,3),(4,4), (1,2),(2,1)} Notice that: R1 is both symmetric and anti-symmetric. It is symmetric because for every (a,b) in R1, (b,a) is also in R1: (a,b) = (1,1) is in R1 and (b,a) = (1,1) is in R1 (a,b) = (2,2) is in R1 and (b,a) = (2,2) is in R1 (a,b) = (3,3) is in R1… [cont.] Answered by Billy C - Wed Sep 10 10:14:52 2008 where can i find a website that explain everything about set theory?
Q. where can i find a website that explain everything about set theory? Asked by sochn9022jkl - Mon Mar 26 09:55:03 2007 - - 1 Answers - 0 Comments A. check these URL's 1) 2) 3) Answered by tobi - Mon Mar 26 10:27:20 2007 From Yahoo Answer Search: "Set theory" |
