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| {{other uses|Negation (disambiguation)|NOT gate}}
| | We have a objective to lose weight quick plus these rapidly fat loss tricks are written to aid we reach that objective. Losing weight quickly can happen for we however I will warn you which in the event you are not ready to place forth the effort needed you will not get the results you need. These strategies might need the effort but if you have the desire to receive the fat off your body today, this article will show you how.<br><br>Ditch the Soda. Colas are loaded with sugar which leads to excess weight gain. One cup of soda has about 180 calories whilst contributing no dietary value to your diet, thus imagine how several empty calories are inside a Big Gulp. Try switching a soda for water if you need to lose weight fast.<br><br>To lose weight too quick usually place a strain on your system plus may aggravate some of the underlying diseases you have. You have to lose the weight the same way we gained it: One pound at a time.<br><br>For your info, whenever a doctor enables you to test an HCG treatment, they might additionally tell you to go on a low calorie diet. Then a low calorie diet on its own will cause you to lose fat. So the question is, should you combine HCG supplements and a diet low inside calories, how are you able to tell that of the 2 techniques is causing the weight reduction?<br><br>This is one of the best choices for losing fat inside a brief time span. Lemon water, equally known because the master cleanse assists inside [http://safedietplansforwomen.com/how-to-lose-weight-fast lose weight fast] emulsification of fats inside the body. Consume a glass of warm water mixed with a half sized lemon plus one teaspoon of honey. Drink this early morning and before going to bed. Along with this you must follow a diet that contains negligible carbohydrates. For a meals you can have salsa, baked poultry and a lot of salads.<br><br>As my fianc plus I were preparing the soup, I made the comment which, "Geez, no question we lose thus much fat found on the diet! I'm burning a zillion calories getting it prepared!" We had to peel 2 bags of carrots and chop up a ton of vegetables. As I place everything inside the pots (I never have a stew pot, so I used 2 large pots) I couldn't enable nevertheless think of how healthy it looked.<br><br>It is one thing to lose fat rapidly plus effectively and another thing to do it quickly and unsuccessfully. The majority of people, whom desire quick results create a huge calorie deficit, by cutting their calories. Although this way could seem to be functioning well, at the beginning, nevertheless it constantly backfires. It is better to cut your calories by 20% or thus plus then burn a great deal of calories with exercise. |
| {{no footnotes|date=March 2013}}
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| {{Use dmy dates|date=September 2010}}
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| In [[logic]], '''negation''', also called '''logical complement''', is an [[operation (mathematics)|operation]] that essentially takes a [[proposition]] ''p'' to another proposition "not ''p''", written ''¬p'', which is interpreted intuitively as being true when ''p'' is false and false when ''p'' is true. Negation is thus a unary (single-argument) [[logical connective]]. It may be applied as an operation on [[proposition]]s, [[truth value]]s, or [[interpretation (logic)|semantic values]] more generally. In [[classical logic]], negation is normally identified with the [[truth function]] that takes ''truth'' to ''falsity'' and vice versa. In [[intuitionistic logic]], according to the [[Brouwer–Heyting–Kolmogorov interpretation]], the negation of a proposition ''p'' is the proposition whose proofs are the refutations of ''p''.
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| ==Definition==
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| No agreement exists as to the possibility of defining negation, as to its logical status, function, and meaning, as to its field of applicability..., and as to the interpretation of the negative judgment, (F.H. Heinemann 1944).<ref name=Horn>{{cite book |last=Horn |first=Laurence R |date=2001 |title=A NATURAL HISTORY OF NEGATION |url=http://emilkirkegaard.dk/en/wp-content/uploads/A-natural-history-of-negation-Laurence-R.-Horn.pdf |location=Stanford University |chapter=Chapter 1 |page=1 |publisher=CLSI Publications |isbn=1-57586-336-7 |accessdate=29 Dec 2013 }}</ref>
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| ''Classical negation'' is an [[logical operation|operation]] on one [[logical value]], typically the value of a [[proposition]], that produces a value of ''true'' when its operand is false and a value of ''false'' when its operand is true. So, if statement ''A'' is true, then ''¬A'' (pronounced "not A") would therefore be false; and conversely, if ''¬A'' is true, then ''A'' would be false.
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| The [[truth table]] of ''¬p'' is as follows:
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| {| class="wikitable"
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| |+ Truth table of ¬p
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| ! style="width:35px;background:#aaaaaa;" | p
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| ! style="width:35px" | ¬p
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| |-
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| | True || False
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| |-
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| | False || True
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| |}
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| Classical negation can be defined in terms of other logical operations. For example, ¬''p'' can be defined as ''p'' → ''F'', where "→" is [[logical consequence]] and ''F'' is absolute falsehood. Conversely, one can define ''F'' as ''p'' & ¬''p'' for any proposition ''p'', where "&" is [[logical conjunction]]. The idea here is that any [[contradiction]] is false. While these ideas work in both classical and intuitionistic logic, they do not work in [[Brazilian logic]], where contradictions are not necessarily false. But in classical logic, we get a further identity: ''p'' → ''q'' can be defined as ¬''p'' ∨ ''q'', where "∨" is [[logical disjunction]]: "not ''p'', or ''q''".
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| Algebraically, classical negation corresponds to [[Complement (order theory)|complementation]] in a [[Boolean algebra (structure)|Boolean algebra]], and intuitionistic negation to pseudocomplementation in a [[Heyting algebra]]. These algebras provide a [[algebraic semantics (mathematical logic)|semantics]] for classical and intuitionistic logic respectively.
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| ==Notation==
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| The negation of a proposition ''p'' is notated in different ways in various contexts of discussion and fields of application. Among these variants are the following:
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| {| class="wikitable"
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| |- style="background:paleturquoise"
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| ! style="text-align:center" | Notation
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| ! Vocalization
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| |-
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| | style="text-align:center" | ¬''p''
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| | not ''p''
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| |-
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| | style="text-align:center" | −''p''
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| | not ''p''
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| |-
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| | style="text-align:center" | ~''p''
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| | not ''p''
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| |-
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| | style="text-align:center" | ''Np''
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| | en ''p''
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| |-
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| | style="text-align:center" | <math>p'\!</math>
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| | ''p'' prime,<br/> ''p'' complement
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| |-
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| | style="text-align:center" | <math>\bar{p}</math>
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| | ''p'' bar,<br/> bar ''p''
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| |-
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| | style="text-align:center" | <math>!p\!</math>
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| | bang ''p''<br/>not ''p''
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| |-
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| |}
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| In [[Set_theory#Basic_concepts|Set Theory]] \ is also used to indicate 'not member of': U \ A is the set of all members of U that are not members of A.
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| No matter how it is notated or [[List of logic symbols|symbolized]], the negation ¬''p'' / −''p'' can be read as "it is not the case that ''p''", "not that ''p''", or usually more simply (though not grammatically) as "not ''p''".
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| ==Properties==
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| ===Double negation===
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| Within a system of [[classical logic]], double negation, that is, the negation of the negation of a proposition ''p'', is [[logically equivalent]] to ''p''. Expressed in symbolic terms, ¬¬''p'' ⇔ ''p''. In [[intuitionistic logic]], a proposition implies its double negation but not conversely. This marks one important difference between classical and intuitionistic negation. Algebraically, classical negation is called an [[involution (mathematics)|involution]] of period two.
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| However, in [[intuitionistic logic]] we do have the equivalence of ¬¬¬''p'' and ¬''p''. Moreover, in the propositional case, a sentence is classically provable if its double negation is intuitionistically provable. This result is known as [[Glivenko's theorem]].
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| ===Distributivity===
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| [[De Morgan's laws]] provide a way of [[distributivity|distributing]] negation over [[logical disjunction|disjunction]] and [[logical conjunction|conjunction]] :
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| :<math>\neg(a \vee b) \equiv (\neg a \wedge \neg b)</math>, and
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| :<math>\neg(a \wedge b) \equiv (\neg a \vee \neg b)</math>.
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| ===Linearity===
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| In [[Boolean algebra (logic)|Boolean algebra]], a linear function is one such that:
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| If there exists a<sub>0</sub>, a<sub>1</sub>, ..., a<sub>n</sub> <math>\in</math> {0,1} such that
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| f(b<sub>1</sub>, ..., b<sub>n</sub>) = a<sub>0</sub> ⊕ (a<sub>1</sub> <math>\land</math> b<sub>1</sub>) ⊕ ... ⊕ (a<sub>n</sub> <math>\land</math> b<sub>n</sub>), for all b<sub>1</sub>, ..., b<sub>n</sub> <math>\in</math> {0,1}.
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| Another way to express this is that each variable always makes a difference in the [[truth-value]] of the operation or it never makes a difference. Negation is a linear logical operator.
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| ===Self dual===
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| In [[Boolean algebra (logic)|Boolean algebra]] a self dual function is one such that:
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| f(a<sub>1</sub>, ..., a<sub>n</sub>) = ~f(~a<sub>1</sub>, ..., ~a<sub>n</sub>) for all a<sub>1</sub>, ..., a<sub>n</sub> <math>\in</math> {0,1}. Negation is a self dual logical operator.
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| ==Rules of inference==
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| There are a number of equivalent ways to formulate rules for negation. One usual way to formulate classical negation in a [[natural deduction]] setting is to take as primitive rules of inference ''negation introduction'' (from a derivation of ''p'' to both ''q'' and ¬''q'', infer ¬''p''; this rule also being called ''[[reductio ad absurdum]]''), ''negation elimination'' (from ''p'' and ¬''p'' infer q; this rule also being called ''ex falso quodlibet''), and ''double negation elimination'' (from ¬¬''p'' infer ''p''). One obtains the rules for intuitionistic negation the same way but by excluding double negation elimination.
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| Negation introduction states that if an absurdity can be drawn as conclusion from ''p'' then ''p'' must not be the case (i.e. ''p'' is false (classically) or refutable (intuitionistically) or etc.). Negation elimination states that anything follows from an absurdity. Sometimes negation elimination is formulated using a primitive absurdity sign ⊥. In this case the rule says that from ''p'' and ¬''p'' follows an absurdity. Together with double negation elimination one may infer our originally formulated rule, namely that anything follows from an absurdity.
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| Typically the intuitionistic negation ¬''p'' of ''p'' is defined as ''p''→⊥. Then negation introduction and elimination are just special cases of implication introduction ([[conditional proof]]) and elimination ([[modus ponens]]). In this case one must also add as a primitive rule ''ex falso quodlibet''.
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| ==Programming==
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| As in mathematics, negation is used in [[computer science]] to construct logical statements.
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| <source lang="cpp">
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| if (!(r == t))
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| {
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| /*...statements executed when r does NOT equal t...*/
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| }
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| </source>
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| The "<code>!</code>" signifies logical NOT in [[B (programming language)|B]], [[C Programming Language|C]], and languages with a C-inspired syntax such as [[C++]], [[Java (programming language)|Java]], [[JavaScript]], [[Perl]], and [[PHP]]. "<code>NOT</code>" is the operator used in [[ALGOL 60]], [[BASIC programming language|BASIC]], and languages with an ALGOL- or BASIC-inspired syntax such as [[Pascal programming language|Pascal]], [[Ada programming language|Ada]], [[Eiffel (programming language)|Eiffel]] and [[Seed7]]. Some languages (C++, Perl, etc.) provide more than one operator for negation. A few languages like [[PL/I]] and [[Ratfor]] use <code>¬</code> for negation. Some modern computers and [[operating systems]] will display <code>¬</code> as <code>!</code> on files encoded in [[ASCII]]. Most modern languages allow the above statement to be shortened from <code>if (!(r == t))</code> to <code>if (r != t)</code>, which allows sometimes, when the compiler/interpreter is not able to optimize it, faster programs.
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| In computer science there is also ''bitwise negation''. This takes the value given and switches all the [[binary numeral system|binary]] 1s to 0s and 0s to 1s. See [[bitwise operation]]. This is often used to create [[signed number representations|ones' complement]] or "<code>~</code>" in C or C++ and [[two's complement]] (just simplified to "<code>-</code>" or the negative sign since this is equivalent to taking the arithmetic negative value of the number) as it basically creates the opposite (negative value equivalent) or mathematical complement of the value (where both values are added together they create a whole).
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| To get the absolute (positive equivalent) value of a given integer the following would work as the "<code>-</code>" changes it from negative to positive (it is negative because "<code>x < 0</code>" yields true)
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| <source lang="cpp">
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| unsigned int abs(int x)
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| {
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| if (x < 0)
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| return -x;
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| else
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| return x;
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| }
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| </source>
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| To demonstrate logical negation:
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| <source lang="cpp">
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| unsigned int abs(int x)
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| {
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| if (!(x < 0))
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| return x;
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| else
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| return -x;
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| }
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| </source>
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| Inverting the condition and reversing the outcomes produces code that is logically equivalent to the original code, i.e. will have identical results for any input (note that depending on the compiler used, the actual instructions performed by the computer may differ).
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| This convention occasionally surfaces in written speech, as computer-related [[slang]] for ''not''. The phrase <code>!voting</code>, for example, means "not voting".
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| ==Kripke semantics==
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| In [[Kripke semantics]] where the semantic values of formulae are sets of [[possible world]]s, negation can be taken to mean [[set-theoretic complement]]ation.{{citation needed|date=August 2012}} (See also [[possible world semantics]].)
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| ==See also==
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| * [[Logical conjunction]]
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| * [[Logical disjunction]]
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| * [[NOT gate]]
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| * [[Bitwise operation#NOT|Bitwise NOT]]
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| * [[Ampheck]]
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| * [[Apophasis]]
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| * [[Cyclic negation]]
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| * [[Double negative elimination]]
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| * [[Grammatical polarity]]
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| * [[Negation (linguistics)]]
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| * [[Negation as failure]]
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| * [[Square of opposition]]
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| * [[Binary opposition]]
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| ==References==
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| {{reflist}}
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| == Further reading ==
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| * [[Dov Gabbay|Gabbay, Dov]], and Wansing, Heinrich, eds., 1999. ''What is Negation?'', [[Kluwer]].
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| * [[Laurence R. Horn|Horn, L.]], 2001. ''A Natural History of Negation'', [[University of Chicago Press]].
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| * [[G. H. von Wright]], 1953–59, "On the Logic of Negation", ''Commentationes Physico-Mathematicae 22''.
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| * Wansing, Heinrich, 2001, "Negation", in Goble, Lou, ed., ''The Blackwell Guide to Philosophical Logic'', [[Wiley-Blackwell|Blackwell]].
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| * Marco Tettamanti, Rosa Manenti, Pasquale A. Della Rosa, Andrea Falini, Daniela Perani, Stefano F. Cappa and Andrea Moro (2008). "Negation in the brain: Modulating action representation", NeuroImage Volume 43, Issue 2, 1 November 2008, pages 358–367, http://dx.doi.org/10.1016/j.neuroimage.2008.08.004/
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| ==External links==
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| * {{springer|title=Negation|id=p/n066170}}
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| * [http://mathworld.wolfram.com/NOT.html NOT], on [[MathWorld]]
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| {{Logical connectives}}
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| {{logic}}
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| [[Category:Grammar]]
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| [[Category:Semantics]]
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| [[Category:Logical connectives]]
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We have a objective to lose weight quick plus these rapidly fat loss tricks are written to aid we reach that objective. Losing weight quickly can happen for we however I will warn you which in the event you are not ready to place forth the effort needed you will not get the results you need. These strategies might need the effort but if you have the desire to receive the fat off your body today, this article will show you how.
Ditch the Soda. Colas are loaded with sugar which leads to excess weight gain. One cup of soda has about 180 calories whilst contributing no dietary value to your diet, thus imagine how several empty calories are inside a Big Gulp. Try switching a soda for water if you need to lose weight fast.
To lose weight too quick usually place a strain on your system plus may aggravate some of the underlying diseases you have. You have to lose the weight the same way we gained it: One pound at a time.
For your info, whenever a doctor enables you to test an HCG treatment, they might additionally tell you to go on a low calorie diet. Then a low calorie diet on its own will cause you to lose fat. So the question is, should you combine HCG supplements and a diet low inside calories, how are you able to tell that of the 2 techniques is causing the weight reduction?
This is one of the best choices for losing fat inside a brief time span. Lemon water, equally known because the master cleanse assists inside lose weight fast emulsification of fats inside the body. Consume a glass of warm water mixed with a half sized lemon plus one teaspoon of honey. Drink this early morning and before going to bed. Along with this you must follow a diet that contains negligible carbohydrates. For a meals you can have salsa, baked poultry and a lot of salads.
As my fianc plus I were preparing the soup, I made the comment which, "Geez, no question we lose thus much fat found on the diet! I'm burning a zillion calories getting it prepared!" We had to peel 2 bags of carrots and chop up a ton of vegetables. As I place everything inside the pots (I never have a stew pot, so I used 2 large pots) I couldn't enable nevertheless think of how healthy it looked.
It is one thing to lose fat rapidly plus effectively and another thing to do it quickly and unsuccessfully. The majority of people, whom desire quick results create a huge calorie deficit, by cutting their calories. Although this way could seem to be functioning well, at the beginning, nevertheless it constantly backfires. It is better to cut your calories by 20% or thus plus then burn a great deal of calories with exercise.