Logical Negation (NOT)

#math/discrete #cs

In logic, negation, also called the logical not or logical complement, is an operation that takes a proposition $P$ to another proposition "not $P$ ", written $\neg P$ , $\sim P$ , or $\overset{―}{P}$ (or represented as ! $P$ in Computer Science). It is interpreted as true when $P$ is false, and false when $P$ is true. Negation is a unary logical connective.

Info

In intuitionistic logic, accoding to the Brouwer-Heyting-Kolmogorov interpretation, the negation of a proposition $P$ is the proposition whose proofs are the refutations of $P$

$P$	$\neg P$
True	False
False	True

Not vs Negation in Computer Science

In Computer Science, Not(~) is bitwise negation, where each bit in a number is flipped. For example, $10010_{2}$ would become $01101_{2}$ . On the other hand, Negation(!) turns anything that is not 0 to 0, and 0 to 1. In most programming languages, 0 is considered false, and every other number is considered true.