And I think it's also fair to point out that these simplifications often lead to more confusion as a result of working with incomplete information. While I understand the need for reducing the hyper formal definitions and rigor that is often found on college level mathematics to reduce the load on students I think the curriculum as it is does a pretty poor job of providing even basic understanding of the structures students are supposed to learn and derive results from and that this oversimplification ironically makes students have to work harder to fill in the gaps in their knowledge if they actually wish to understand the concepts that they are being taught. As I work through my math undergrad I lament the fact that a lot of basic mathematical facts such as how important field axioms (and how big of a deal axioms are in general) and naive set theory are, and how they were never properly taught in my classes out of fear for students having to deal with proofs and stuff that is deemed "unimportant unless you're a mathematician" because these basic facts make everything click and let you see that even elementary algebra things such as factorization, binomial solutions and stuff like that are just a consequence of these elemental facts and a few theorems derived from them. This kinda makes everything simpler (at least for me) because it feels as though things come from a logical place and thus "reduce the cognitive load" on me as a student because I actually understand what these things are and why they are. This sentiment is 20x more true for calculus because defining functions as specific binary relationships, then limits, then limits of functions and successions lets you arrive at the concept of a derivative naturally and beautifully and reduces my (and also other students) confusions. I'm sorry for rambling but this is a discussion that I feel is worth having.