en>My name is not dave at 21:25, 5 December 2013

2013-12-05T21:25:33Z

← Older revision		Revision as of 23:25, 5 December 2013
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	~~Jayson Berryhill~~ is ~~how I~~'~~m known~~ as and ~~my spouse doesn~~'~~t like it at all~~. ~~He works as~~ a ~~bookkeeper~~. ~~One~~ of the ~~extremely very best psychics~~, ~~[http:~~//~~gcjcteam~~.~~org/index~~.~~php?mid~~=~~etc_video&document_srl~~=~~696611&sort_index~~=~~regdate&order_type~~=~~desc gcjcteam.org~~], ~~things~~ in ~~the globe for him~~ is ~~doing ballet~~ and he'll be ~~starting something else alongside with it~~. ~~Alaska~~ is ~~where I've always been living~~.		{{merge\|Two-element Boolean algebra\|discuss=Wikipedia talk:WikiProject Logic/Boolean algebra task force#Two-element Boolean algebra\|date=February 2012}}
			In [[mathematics]] and [[abstract algebra]], a '''Boolean domain''' is a [[Set (mathematics)\|set]] consisting of exactly two elements whose interpretations include ''false'' and ''true''. In [[logic]], mathematics and [[theoretical computer science]], a Boolean domain is usually written as {0, 1},<ref>[[Dirk van Dalen]], ''Logic and Structure''. Springer (2004), page 15.</ref><ref>[[David Makinson]], ''Sets, Logic and Maths for Computing''. Springer (2008), page 13.</ref><ref>[[George Boolos\|George S. Boolos]] and [[Richard C. Jeffrey]], ''Computability and Logic''. Cambridge University Press (1980), page 99.</ref> {false, true}, {F, T},<ref>[[Elliott Mendelson]], ''Introduction to Mathematical Logic (4th. ed.)''. Chapman & Hall/CRC (1997), page 11.</ref> or <math>\left \{ \bot,\top \right \}</math>.<ref>[[Eric C. R. Hehner]], ''A Practical Theory of Programming''. Springer (1993, 2010), page 3.</ref>

			The [[algebraic structure]] that naturally builds on a Boolean domain is the [[two-element Boolean algebra\|Boolean algebra with two elements]]. The [[initial object]] in the [[category (mathematics)\|category]] of [[bounded lattice]]s is a Boolean domain.

			In [[computer science]], a Boolean variable is a [[Variable (programming)\|variable]] that takes values in some Boolean domain. Some [[programming language]]s feature [[reserved word]]s or symbols for the elements of the Boolean domain, for example <code>false</code> and <code>true</code>. However, many programming languages do not have a [[Boolean datatype]] in the strict sense. In [[C (programming language)\|C]] or [[BASIC]], for example, falsity is represented by the number 0 and truth is represented by the number 1 or −1 respectively, and all variables that can take these values can also take any other numerical values.

			== Generalizations ==
			The Boolean domain {0, 1} can be replaced by the [[unit interval]] {{closed-closed\|0,1}}, in which case rather than only taking values 0 or 1, any value between and including 0 and 1 can be assumed. Algebraically, negation (NOT) is replaced with <math>1-x,</math> conjunction (AND) is replaced with multiplication (<math>xy</math>), and disjunction (OR) is defined via [[De Morgan's law]] to be <math>1-(1-x)(1-y)</math>.

			Interpreting these values as logical [[truth value]]s yields a [[multi-valued logic]], which forms the basis for [[fuzzy logic]] and [[probabilistic logic]]. In these interpretations, a value is interpreted as the "degree" of truth – to what extent a proposition is true, or the probability that the proposition is true.

			==See also==
			* [[Boolean-valued function]]

			==Notes==
			{{reflist}}

			{{DEFAULTSORT:Boolean Domain}}
			[[Category:Boolean algebra]]


			{{Mathlogic-stub}}

en>Jorgecarleitao: Added some properties of a homoclinic point and two references to them

2011-11-27T23:35:55Z

Added some properties of a homoclinic point and two references to them

New page

Jayson Berryhill is how I'm known as and my spouse doesn't like it at all. He works as a bookkeeper. One of the extremely very best psychics, [http://gcjcteam.org/index.php?mid=etc_video&document_srl=696611&sort_index=regdate&order_type=desc gcjcteam.org], things in the globe for him is doing ballet and he'll be starting something else alongside with it. Alaska is where I've always been living.

Homoclinic orbit - Revision history

en>My name is not dave at 21:25, 5 December 2013

en>Jorgecarleitao: Added some properties of a homoclinic point and two references to them