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 \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.