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I don’t particularly agree about the math jargon. On the one hand, it might be annoying for people already familiar with the jargon to change the wording they use, but on the other hand, descriptive wording is easier to remember for people who are unfamiliar with a term and using an index to automatically replace the term on demand doesn’t necessarily affect anyone already familiar with the jargon. Perhaps this needs to be studied more, but this seems obvious to me. If “linearity” is exactly when A(cx) = cA(x) and A(x+y) = A(x) + A(y), there is no reason “straight-line property” can’t also mean exactly that, but straight-line property is easier to remember because it’s more descriptive of the concept of linearity.
Also, I can see how the shorthand is useful, but you could just say “linearity is when a function has both the properties of homogeneity and additivity” and that would seem less daunting to many new learners to whom that shorthand reads like ancient Greek. I could make more descriptive replacement words for those concepts as well and it might make it even easier to understand the concept of linearity.