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 Mar31 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)... Mar31 asked Sufficient conditions for a quotient algebra to be finite? Dec8 accepted Möbius inversion for locally finite poset Dec3 comment Möbius inversion for locally finite poset Thanks, the suggestion was that you add this explanation to your answer. Dec3 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? Dec3 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 $f^{-1}$. Dec2 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? Dec2 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. Dec2 comment Möbius inversion for locally finite poset @GitGud In the sense described in the square brackets in the second paragraph. Dec2 asked Möbius inversion for locally finite poset Nov19 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 ..."). Oct31 awarded Good Question Jul21 awarded Yearling Jul2 awarded Curious Jun17 awarded Notable Question Mar22 accepted Finite additivity, atomlessness and countable additivity Nov7 awarded Good Answer Jul27 comment Open math problems which high school students can understand The fact that most of the problems listed here are number theory problems is interesting. Does anyone have an intuition as to why this might be the case? Is there a sociological explanation or is there something about number theory that makes it especially rich in easy to state hard to prove conjectures? Jul21 awarded Yearling Jul3 awarded Nice Question