Can anyone suggest a good candidate for a symbol to be used for "equal by abuse of notation"?

I can only think of "$\stackrel{\text{def}}{=}$", but it does not seem to be quite appropriate.

For example, in "$m = m\otimes 1$", are there any suggestions what would fit here better than "$=$"?

This is to write a sequence of computations without interrupting it with "by abuse of notation, write ... instead of ...".

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    $\begingroup$ Put quotation marks around it. A bit typographically difficult, but sure to be understood! $\endgroup$ – Zhen Lin Jun 11 '14 at 9:44
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    $\begingroup$ Would either $~\overset{\text{well, not really}}=~$, $~\overset{\text{sort of}}=~$, $~\overset{\text{kinda}}=~$, or $~\overset{\text{yeah, right!}}=~$ be, ahem, ‘acceptable’ ? :-) $\endgroup$ – Lucian Jun 11 '14 at 16:12
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    $\begingroup$ Well, not really, sort of! $\endgroup$ – Alexey Jun 11 '14 at 21:39
  • $\begingroup$ I would say it's probably better to go for "is isomorphic to" (with $a \cong b$) or "is in the same equivalence class as" (with $\langle a \rangle = \langle b\rangle$) if possible - why be informal, when it would clearly be stronger to formalize it? $\endgroup$ – Milo Brandt Dec 23 '14 at 4:35

I have seen quotes used by professional mathematicians, but not in publications- just during presentations when they did not want to be too explicit; in these cases, the quotes were indicative not just of abuse of notation, but also of a general sense of wrongness about the expression, even as it gave the general idea/impression of the correct thing. As a more general "beware"/"caution" warning, putting the Bourbaki dangerous bend symbol above the equals sign might work. I have certain uses of squiggly lines (such as $\approx$), but that is not very clear or uniquely descriptive. Possibly: $\stackrel{\text{abuse}}{=}$, $\stackrel{\text{A}}{=}$. I personally use the quote method (although I despise it) when I do not have time to be more careful about what I am writing (such as when taking notes), use the Bourbaki dangerous bend symbol in the margin and/or above the equals sign when something is amiss (and then I explain what it is later), or the last two suggestions (which are my own inventions) when I am being a little more explicit (and then I usually try to later explain both why it is an abuse of notation and what I mean by it).

I am not sure that any single notation is well recognized, although some of these options probably would be understood fairly well without too much explanation.


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