Attacko's Babylonian Maneuver

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I feel we are dragging this thread away from the main point, but I have some comments on the subject of Venn diagrams:

Counting the mutual sets and the universal set, it is impossible to reach an amount of set that is a power of 2, as there will always be an uneven amount of sets.

A Venn diagram with 2 basic sets has 3 sets,
A Venn diagram with 3 basic sets has 7 sets,
A Venn diagram with 4 basic sets has 13 sets,
A Venn diagram with 5 basic sets has 21 sets,
A Venn diagram with 6 basic sets has 31 sets,
A Venn diagram with 7 basic sets has 43 sets,
A Venn diagram with 8 basic sets has 57 sets,
A Venn diagram with 9 basic sets has 73 sets,
A Venn diagram with 10 basic sets has 101 sets,
andsoforth.

This is counting that all set combinations exist, which is what I believe is true. If there is any Venn diagram expert out there (Attacko!), please do correct me if I am wrong.
 
Not all combinations need to exist (i.e intersections could be the empty set, a set could be a proper subset of another, etc.).

With 1 set A and the universal set there are 2 sets, E (can't do the universal set squiggly E here) and A which is a proper subset of E.

With 2 sets A and B you can have 3 sets (E, A and B which is a proper subset of A i.e. A intersect B is the set A itself) or you can have the case where A and B are disjoint so A intersect B is the empty set, or 4 sets (E, A, B, and A intersect B).

That's just the simple case where neither A and B are themselves the universal set, and A is not the same set as B.

Hope that clears things up.

EDIT: One thing I wouldn't mind Attacko explaining, if we have 2 sets, one which contains all sets which contain themselves as a subset, and another which contains all sets which do not contain themselves, will this naive set theory model be consistent with regards to Peano arithmetic? Or is a set which can contain itself as a member not in fact a set but a class?
 
Diamondeye said:
I feel we are dragging this thread away from the main point, but I have some comments on the subject of Venn diagrams:

Counting the mutual sets and the universal set, it is impossible to reach an amount of set that is a power of 2, as there will always be an uneven amount of sets.

A Venn diagram with 2 basic sets has 3 sets,
Click to expand...

This is not quite right. Each object can potentially be
A) a member of the set (or)
B) not a member of the set.

Given 1 set Alpha, all objects are put into 2 categories: Member Alpha or not-Member Alpha.

Given 2 sets, Alpha and Beta, all objects will be put into 4 categories.
1 Member Alpha/Member Beta
2 Member Alpha/not-Member Beta
3 not-Member Alpha/Member Beta
4 not-Member Alpha/not-member Beta

This trend continues with more sets available. I think that you were leaving out the not-member for all sets when you made your list of options on the first two and then your later ones were just completely wrong. Just keep in mind that for each set, the only options at this level are "member" or "not-member" and you'll see that it must end up with powers of two.

Edit: Just to state it explicitly, I'm leaving out sets of sets because recursion is what makes some reasonable folks argue that set theory isn't properly a branch of mathematics at all because it leads to inherent problems of paradox. Goedel, Escher and Bach is a very good and very readable book on this subject and a quick look at the liar's paradox on Wikipedia should give a decent introduction to the problem (as would a google search on "sets which contain themselves").

Edit the Second:
http://en.wikipedia.org/wiki/Russell's_paradox
link to the Wikipedia article that has a neat explanation on this issue. Completely unnecessary to understand Venn diagrams, but very necessary if someone wants to argue with me that there are more options in set theory than "Member" vs. "not-Member"
 
Cross posted with popejubal I guess. I was hinting at the difference between a set and a class in my edit.

Venn diagrams aren't that useful anyway because there are only so many interactions you can show between sets in 2d space. If we move to higher dimensions I think we are still limited by the kissing number of hyperspheres I believe. Even then, many higher dimensional kissing numbers are not yet known exactly, only a lower bound, which as everyone knows is

k >= RiemannZetaFunction(n) / power(2, n-1)

where k is the n dimensional kissing number.
 
I am going to make a Venn diagram TODAY, no matter what anyone else says! HAHAHAH!
 
Ok, I made a diagram, showing the difference and similarities between men, women, Babylon, and Waffles. I apologize for blurriness- if all else fails blame poor psyche or poor aura or whatever.

 
ParadigmShifter said:
I think he means the number of sets in the Venn diagram should be a multiple of 2, because
of something to do with binary.

However:

a) Shouldn't that be a power of 2 and not a multiple of 2?
b) Why is the universal set not counted as a set in the Venn diagram? Is it not a set? Oh look, it is a set. That's why it has the word "set" in its name. ;)
Click to expand...


Don't forget the empty set, ParadigmShifter! :p
 
Apologies to teh extreme- I forgot about the law of advanced purplism.
 
PieceOfMind said:
Don't forget the empty set, ParadigmShifter! :p
Click to expand...

The empty set is there in a Venn diagram of course, it's a member of the Universal Set ;)

Presumably the posted Venn diagram uses fuzzy-logic hence why the text isn't readable.
 
ParadigmShifter said:
The empty set is there in a Venn diagram of course, it's a member of the Universal Set ;)

Presumably the posted Venn diagram uses fuzzy-logic hence why the text isn't readable.
Click to expand...

One of the things that absolutely blew my mind during college was the fact that some girls were willing make out with me just because I didn't treat them like garbage.

One of the other things that blew my mind during college was the fact that there are things that can't actually be put into a Venn diagram. I wonder if Troy knows about these things.
 
Maybe we need Moonsinger and Misotu to give Attacko a good civ kicking.

Now I think about Venn diagrams I'm not sure the universal set is in fact a set but a proper class instead (since I don't think a set can contain all other sets and still remain a set). I think my high school teacher may have been telling porkies. Perhaps Attacko can clear this up for us.
 
'Maybe we need Moonsinger and Misotu to give Attacko a good civ kicking.'

lol. one thing is for certain- you'd need at least two probably four to make it even.
Mudslinger, Mr Mitshu? never heard of them, but average civ4 players are not any big deal for ol Attacko.:scan:
 
Venn diagrams or set diagrams are diagrams that show all hypothetically possible logical relations between a finite collection of sets (groups of things). Venn diagrams were conceived around 1880 by John Venn. They are used in many fields, including set theory, probability, logic, statistics, and computer science.

holypedia

Tesla, John Venn-like theories applied to Civ4 via the Attacko method.
The electric connections made can be rerouted by adjusting settings such as clicking off sid tips and the blue city circle suggestion.

Likewise a good attack is based on confusing the enemy- ie cutting off troop supply roads so you don't have to fight four hundred and fifty two archers.
 
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