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Sep
24
comment Compositions of filters on finite unions of Cartesian products
I thought (without writing a detailed proof), that this my question is equivalent to an other open problem I work about. Now I see my problem does not follow trivially from this question. Because my open problem is more hard, I thought this question is also hard and stupidly overlooked a trivial solution. It is one of my biggest mistakes. Thanks anyway and get my bounty
Sep
24
accepted Compositions of filters on finite unions of Cartesian products
Sep
22
revised Order on the set of partitions (terminology)
edited tags
Sep
21
asked Order on the set of partitions (terminology)
Sep
18
revised Compositions of filters on finite unions of Cartesian products
typo
Sep
17
revised Compositions of filters on finite unions of Cartesian products
added 123 characters in body
Sep
16
asked Compositions of filters on finite unions of Cartesian products
Sep
14
revised Another conjecture about filters and cartesian products
deleted 1718 characters in body
Sep
14
comment Another conjecture about filters and cartesian products
In mathematics21.org/binaries/funcoids-are-filters.pdf I have shown that $\Gamma$ in both my questions are the same. So the answer to this question is: yes, it can be proved
Sep
14
answered A conjecture about filters and finite unions of cartesian products
Sep
14
comment A conjecture about filters and finite unions of cartesian products
I provided a counter-example as an answer. That counter-example was wrong.
Sep
14
accepted A “rearrangement” of a finite set
Sep
14
awarded  Necromancer
Sep
11
answered A “rearrangement” of a finite set
Sep
11
comment A “rearrangement” of a finite set
For pairwise non-equivalent elements $a_0, \ldots, a_k$ we have $\forall i, j \in \{ 0, \ldots, k \} : (i \neq j \Rightarrow a_i \not\in X_{i, j} \wedge a_j \in X_{i, j})$ where $X_{i, j} \in T$. How to derive that $k \leqslant 2^n$?
Sep
11
comment A “rearrangement” of a finite set
@ThomasAndrews: I've spent more then a hour trying to prove this. I feel I am very near to the solution, but something prevents me to find it. Please explain how to derive the solution. It is not a homework and your help won't harm
Sep
11
comment A “rearrangement” of a finite set
@ThomasAndrews I feel that I am near to the answer. Probably I need to select a canonical representative element from every equivalence class
Sep
11
comment A “rearrangement” of a finite set
@ThomasAndrews I am stalled in the attempt to figure out the property of equivalence relations which corresponds to finiteness. Why would you not give me an answer? It is not a homework
Sep
11
comment A “rearrangement” of a finite set
@ThomasAndrews Maybe this is an eclipse in my mind. Why $S$ has at most $2^n$ elements?
Sep
11
comment A “rearrangement” of a finite set
@Hippalectryon I tried to meditate a half of minute and had no ideas