Comment by svat
> I would of course explain that the equality sign is not symmetric with respect to such notations; we have 3=A(5) and 4=A(5) but not 3=4, nor can we say that A(5)=4. We can, however, say that A(0)=0. As de Bruijn points out in [1, 1.2], mathematicians customarily use the = sign as they use the word “is” in English: Aristotle is a man, but a man isn’t necessarily Aristotle.
— Donald Knuth, Teach Calculus via O Notation (https://shreevatsa.wordpress.com/2014/03/13/big-o-notation-a... or http://micromath.wordpress.com/2008/04/14/donald-knuth-calcu...)
Off: mathematics is kind of moving away from the asymmetric element symbol "∈" to the symmetric type of symbol ":", which, I think is a loss. I'm sad about it.
For example with the element symbol you can do
and you also can do Which you can't do with the type of symbol. I'm probably more picky about the notations following the sound in my head than the rest, but I still think that an asymmetric typeof symbol would be a net win.