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  Selected Sites   (see also All Sites in this category)

  1. The Beginnings of Set Theory - MacTutor Math History Archives
    Linked essay describing the rise of set theory from Cantor (with discussion of earlier contributions) through the first half of the 20th century, with another web site and 25 references (books/articles). more>>

  2. Set Theory - Dave Rusin; The Mathematical Atlas
    A short article designed to provide an introduction to set theory. Naive set theory considers elementary properties of the union and intersection operators - Venn diagrams, the DeMorgan laws, elementary counting techniques such as the inclusion-exclusion principle, partially ordered sets, and so on. This is perhaps as much of set theory as the typical mathematician uses. Indeed, one may "construct" the natural numbers, real numbers, and so on in this framework. However, situations such as Russell's paradox show that some care must be taken to define what, precisely, is a set. Axiomatic Set Theory studies the axioms used to describe sets. While alternatives have been proposed (for example the von Neumann-Bernays-Godel and Morse-Kelley formulations), most sets of axioms for Set Theory include the Zermelo-Frankl axioms (ZF). Again, within this formulation one may define the natural numbers, the real numbers, and so on, and thus in principle carry out most ordinary mathematics. This formulation is rich enough to prove, for example, the Schoeder-Bernstein theorem (If X and Y are isomorphic to subsets of each other, then they are isomorphic). History; applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus. more>>


 

Mason error

 
component stack:   /library/branch.html
/library/dhandler
code stack:   /var/lib/mason/obj/library/branch.html:208
/usr/lib/perl5/site_perl/5.6.0/HTML/Mason/Commands.pm:70
/var/lib/mason/obj/library/dhandler:90

debug info:   Debug file is '/var/lib/mason/debug/anon/19'.

raw_error





























raw error:
 






























error while executing /library/branch.html:
Server message number=1105 severity=17 state=4 line=1 text=Can't allocate space for object 'syslogs' in database 'catalog' because 'logsegment' segment is full/has no free extents. If you ran out of space in syslogs, dump the transaction log. Otherwise, use ALTER DATABASE or sp_extendsegment to increase size of the segment.
Statement=INSERT INTO keystorage ( keys ) VALUES ( '77442;71139;67642;16586;10856;17320;17232;17318;8539;16659;7091;41804;17319;3916;68154;4560;8628;11962;6302;16387;76983;9060;17274;64989;8788;16386;76238;75557;8533;17213;5836;8601;16389;76028;6457;41513;8423;...
HTML::Mason::Interp::__ANON__('Server message number=1105 severity=17 state=4 line=1 text=Can\'...') called at /usr/lib/perl5/site_perl/5.6.0/Forum/Key.pm line 284
Forum::Key::store('Forum::Key=HASH(0x8f0f368)') called at /var/lib/mason/obj/library/branch.html line 208
HTML::Mason::Commands::__ANON__('passed_args', 'HASH(0x8eaf2fc)', 'tree', 'topics', 'branch', 'set_theory') called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/Component.pm line 131
HTML::Mason::Component::run('HTML::Mason::Component::FileBased=HASH(0x8f7c074)', 'passed_args', 'HASH(0x8eaf2fc)', 'tree', 'topics', 'branch', 'set_theory') called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/Request.pm line 653
require 0 called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/Request.pm line 653
HTML::Mason::Request::comp('HTML::Mason::Request::ApacheHandler=HASH(0x8e915e4)', '/library/branch.html', 'passed_args', 'HASH(0x8eaf2fc)', 'tree', 'topics', 'branch', 'set_theory') called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/Commands.pm line 70
HTML::Mason::Commands::mc_comp('/library/branch.html', 'passed_args', 'HASH(0x8eaf2fc)', 'tree', 'topics', 'branch', 'set_theory') called at /var/lib/mason/obj/library/dhandler line 90
HTML::Mason::Commands::__ANON__('start_at', 1, 'num_to_see', 50, 'keyid', 40929051) called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/Component.pm line 131
HTML::Mason::Component::run('HTML::Mason::Component::FileBased=HASH(0x8ed991c)', 'HTML::Mason::Component::FileBased=HASH(0x8ed991c)', 'start_at', 1, 'num_to_see', 50, 'keyid', 40929051) called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/Request.pm line 653
require 0 called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/Request.pm line 653
HTML::Mason::Request::comp('HTML::Mason::Request::ApacheHandler=HASH(0x8e915e4)', '/library/topics/set_theory/?keyid=40929051&start_at=1&num_to_see...', 'HTML::Mason::Request::ApacheHandler=HASH(0x8e915e4)', 'HASH(0x8eaedd4)', 'HTML::Mason::Component::FileBased=HASH(0x8ed991c)', 'start_at', 1, 'num_to_see', ...) called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/Request.pm line 159
require 0 called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/Request.pm line 159
HTML::Mason::Request::exec('HTML::Mason::Request::ApacheHandler=HASH(0x8e915e4)', '/library/topics/set_theory', 'start_at', 1, 'num_to_see', 50, 'keyid', 40929051) called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/ApacheHandler.pm line 914
HTML::Mason::ApacheHandler::handle_request_1('HTML::Mason::ApacheHandler=HASH(0x8de4734)', 'Apache=SCALAR(0x8e562f8)', 'HTML::Mason::Request::ApacheHandler=HASH(0x8e915e4)', 'HASH(0x8e93970)') called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/ApacheHandler.pm line 560
require 0 called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/ApacheHandler.pm line 560
HTML::Mason::ApacheHandler::handle_request('HTML::Mason::ApacheHandler=HASH(0x8de4734)', 'Apache=SCALAR(0x8e562f8)') called at /etc/httpd/conf/handler.pl line 97
HTML::Mason::handler('Apache=SCALAR(0x8e562f8)') called at /dev/null line 0
require 0 called at /dev/null line 0