> it seems to me that the definition of equality needs a context That's precisely it. Mathematicians are often casual with terminology even when being complete

> it seems to me that the definition of equality needs a context That's precisely it. Mathematicians are often casual with terminology even when being completely precise inside their context. I did not get beyond introductory graduate-level mathematics, but I distinctly remember a professor announcing this in the third or fourth lecture of an algebra class: "From today until the end of the semester, when I say 'ring' I will mean a commutative ring, except on occasion when it will be obvious that the ring is not commutative." Some professors/authors were more fastidious about using unambiguous terminology, but many preferred to slap the easiest word possible on whatever relationship felt the most important in the context. So one professor would say "what we're really interested in is the quotients modulo 10," and another would say "12 is equal to 2" and expect you to understand the same thing from it.