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 Dec 4 awarded Nice Question Oct 15 awarded Good Answer Jul 21 awarded Yearling May 30 awarded Popular Question Mar 31 comment Sufficient conditions for a quotient algebra to be finite? Ok, well, I guess I'm interested in the cases where there is a solution. For example, If you have "and" "or" and "not" of classical propositional logic as your connectives, then you show that every well formed formula is a unique disjunction of atoms, and there are finitely many atoms. That's the DNF. I'm guessing a similar thing can be done for a distributive lattice (but I'm not sure)... Mar 31 asked Sufficient conditions for a quotient algebra to be finite? Dec 8 accepted Möbius inversion for locally finite poset Dec 3 comment Möbius inversion for locally finite poset Thanks, the suggestion was that you add this explanation to your answer. Dec 3 comment Möbius inversion for locally finite poset Looking at this more carefully, this isn't quite what I need. Note that the summation in your version is over $x < z \le y$ while in the version Rota appeals to, it is $x\le z < y$. I guess this is what Nishant meant be his/her comment on the question. Could you perhaps expand on that step? Dec 3 comment Möbius inversion for locally finite poset Oh I think I see. Sorry, I was tired when I read this last night. Perhaps you could expand on the "so" in your answer. i.e. just say that you rearrange the equation above to get an expression for $f^{-1}$. Dec 2 comment Möbius inversion for locally finite poset This seems to fundamentally misunderstand the question. I don't want a function such that $f(x,x)f^{-1}(x,x) = d(x,x)$, I want a function such that $\sum_{x\le z \le y} f(x,z)f^{-1}(z,y) = d(x,y)$. On a partially ordered set, what does $\frac{1}{f(x,x)}$ even mean? Dec 2 comment Möbius inversion for locally finite poset In fact, I'm not bothered that it's an "inverse" in any sense, I just want to understand how the $\mu$ so defined is related to the $\zeta$ and $\delta$ so defined. Dec 2 comment Möbius inversion for locally finite poset @GitGud In the sense described in the square brackets in the second paragraph. Dec 2 asked Möbius inversion for locally finite poset Nov 19 comment Why do proof authors use natural language sentences to write proofs? There seems to be a presumption that natural language can't be part of a formal proof system. Mathematical language seems regimented enough that it might qualify as a formal system. For example, very specific meanings are given to some natural language constructions (like "almost everywhere" or "if ... then ..."). Oct 31 awarded Good Question Jul 21 awarded Yearling Jul 2 awarded Curious Jun 17 awarded Notable Question Mar 22 accepted Finite additivity, atomlessness and countable additivity