Broadly speaking... I certainly sympathize with the OP; my frustration dates back to junior high school when some cad said 'well, we'll use an imaginary number...'
I think is difficult is for someone who has mastered a skill to recognize, in a very positive sense, how much they know. And when you are at that level of skill perhaps one of the defining notions is that you can start with 'we'll assume...,' while the beginner is mystified, perhaps, that the 'assumed value' works at all.
Ah, to hell with it. This could be a 3,000 word essay; I'm not writing it, you're not reading it. Be curious, have fun, allow for a couple mistakes.
Oh, Dave, on the 'French question.' That is how 'other' languages are taught. If you speak Chinese, and you wish to learn English as ESL, you would be taught so much about verbs and nouns and adjectives and nominatives and past-perfect. The list goes on. But you'll also be taught that you can't start a sentence with 'but,' but you can. In Montreal a local guy, Quebecois, said that if I wanted to learn French, get a local girlfriend. I guess your options are limited to French classes. ; )
Oh, please, I beseech thee, do pull-up resistors. And, as Sgt Rock has intimated, throw in the pull-downs as well.