Symbols:Set Theory/Negation

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Negation

$\not \in, \not \exists, \not \subseteq, \not \subset, \not \supseteq, \not \supset$

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 that $\not \subsetneq$ and $\not \supsetneq$ can be confusing due to the strike through of the symbol as a whole and the strike through of the equivalence bar on the bottom, and hence should likely be avoided.


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

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


Beware

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.