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| {{redirect|Existential quantifier|the symbol conventionally used for this quantifier|Turned E}}
| | Today I am sharing a dark experience with you because I am out of this darkness today. Whoa! Google Chrome has crashed was the disaster that struck on me early this morning. My blood flow appeared to stop for a limited minutes. Then I regained my senses plus decided to fix Chrome crash.<br><br>Google Chrome crashes on Windows 7 by the corrupted cache contents plus difficulties with all the stored browsing information. Delete the browsing data and well-defined the contents of the cache to solve this issue.<br><br>The 'registry' is a central database that stores information, settings plus options for the computer. It's really the most usual reason why XP runs slow and in the event you fix this problem, we could create your computer run a lot quicker. The problem is the fact that the 'registry' stores a great deal of settings plus details regarding the PC... plus considering Windows needs to employ numerous of these settings, any corrupted or damaged ones might directly affect the speed of your system.<br><br>The problem with almost all of the individuals is that they do not wish To invest cash. In the damaged variation one does not have to pay anything plus will download it from web easily. It is easy to install as well. But, the issue comes whenever it is very unable to identify all possible viruses, spyware plus malware in the system. This really is because it's obsolete in nature plus does not get any usual changes from the website downloaded. Thus, your system is accessible to difficulties like hacking.<br><br>Besides, should you may receive a [http://bestregistrycleanerfix.com/fix-it-utilities fix it utilities] that can do the job for you effectively plus swiftly, then why not? There is 1 such system, RegCure that is quite good plus complete. It has qualities that different cleaners never have. It is the many recommended registry cleaner now.<br><br>Your system is designed and built for the purpose of helping you accomplish tasks and not be pestered by windows XP error messages. When there are errors, what do we do? Some individuals pull their hair and cry, whilst those sane ones have their PC repaired, while those absolutely wise ones analysis to have the mistakes fixed themselves. No, these mistakes were not moreover tailored to rob you off a cash and time. There are factors to do to actually prevent this from happening.<br><br>Perfect Optimizer is a advantageous Registry Product, updates consistently and has many attributes. Despite its cost, you will find that the update are absolutely practical. They provide plenty of support through phone, send and forums. We could wish To go and visit the free trial to check it out for oneself.<br><br>Thus, the greatest thing to do whenever your computer runs slow is to purchase an authentic and legal registry repair tool that would enable you eliminate all difficulties related to registry and aid you enjoy a smooth running computer. |
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| In [[predicate logic]], an '''existential quantification''' is a type of [[quantification|quantifier]], a [[logical constant]] which is [[interpretation (logic)|interpreted]] as "there exists," "there is at least one," or "for some." It expresses that a [[propositional function]] can be [[satisfiability|satisfied]] by at least one [[element (mathematics)|member]] of a [[domain of discourse]]. In other terms, it is the [[Predicate (mathematical logic)|predication]] of a [[property (philosophy)|property]] or [[binary relation|relation]] to at least one member of the domain. It [[logical assertion|asserts]] that a predicate within the [[free variables and bound variables|scope]] of an existential quantifier is true of at least one [[Valuation (logic)|value]] of a [[predicate variable]].
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| It is usually denoted by the [[turned E]] (∃) [[logical connective|logical operator]] [[Symbol (formal)|symbol]], which, when used together with a predicate variable, is called an '''existential quantifier''' ("∃x" or "∃(x)"). Existential quantification is distinct from [[universal quantification|''universal'' quantification]] ("for all"), which asserts that the property or relation holds for ''all'' members of the domain.
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| Symbols are encoded {{unichar|2203|THERE EXISTS|note=as a mathematical symbol|html=|ulink=}} and {{unichar|2204|THERE DOES NOT EXIST|html=}}.
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| == Basics ==
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| Consider a formula that states that some [[natural number]] multiplied by itself is 25.
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| : <blockquote>0·0 = 25, '''or''' 1·1 = 25, '''or''' 2·2 = 25, '''or''' 3·3 = 25, and so on.</blockquote>
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| This would seem to be a [[logical disjunction]] because of the repeated use of "or". However, the "and so on" makes this impossible to integrate and to interpret as a disjunction in [[formal logic]].
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| Instead, the statement could be rephrased more formally as
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| :<blockquote>For some natural number ''n'', ''n''·''n'' = 25.</blockquote>
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| This is a single statement using existential quantification.
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| This statement is more precise than the original one, as the phrase "and so on" does not necessarily include all [[natural number]]s, and nothing more. Since the domain was not stated explicitly, the phrase could not be interpreted formally. In the quantified statement, on the other hand, the natural numbers are mentioned explicitly.
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| This particular example is true, because 5 is a natural number, and when we substitute 5 for ''n'', we produce "5·5 = 25", which is true.
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| It does not matter that "''n''·''n'' = 25" is only true for a single natural number, 5; even the existence of a single [[solution]] is enough to prove the existential quantification true.
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| In contrast, "For some [[even number]] ''n'', ''n''·''n'' = 25" is false, because there are no even solutions.
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| The ''[[domain of discourse]]'', which specifies which values the variable ''n'' is allowed to take, is therefore of critical importance in a statement's trueness or falseness. [[Logical conjunction]]s are used to restrict the domain of discourse to fulfill a given predicate. For example:
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| :<blockquote>For some positive odd number ''n'', ''n''·''n'' = 25 </blockquote>
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| is [[logically equivalent]] to | |
| :<blockquote>For some natural number ''n'', ''n'' is odd and ''n''·''n'' = 25.</blockquote>
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| Here, "and" is the logical conjunction.
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| In [[First-order logic|symbolic logic]], "∃" (a backwards letter "[[E]]" in a [[sans-serif]] font) is used to indicate existential quantification.<ref>This symbol is also known as the ''[[existential operator]]''. It is sometimes represented with ''V''.</ref> Thus, if ''P''(''a'', ''b'', ''c'') is the predicate "''a''·''b'' = c" and <math>\mathbb{N}</math> is the [[Set (mathematics)|set]] of natural numbers, then
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| : <math> \exists{n}{\in}\mathbb{N}\, P(n,n,25) </math>
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| is the (true) statement
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| : <blockquote>For some natural number ''n'', ''n''·''n'' = 25.</blockquote>
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| Similarly, if ''Q''(''n'') is the predicate "''n'' is even", then
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| : <math> \exists{n}{\in}\mathbb{N}\, \big(Q(n)\;\!\;\! {\wedge}\;\!\;\! P(n,n,25)\big) </math>
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| is the (false) statement | |
| : <blockquote>For some natural number ''n'', ''n'' is even and ''n''·''n'' = 25.</blockquote>
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| In [[mathematical proof|mathematics]], the proof of a "some" statement may be achieved either by a [[constructive proof]], which exhibits an object satisfying the "some" statement, or by a [[nonconstructive proof]] which shows that there must be such an object but without exhibiting one.
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| == Properties ==
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| ===Negation===
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| A quantified propositional function is a statement; thus, like statements, quantified functions can be negated. The <math>\lnot\ </math> symbol is used to denote negation.
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| For example, if P(''x'') is the propositional function "x is between 0 and 1", then, for a domain of discourse ''X'' of all natural numbers, the existential quantification "There exists a natural number ''x'' which is between 0 and 1" is symbolically stated:
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| :<math>\exists{x}{\in}\mathbf{X}\, P(x)</math>
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| This can be demonstrated to be irrevocably false. Truthfully, it must be said, "It is not the case that there is a natural number ''x'' that is between 0 and 1", or, symbolically:
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| :<math>\lnot\ \exists{x}{\in}\mathbf{X}\, P(x)</math>.
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| If there is no element of the domain of discourse for which the statement is true, then it must be false for all of those elements. That is, the negation of
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| :<math>\exists{x}{\in}\mathbf{X}\, P(x)</math>
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| is logically equivalent to "For any natural number ''x'', x is not between 0 and 1", or: | |
| :<math>\forall{x}{\in}\mathbf{X}\, \lnot P(x)</math>
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| Generally, then, the negation of a [[propositional function]]'s existential quantification is a [[universal quantification]] of that propositional function's negation; symbolically,
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| :<math>\lnot\ \exists{x}{\in}\mathbf{X}\, P(x) \equiv\ \forall{x}{\in}\mathbf{X}\, \lnot P(x)</math>
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| A common error is stating "all persons are not married" (i.e. "there exists no person who is married") when "not all persons are married" (i.e. "there exists a person who is not married") is intended:
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| :<math>\lnot\ \exists{x}{\in}\mathbf{X}\, P(x) \equiv\ \forall{x}{\in}\mathbf{X}\, \lnot P(x) \not\equiv\ \lnot\ \forall{x}{\in}\mathbf{X}\, P(x) \equiv\ \exists{x}{\in}\mathbf{X}\, \lnot P(x)</math>
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| Negation is also expressible through a statement of "for no", as opposed to "for some":
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| :<math>\nexists{x}{\in}\mathbf{X}\, P(x) \equiv \lnot\ \exists{x}{\in}\mathbf{X}\, P(x)</math>
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| Unlike the universal quantifier, the existential quantifier distributes over logical disjunctions:
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| <math> \exists{x}{\in}\mathbf{X}\, P(x) \or Q(x) \to\ (\exists{x}{\in}\mathbf{X}\, P(x) \or \exists{x}{\in}\mathbf{X}\, Q(x))</math>
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| ===Rules of Inference===
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| {{Transformation rules}}
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| A [[rule of inference]] is a rule justifying a logical step from hypothesis to conclusion. There are several rules of inference which utilize the existential quantifier.
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| ''[[List of rules of inference#Rules_of_classical_predicate_calculus|Existential introduction]]'' (∃I) concludes that, if the propositional function is known to be true for a particular element of the domain of discourse, then it must be true that there exists an element for which the proposition function is true. Symbolically,
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| :<math> P(a) \to\ \exists{x}{\in}\mathbf{X}\, P(x)</math>
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| Existential elimination, when conducted in a Fitch style deduction, proceeds by entering a new sub-derivation while substituting an existentially quantified variable for a subject which does not appear within any active sub-derivation. If a conclusion can be reached within this sub-derivation in which the substituted subject does not appear, then one can exit that sub-derivation with that conclusion. The reasoning behind existential elimination (∃E) is as follows: If it is given that there exists an element for which the proposition function is true, and if a conclusion can be reached by giving that element an arbitrary name, that conclusion is [[logical truth|necessarily true]], as long as it does not contain the name. Symbolically, for an arbitrary ''c'' and for a proposition Q in which ''c'' does not appear:
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| :<math> \exists{x}{\in}\mathbf{X}\, P(x) \to\ ((P(c) \to\ Q) \to\ Q)</math>
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| <math>P(c) \to\ Q</math> must be true for all values of ''c'' over the same domain ''X''; else, the logic does not follow: If ''c'' is not arbitrary, and is instead a specific element of the domain of discourse, then stating P(''c'') might unjustifiably give more information about that object. | |
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| === The empty set ===
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| The formula <math>\exists {x}{\in}\emptyset \, P(x)</math> is always false, regardless of ''P''(''x''). This is because <math>\emptyset</math> denotes the [[empty set]], and no ''x'' of any description – let alone an ''x'' fulfilling a given predicate ''P''(''x'') – exist in the empty set. See also [[vacuous truth]].
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| == As adjoint ==
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| {{main|Universal quantification#As adjoint}}
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| In [[category theory]] and the theory of [[elementary topos|elementary topoi]], the existential quantifier can be understood as the [[left adjoint]] of a [[functor]] between [[power set]]s, the [[inverse image]] functor of a function between sets; likewise, the [[universal quantifier]] is the [[right adjoint]].<ref>Saunders Mac Lane, Ieke Moerdijk, (1992) ''Sheaves in Geometry and Logic'' Springer-Verlag. ISBN 0-387-97710-4 ''See page 58''</ref>
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| == See also ==
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| * [[First-order logic]]
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| * [[List of logic symbols]] - for the unicode symbol ∃
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| * [[Quantifier variance]]
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| * [[Quantifier]]s
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| * [[Uniqueness quantification]]
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| == Notes ==
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| <references/>
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| ==References==
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| *{{cite book | author = Hinman, P. | title = Fundamentals of Mathematical Logic | publisher = A K Peters | year = 2005 | isbn = 1-56881-262-0}}
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| [[Category:Logic symbols]]
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| [[Category:Quantification]]
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Today I am sharing a dark experience with you because I am out of this darkness today. Whoa! Google Chrome has crashed was the disaster that struck on me early this morning. My blood flow appeared to stop for a limited minutes. Then I regained my senses plus decided to fix Chrome crash.
Google Chrome crashes on Windows 7 by the corrupted cache contents plus difficulties with all the stored browsing information. Delete the browsing data and well-defined the contents of the cache to solve this issue.
The 'registry' is a central database that stores information, settings plus options for the computer. It's really the most usual reason why XP runs slow and in the event you fix this problem, we could create your computer run a lot quicker. The problem is the fact that the 'registry' stores a great deal of settings plus details regarding the PC... plus considering Windows needs to employ numerous of these settings, any corrupted or damaged ones might directly affect the speed of your system.
The problem with almost all of the individuals is that they do not wish To invest cash. In the damaged variation one does not have to pay anything plus will download it from web easily. It is easy to install as well. But, the issue comes whenever it is very unable to identify all possible viruses, spyware plus malware in the system. This really is because it's obsolete in nature plus does not get any usual changes from the website downloaded. Thus, your system is accessible to difficulties like hacking.
Besides, should you may receive a fix it utilities that can do the job for you effectively plus swiftly, then why not? There is 1 such system, RegCure that is quite good plus complete. It has qualities that different cleaners never have. It is the many recommended registry cleaner now.
Your system is designed and built for the purpose of helping you accomplish tasks and not be pestered by windows XP error messages. When there are errors, what do we do? Some individuals pull their hair and cry, whilst those sane ones have their PC repaired, while those absolutely wise ones analysis to have the mistakes fixed themselves. No, these mistakes were not moreover tailored to rob you off a cash and time. There are factors to do to actually prevent this from happening.
Perfect Optimizer is a advantageous Registry Product, updates consistently and has many attributes. Despite its cost, you will find that the update are absolutely practical. They provide plenty of support through phone, send and forums. We could wish To go and visit the free trial to check it out for oneself.
Thus, the greatest thing to do whenever your computer runs slow is to purchase an authentic and legal registry repair tool that would enable you eliminate all difficulties related to registry and aid you enjoy a smooth running computer.