Negated Operators

Sometimes you need to enter a negated operator like ≠. If you’re a C/C++ programmer, you might think that != should map to ≠, since that’s what != means in those languages (and some others). But since in mathematics ! means factorial, this choice is a bad idea for inputting ≠ into mathematical text. You can type in \ne to get ≠, but there’s the simpler combination: /=. In the linear format used in Microsoft Office math, / is used for “stacked” fractions. But /= building up to a fraction with an empty denominator followed by an equal sign isn’t very useful. Also if you really want such a fraction, you can get it by typing /<space>.

Accordingly in Office 2010 math entry, /= builds up to ≠. This approach can be used to input many other negated operators as listed in the following table

Operator	Negated op	Input
<	≮	/<
=	≠	/=
>	≯	/>
∃	∄	/\exists
∈	∉	/\in
∋	∌	/\ni
∼	≁	/\sim
≃	≄	/\simeq
≅	≇	/\cong
≈	≉	/\approx
≍	≭	/\asymp
≡	≢	/\equiv
≤	≰	/\le
≥	≱	/\ge
≶	≸	/\lessgtr
≷	≹	/\gtrless
≽	⋡	/\succeq
≺	⊀	/\prec
≻	⊁	/\succ
≼	⋠	/\preceq
⊂	⊄	/\subset
⊃	⊅	/\supset
⊆	⊈	/\subseteq
⊇	⊉	/\supseteq
⊑	⋢	/\sqsubseteq
⊒	⋣	/\sqsupseteq

All of these operators are in the U+2200 Unicode block (Mathematical Operators) except for the ASCII characters <, =, and >. TeX has a similar, but more verbose approach that uses the control word \not followed by the name of the operator. For example, in TeX, \not\exists produces ∄.

Note that if you don’t like an automatic translation when entering math, you can undo the translation by typing ctrl+z. This way of entering negated operators along with some other extensions to the linear format will be documented in a future version of Unicode Technical Note #28.

Comments

• Anonymous
  February 09, 2010
  This new way for inputting negated operators is very useful and easy to use. Thank you for this improvement.

• Anonymous
  September 24, 2010
  I've found that some automatic translations cannot be undone without losing the entire equation. Instead I use the arrow right keys to avoid automatic translation.

• Anonymous
  September 26, 2010
  Word, OneNote, and PowerPoint each have their own undo facilities. The automatic translations can be undone with varying granularities. Word seems to have the finest granularity, followed by PowerPoint. I do notice that typing a/=b into a OneNote math zone followed by ctrl+z (undo), in fact, deletes the entire equation. Thanks for the bug report.

• Anonymous
  February 20, 2011
  That's great, but what about operators that are not in your list? The Cambria Math font doesn't contain a symbol for the negated versions of some operators, e.g., the equivalent of the LaTeX leadsto. Is there no way to negate these operators?

• Anonymous
  February 20, 2011
  Is leadsto the same as U+2933 "wavy arrow pointing directly right"? If so, you can enter it as 2933 alt+x and you can add it to your math autocorrect list as leadsto. To negate it, the first thing that comes to mind is to follow it with U+0338 "combining long solidus overlay", but I tried it and it's not currently supported by the math accent object although it should be. Thanks for the question.

• Anonymous
  February 26, 2017
  Nice, but it could be better. For example, for logicians, /\models and /\vdash, do not work. How can we make it work ?