Symbols:General/Negation

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Negation

$\not=, \ \not>, \ \not<, \ \not \ge, \ \not \le, \ \not \in, \ \not \exists, \ \not \subseteq, \ \not \subset, \ \not \supseteq, \ \not \supset$

The above symbols all mean the opposite of the non struck through version of the symbol.

For example, $x \not\in S$ means that $x$ is not an element of $S$.

The slash $/$ through a symbol can be used to reverse the meaning of essentially any mathematical symbol (especially relations), although it is used most frequently with those listed above.


Note
Using $/$ with \subsetneq and \supsetneq can be confusing:
$\not \subsetneq, \ \not \supsetneq$
as the strike through of the symbol as a whole obscures the clarity of the strike through of the equivalence bar on the bottom, and hence should be avoided.
The constructs \not \subsetneqq and \not \supsetneqq can be used instead, but these are unwieldy and look suboptimal:
$\not \subsetneqq, \ \not \supsetneqq$
and it is suggested that a statement that requires this concept be restructured so as to avoid such a construct.


The $\LaTeX$ code for negation is \not followed by the code for whatever symbol you want to negate.

For example, \not \in will render $\not \in$.


Note that several of the above relations also have their own $\LaTeX$ commands for their negations, for example \ne or \neq for \not =, and \notin for \not \in.


Also see

See Definition:Logical Not.

See Arithmetic and Algebra and Set Operations and Relations for the definitions of the symbols above.