Symbols:Set Theory/Negation

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  followed by the code for whatever symbol you want to negate.

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

Beware
Using $/$ with  and   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  and   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.