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Algebra in school is like a compiler with shitty type inference: you rarely have to write type annotations and you can easily end up with impossible states.
My experience with math class has been quite different. Most exercises specify the domain of the equations, and I’ve been taught to always work out the set of possible solutions (when it’s non-obvious) before solving an equation, though I usually forget to do this and still end up with impossible states…
That sounds exhaustive in the good sense. Rigorous. Would you say your math education was particularly good compared to that of, for example, the rest of your country? Could you know, perhaps through standardized testing, if it was good compared to the rest of the world? Would you attribute the exhaustive domain and range statements to just the book, just the teacher, or just the school administration, or some combination of them?
I am lucky enough to have received an above-average education, in maths at least. It’s definetly not the norm in Romania, especially in the countryside, and I could talk a lot more about the various issues that relate to this, but that’s a bit beside the point.
I’m not really familiar with the education systems of the rest of the world, much less with their maths curricula, but I think that we generally cover more material in a shorter amount of time (which is not really a good thing, in my opinion, but it is what it is).
There was a lot of talk in the media a couple of years back about how our country performs poorly in the PISA tests, so our education is worse overall than the rest of the world. I can’t really research the exact numbers right now, but I will try when I get the chance.
I would attribute the exhaustiveness mostly to my teachers. The books I used most were reasonably exhaustive in terms of range and domain definitions, but in all honesty I’ve also seen many books that were atrocious in this regard. Teachers here have quite a lot of freedom when it comes to details like these, so as long as they cover all the material, no one (in the administration) really cares about how they do it.
If I remember correctly, good textbooks always specified the type. There were even exercises like “find the maximum possible domain of this function”. And in higher-level mathematics, it’s pretty much a sin to not specify the type.