The notation I've used is $a$~$b$, but one of my teachers said that the correct notation was $a\approx b$. Is this notation really used, and if so, are there any uses of this in literature? I haven't found any.
He also says that $a\approx b$ can't be used for, "approximately equal to $b$" for this reason, and instead, $\dot{=}$ should be used, but I don't think this is true ("\approx" is the latex notation for $\approx$), and I can't even find any uses of $\dot{=}$ online! This wikipeda page has a similar symbol at the bottom, saying that a similar one is commonly used in Japan and Korea.
(This was in a class which has absolutely nothing to do with asymptotic anything, so it isn't notation used in-class during the semester.)