[syzarian]

My example was geared toward those people learning beginning algebra in 9th grade or so or the great many students who place into pre college level math during their first semester of undergrad. I used the word “ring” because as I was writing my comment I didn’t want any readers to think my example only applied to integers, or rationals, or reals. So I said “ring” trying to capture a nuance that very few people would appreciate.

I contend you are an outlier in the extreme. I think very few people can read a math book and get anything out of it unless they have had training. For one thing, in lower level math we lie to students all the time. We just can’t be honest about things because students at that level can’t appreciate the insane number of nuances. For example, ask a first year calculus student what “dx” means and their answer will be complete nonsense but they don’t know that. We can’t tell students what “dx” really is because it is quite beyond their level of understanding.

Thanks for the discussion. I appreciate your perspective.

[rrrrrrrrrrrr2]

Obligatory: https://www.smbc-comics.com/comics/20141206.png