4 ms·
I don't think they are completely wrong - "=>" is just implication. A hidden assumption in their diagrams is that circles of different colours are assumed to be
by bubblyworld 6mo ago
I don't think they are completely wrong - "=>" is just implication. A hidden assumption in their diagrams is that circles of different colours are assumed to be different elements.
A morphism from orange to yellow means "O <= Y". From this, antisymmetry (and the hidden assumption) implies that "Y not <= O".
Totality is just the other way around (all two distinct elements are comparable in one direction).
- gobdovan 6mo agoIf this is meant to be an explainer, that can't be simply implicit. The text actually seems full of imprecise claims, such as: "All diagrams that look something different than the said chain diagram represent partial orders" "The different linear orders that make up the partial order are called chains" The Birkhoff theorem statement, which is materially wrong. A finite distributive lattice is not isomorphic to "the inclusion order of its join-irreducible elements".
- bubblyworld 6mo agoI mean, it's a blog post, those statements are correct in spirit. A taste thing, I think. I agree about the birkhoff theorem though.