[cnity]

> or all the symbols mean completely different things

It's actually not entirely unproductive to consider this line of thought, whereby in this formulation equality actually means something like "arrivable via some number of zero divisions". I'm sure you could find all sorts of curiosities with this mathematical "toy".

[gallopingcomp]

Yup. You run into that all the time in abstract algebra. Although people usually don’t like to touch the equality sign; the usual practice (based on my limited exposure) is to invent equivalent operator notations.