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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
Nov
7
awarded  Good Answer
Jul
27
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?