Earlier quoted context omitted.
> Still kind of glossing over "=" as a "simplify" operator, but it's still an improvement over when I was a kid when it was really easy to pick up the idea that the "=" operator was actually a function meaning "take the expression on the left and simplify it". What? No. De '=' sign is very simple: what's written to the left of it is equal to what's written on its right.
The takeaway that many students have is that the equals sign if equivalent to the -> sign, which definitely implies simplification. I know I was set straight as a university freshman in the 1980s, and I have read many things since about that same confusion. Outside of math it probably doesn't matter. Inside of math it matters a lot. Programming is math.
And I was solving systems of equations with substitution and doing all the usual things to equations one does in math classes, and to all external appearances I would have looked like I understood equality prior to that. But I didn't. Not fully. In hindsight, the best evidence of this was in physics class, where I was perfectly adequate at taking the provided equations and using them, and I understood their derivation, but I still wasn't all that great at combining them fluidly; F = ma, yes, but it still didn't quite fully register that that meant anywhere I saw an F, in any other equation in which it appeared, I could drop in an ma. It's not that F is "convertable" to ma, or that ma simplifies to F, or that the name of ma is F... it's that they ARE each other, there is no conceivable way you can separate them, there is no conceivably witnessable in any way, mathematically or practically, effect from substituting one for the other, there is only one entity that can be named in various ways. I did not fluidly combine them the way I should. If I had the class to do over again, I would do way better this time, even we could somehow erase my first pass entirely from my mind.