alt Hacker NewsThe syntax in the article is not scheme, you can clearly see it in my comment you're responding to.
As for your 'light introduction' comment: even ignoring the code, these are not pedantic complaints but basic mathematical and factual errors.
For example, the statement of Birkhoff’s Representation Theorem is wrong. The article says:
> Each distributive lattice is isomorphic to an inclusion order of its join-irreducible elements.
That is simply not the theorem. The theorem says "Theorem. Any finite distributive lattice L is isomorphic to the lattice of lower sets of the partial order of the join-irreducible elements of L.". You can read the definition on Wikipedia [0]
The article is plain wrong. The join-irreducibles themselves form a poset. The theorem is about the lattice of down-sets of that poset, ordered by inclusion. So the article is NOT simplifying, but misstating one of the central results it tries to explain. Call it a 'light introduction' as long as you want. This does not excuse the article from reversing the meaning of the theorem.
It's basically like saying 'E=m*c' is a simplification of 'E=m*c^2'.
[0] https://en.wikipedia.org/wiki/Birkhoff%27s_representation_th...
> That is simply not the theorem.
> The article is plain wrong.
> This does not excuse the article from reversing the meaning of the theorem.
What's with this hyperbole? Even the best math books have loads of errors (typographical, factual, missing conditions, insufficient reasoning, incorrect reasoning, ...). Just look at any errata list published by any university for their set books! Nobody does this kind of hyperbole for errors in math books. Only on HN do you see this kind of takedown, which is frankly very annoying. In universities, professors and students just publish errata and focus on understanding the material, not tearing it down with such dismissive tone. It's totally unnecessary.
I don't know if you've got an axe to grind here or if you're generally this dismissive but calling it "simply not the theorem" or "plain wrong" is a very annoying kind of exaggeration that misses all nuance and human fallibility.
Yes, the precise statement of Birkhoff's representation theorem involves down-sets of the poset of join-irreducibles. Yes, the article omits that. I agree that it is imprecise.
But it's not "reversing the meaning". It still correctly points to reconstructing the lattice via an inclusion order built from join-irreducibles. What's missing is a condition. It is sloppy wording but not a fundamental error like you so want us to believe.
Feels like the productive move here is just to suggest the missing wording to the author. I'm sure they'll appreciate it. I don't really get the impulse to frame it as a takedown and be so dismissive when it's a small fix.