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 ...".
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.