Why is 'abuse of notation' tolerated? I've personally tripped up on a few concepts that came down to an abuse of notation, and I've read of plenty more on stack exchange.  It seems to all be forgiven with a wave of the hand.  Why do we tolerate it at all?
I understand if later on in one's studies if things are assumed to be in place, but there are plenty of textbooks out there assuming certain things are known before teaching them.  This is a very soft question, but I think it ought to be asked.

When one writes/talks mathematics, in 99.99% of the cases the intended recipient of what one writes is a human, and humans are amazing machines: they are capable of using context, guessing, and all sorts of other information when decoding what we write/say. It is generally immensely more efficient to take advantage of this.
