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In logic, negation, also called the logical not or logical complement, is an operation that takes a proposition to another proposition "not ", written , , ...
The negation "must not" has a stronger meaning (the effect is to apply the logical negation to the following infinitive rather than applying it to the full clause with must). For more details and other similar cases, see the relevant sections of English modal verbs .
It can be made to hold for all real numbers by extending the definition of negation to include zero and negative numbers. Specifically: The negation of 0 is 0, and; The negation of a negative number is the corresponding positive number. For example, the negation of −3 is +3. In general,
A double negative is a construction occurring when two forms of grammatical negation are used in the same sentence. This is typically used to convey a different shade of meaning from a strictly positive sentence ("You're not unattractive" vs "You're attractive").
definition: is defined as metalanguage:= means "from now on, is defined to be another name for ." This is a statement in the metalanguage, not the object language. The notation may occasionally be seen in physics, meaning the same as :=.
Adorno wrote that "Negative Dialectics is a phrase that flouts tradition. As early as Plato, dialectics meant to achieve something positive by means of negation; the thought figure of the 'negation of the negation' later became the succinct term. This book seeks to free dialectics from such affirmative traits without reducing its determinacy."
A negative literal is the negation of an atom (e.g., ). The polarity of a literal is positive or negative depending on whether it is a positive or negative literal. In logics with double negation elimination (where ¬ ¬ x ≡ x {\displaystyle \lnot \lnot x\equiv x} ) the complementary literal or complement of a literal l {\displaystyle l} can ...
Proving a negative or negative proof may refer to: Proving a negative, in the philosophic burden of proof; Evidence of absence in general, such as evidence that there is no milk in a certain bowl; Modus tollens, a logical proof; Proof of impossibility, mathematics; Russell's teapot, an analogy: inability to disprove does not prove