en>Yobot: Autotagging using AWB (9112)

2013-04-28T09:35:59Z

Autotagging using AWB (9112)

← Older revision		Revision as of 11:35, 28 April 2013
Line 1:		Line 1:
	~~Let me initial begin by introducing myself~~. ~~My name~~ is ~~Boyd Butts even though it~~ is ~~not~~ the ~~title~~ on ~~my birth certificate~~. ~~He utilized~~ to be ~~unemployed but now he is~~ a ~~meter reader~~. ~~North Dakota~~ is ~~exactly where me~~ and ~~my husband reside. To gather cash~~ is ~~what her family and her enjoy~~.~~<br><br>Also visit my page~~ ... [~~http~~:~~//telekomxchange.com/groups/prevent-infections-before-hand-using-these-tips/ at home std testing~~]		[[Image:Banach-Tarski Paradox.svg\|thumb\|right\|350px\|The [[Banach–Tarski paradox]] is that a ball can be decomposed into a finite number of point sets and reassembled into two balls identical to the original.]]
			In [[set theory]], a '''paradoxical set''' is a set that has a '''paradoxical decomposition'''. A paradoxical decomposition of a set is a [[partition of a set\|partitioning]] of the set into two subsets, along with an appropriate [[Group (mathematics)\|group]] of functions that operate on some universe (of which the set in question is a subset), such that each partition can be mapped back onto the entire set using only finitely many distinct functions (or compositions thereof) to accomplish the mapping. Since a paradoxical set as defined requires a suitable group <math>G</math>, it is said to be <math>G</math>-paradoxical, or paradoxical with respect to <math>G</math>.

			Paradoxical sets exist as a consequence of the [[Axiom of Infinity]]. Admitting infinite classes as sets is sufficient to allow paradoxical sets.

			== Examples ==
			=== Banach–Tarski paradox ===
			{{main\|Banach–Tarski paradox}}

			The most famous, and indeed motivational, example of paradoxical sets is the [[Banach–Tarski paradox]], which divides the sphere into paradoxical sets for the [[special orthogonal group]]. This result depends on the [[axiom of choice]].

			== References ==
			* S. Wagon, The Banach–Tarski Paradox, Cambridge University Press, 1986.

			{{DEFAULTSORT:Paradoxical Set}}
			[[Category:Set theory]]
			[[Category:Geometric dissection]]

en>Mwtoews: aka BNL

2011-07-03T22:21:08Z

aka BNL

New page

Let me initial begin by introducing myself. My name is Boyd Butts even though it is not the title on my birth certificate. He utilized to be unemployed but now he is a meter reader. North Dakota is exactly where me and my husband reside. To gather cash is what her family and her enjoy.<br><br>Also visit my page ... [http://telekomxchange.com/groups/prevent-infections-before-hand-using-these-tips/ at home std testing]

Block nested loop - Revision history

en>Yobot: Autotagging using AWB (9112)

en>Mwtoews: aka BNL