[rrrrrrrrrrrr2]

Oh. Wow, you are right. I honestly just read the definition in Gallian wrong, and then, even as I was typing it, I swear I thought it said "ba + bc = b(a + c)". What a crazy experience of confirmation bias by me.

I obviously agree that a human is extremely effective at explaining that "equals" is symmetric and not the same as "implies". I'm just arguing that the task also can be done in prose to similar, if inferior, effect.

I did agree however that because math has so many gotchas like this, then no textbook will ever disclaim all potential sources of confusion like the example by GGP. And so our discussion boils down to the tradeoff between the price and time investment of taking a class vs. the increased difficulty of self-studying. And how different people assign value differently to each side of the tradeoff, which I claim is the root of our disagreement.