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It always comes out funky, and I'd like to avoid \nLeftrightarrow. Is there any good way to negate the longer \iff double implication arrow?

Sean Allred
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    What would $A \not\iff B$ even mean mathematically? It seems to me that saying that exactly one of A or B holds is simpler and clearer. – lhf Oct 05 '12 at 12:09
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    @lhf The intended meaning is that A and B are not equivalent, and that neither implies the other. (For example, A could be "n is odd" and B could be "n is prime".) This is different from what you said ("exactly one of A or B holds"). – ShreevatsaR Jun 24 '18 at 18:51

1 Answers1

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You can adapt the solutions form \Rightarrow vs. \implies, and "does not imply" symbol:

enter image description here

Code:

\documentclass{article}
\usepackage{amsmath}
\usepackage{centernot}

\newcommand{\notiff}{%
  \mathrel{{\ooalign{\hidewidth$\not\phantom{"}$\hidewidth\cr$\iff$}}}}


\begin{document}
$A \notiff B$


$A \centernot\iff B$
\end{document}
Community
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Peter Grill
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  • I didn't even know something like centernot existed... one wonders why this isn't default behavior! Thanks!! – Sean Allred Oct 05 '12 at 03:23
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    @vermiculus It isn't the default because those symbols should not be used under any circumstance. They mean nothing, IMHO. – egreg Oct 05 '12 at 06:33
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    @egreg, in many cases, it is clearer to negate an operator than to negate a predicate (especially when writing for other students). – Sean Allred Oct 10 '12 at 04:28
  • @vermiculus You're stating a "metanontheorem". Yesterday I was talking about the noncommutativity of matrix multiplication where one cannot say "AB≠BA". Most usages of "doesn't imply" fall under the same case. – egreg Oct 10 '12 at 09:15
  • @egreg Can you say what should be used instead? (My preference would be to state it in words, but I'm wondering if you have some proposed symbolism...) The intended meaning is non-equivalence of two propositions, that A does not imply B and B does not imply A. Why do you say those symbols are meaningless? – ShreevatsaR Jun 24 '18 at 18:56
  • @ShreevatsaR I have the impression that they can be misleading for untrained people. – egreg Jun 24 '18 at 19:46
  • @egreg Fair enough; I think that's right, and probably, using words is best. (Unless writing notes for oneself or something like that.) – ShreevatsaR Jun 24 '18 at 20:53
  • @ShreevatsaR I've seen “not implies” in symbols in research articles, sometimes various conditions are examined and it's relevant to show their relationships. But, as I said, untrained people such as first year students might be led to wrong beliefs (“Why is AB=BA$? Didn't our teacher say that AB≠BA?” is an example for a slightly different thing). – egreg Jun 24 '18 at 20:59