Is a gymnasium a school in Europe? It's an exercise facility in the USA.
I've gone through high school and taken CS (and a bit of discrete math and logic) in college, and never seen the ⊢ symbol before.
I've gone through high school and taken CS (and a bit of discrete math and logic) in college, and never seen the ⊢ symbol before.
https://en.wikipedia.org/wiki/Gymnasium_(Germany)
And yes, teaching basic notation from mathematical logic is pretty standard in Gymnasium's. I've taught sequent calculi at US high school enrichment programs; honestly, the students get it perfectly fine. The notation is no more difficult to understand than a two column proof.
It's always the teachers who struggle. Every attempt at math ed reform in the US meets that crux -- the teachers' and parents' willingness/ability to learn anything new is always massively over-estimated. The only way to teach real mathematics in US high schools is to smuggle it in through "enrichment" programs.
> I've gone through high school and taken CS (and a bit of discrete math and logic) in college, and never seen the ⊢ symbol before.
Discrete math courses are different from university to university; sometimes formal logic is covered, and sometimes it's more of an "introduction to basic proof techniques and combinatorics" course.
A university course in logic should certainly have shown you a sequent calculus at some point. I'm actually confused about how you would fill a semester-long course on logic without a turnstile ever showing up. What notation were you using to write down your derivations?
They used to say "the US has the best high schools in the world; unfortunately, they're called universities". But the universities have become so watered down that many Americans get university degrees without ever passing through an institution at the level of a good gymnasium.
I've never heard of "sequent calculus" before, and I don't expect anyone I know to have heard it. Apparently it's not calculus.
> They used to say "the US has the best high schools in the world; unfortunately, they're called universities". But the universities have become so watered down that many Americans get university degrees without ever passing through an institution at the level of a good gymnasium.
I don't think universities are watered down because they don't teach notation that most people don't know and find obscure. My university is famous for a difficult admissions process, tough courses that most people only learn 2/3 of the material, and grading curves calibrated so getting 60% on exams is enough for a B or A.
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https://en.wikipedia.org/wiki/Sequent_calculus
Wikipedia says "Sequent calculus is one of several extant styles of proof calculus for expressing line-by-line logical arguments."
I didn't learn "every statement is conditional" logic involving turnstiles, I learned something where the assumptions were given in the problem, and each line was proven based on the previous lines, which boiled down to the initial givens.
https://en.wikipedia.org/wiki/Gymnasium_(school)
> I've gone through high school and taken CS (and a bit of discrete math and logic) in college, and never seen the ⊢ symbol before.
Interesting. I was taught ⊢ first semester in CS in Logic class. Along with most other common logic notation.