Timeline for I am searching for the name of a partition (if it already exists)
Current License: CC BY-SA 2.5
10 events
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| Jun 18, 2010 at 14:28 | comment | added | klaraspina | Well, yes, actually the idea came out because I wanted to consider the connected pieces of a Venn Diagram... I think I am going to relax the requirements of a Boolean Algebra, and possibly to see what happens at its properties... and what about a visualisation of such an algebra? | |
| Jun 18, 2010 at 11:16 | comment | added | Joel David Hamkins | It isn't necessary to actually calculate and represent the whole Boolean algebra. You can describe and index each building block by the in-out membership pattern of points in the modules. | |
| Jun 18, 2010 at 11:07 | comment | added | klaraspina | Closing the algebra is not a good thing for me. First of all because I want to keep in memory which are the given modules. Second, because if I close I have an exponential blowup of sets, and since I want to apply this representation in computer science, it would not be a good thing to do... | |
| Jun 18, 2010 at 11:06 | comment | added | Joel David Hamkins | You could also think in terms of the Venn diagram (en.wikipedia.org/wiki/Venn_diagram). Your buiilding blocks are the smallest spaces appearing in the appropriate Venn diagram of your modules. | |
| Jun 18, 2010 at 11:03 | comment | added | Joel David Hamkins | My proposal was that you should close your modules under intersection, union and complement---this would be the generated Boolean algebra---but that after doing so, you will have the same building blocks, and these are the atoms of that Boolean algebra. | |
| Jun 18, 2010 at 10:06 | comment | added | klaraspina | Thank you! I have to look closer at it, but it seems to be potentially inspiring! Anyway, I do not have a Boolean algebra, because the family is not closed under union and intersection - for example, with my notation, the union of a module is not in general a module, but possibly I have to add some other building blocks. Does something like this already exists? I would be really interested in properties that such a "structure" have! (Otherwise I have to figure out by myself if there are any...) | |
| Jun 18, 2010 at 9:59 | vote | accept | klaraspina | ||
| Jun 18, 2010 at 3:50 | history | edited | Joel David Hamkins | CC BY-SA 2.5 |
Corrected infinite case
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| Jun 18, 2010 at 2:45 | history | edited | Joel David Hamkins | CC BY-SA 2.5 |
added 553 characters in body
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| Jun 18, 2010 at 2:16 | history | answered | Joel David Hamkins | CC BY-SA 2.5 |