Set theory

Hi Arjuna glad to see you back !
...yeah, Set theory is "troublesome" to say the least...

What I'm not getting is the idea that a set isn't the the same thing as the total of its members. It's something else. The set of all moons of the planet earth isn't THE moon. The set is some type of object all by itself. It's sounds like idealism to me.

I'm looking to understand the way mathematicians work around Russell's paradox. Are you familiar with that?

Hope you're doing well. Autumn in Portugal? Hope it's beautiful!

Yes I am familiar with Russell´s paradox, at least as far as a non mathematician can pretend to be familiar with it...

...to make a long story short my point against it, is that say, a triangle of triangles is not a triangle (a false reduction) but a triangle of triangles...so, no such thing as a set belonging to itself (it does n´t fit itself)...actually the very word "belonging" is crystal clear in its relational status...and relational logically imply´s informative, what else ?...informative is precisely that which ads something to something...and on that regard I would like to point out that quantity is the constituent of quality !

simply put:
...while little triangles belong to a bigger triangle, the bigger triangle does not belong to the little triangles...
(a false reduction)

...being a bigger triangle with triangles in it, is not the same as being a "straight" triangle...

(previous post re-edited )
...when pretentiously mentioning a final set of all sets we are saying nothing at all...not that there is n´t a final set of all sets but simply that we cannot define it nor containing it if not allusively...any set but specially a final set of all sets does not belong nor can it be informed to any of its parts...

...in rigour while some patterns are similar but on a close look not alike and we can loosely speculate upon what is equal in them we should reason that what makes them different its their context and functionality, that is, where they fit and what they fit in themselves or behind themselves...
(location location location)
Being "there" and not "here" is a property of any bit of information which distinguishes it from any other...talking about sets is talking about locations as much is talking about patterns...

Is this like theories about Set?

...this is a theory about in depth resolution, about detail, about establishing the boundary´s of a pattern, and how patterns work out of relations...above all any form is primarily a collection of dots, and a pattern very much depends on the relation it establishes with a specific observer, that is what they are doing together, the specific relative relation or the function they establish with each other...

...for instance Set for me is a square, if I think upon him in 3D I see a brick, but it might well be that for you, as he shuts rolling past by you, his "squary" ass form works more as a circle...yeah, shapes are functions, not things...

...its funny that we all come to believe that we can place a house inside its own "houseness"...

Apparently set theory arose out of a need to deal with the idea of infinity... to make it available to reason? The idea of convergent progressions arose from it? I think I'm running before I can walk here, but I keep coming back to this issue: you can relate an entity (numbers are a simple example) to its immediate neighbors . You can't relate a specific number to infinity, though. All numbers become equivalent when you do that. It's because infinity is a negative idea: it's a lack of limitation. It's not a positive thing that's available for relationship... except as a concept it's related negatively with the idea of limitation. That's why it's convenient (and only possible?) to talk about infinite progressions as sets. A single member of the progression can relate to the set because the set is closed or limited even though the number of members isn't.

I think we're loitering around the difference between a thing and its definition. A set is like a club that requires entities to meet certain qualifications for membership. A set is really nothing but criteria. It's when you think of criteria as a bucket capable of holding things that exhibit that criteria... that's when things get weird. You can end up with an infinitely large bucket. I have a suspicion we didn't really escape from the basic problem by introducing set theory. I've bought a book about the history of set theory.. maybe I won't sound so silly after I read it.


Right. Each member implies all the other members and implies the set itself. Location can't be identified by any absolute coordinates... as you said, location is talking about an observer/observed relationship. Man.. it's complicated. Confused is a good place to be, I suppose.

As always,
thanks!

Hi osso! What set does Set belong to?

Did you ever noticed that infinity itself only works out of finity, only makes sense with the most finite set of quality´s ? its always the repeating of one in there...another one and another one and another...

I am trying to downgrade the very idea of quality to quantity...precisely by downgrading all dimensions to one dimension, left and right...functions and sizes of bigger and smaller strings of information create the illusions of more dimensions...on this regard the variety of geometry can be reduced to size and repeating only of the very same thing...

..the ontological question I pose to you Arj is, does ONE (1) belongs to itself ? does it make sense speaking on vectors (belonging) when speaking of metaphysics, or ultimate nature ? I mean geometry is second order, its phenomena...ontologically it does n´t make sense to talk about sets...qualitative sets beyond primary quantitative sets are forms of description from the standing point of relative measurer's as being sub sets... ...they imply relations that can only be asserted and seen do to the limited scope of computing power they have...a final set reduces all forms to the eternal repeating of one nature...its a damn loop...and the set its not only finite but the most finite there is...its one !
How does it work ? binarilly but not with two diferent natures...rather the presence and absence of the same one...1 and 0...

In naive set theory a set can contain itself, but not so in ZFC set theory, where you have the Axiom of Regularity to deny that a set can be a member of itself. There you go.

One way to make sense of the concept of the set is to think of it as a “logical container” (relation) which may or may not have a content. The set of “all living people”, for example, contains some finite number of members (people) that are related to one another by the fact that they are “alive”. On the other hand, the set of “all people who have yet to be born”, although it has no members, still constitutes a valid set. A set then is more that merely the sum of its parts, and this is where many people tend to get into trouble, and especially when they imagine that sets can be members of themselves.

Consider, for example, the set of “all living people”. The relation which binds the members of this set together as a unit or entity is the fact that they (the members) are all living people. However, if all of the members of this set are necessarily living people, then the relation which binds them together as a set cannot itself be a member of that set. Therefore, it is not right to say that any set can be a member of itself, for without a relation, all that remains of a set is a number of disconnected objects. Therefore, even if we take the "set of all that is" (the Universe), the relation which binds the members together (being) cannot itself be a member of that same set, but must transcend it. This is where paradoxes such a Russell's come about. However, since no set can be a member of itself, and since the set of all sets is likewise not a member of itself, no such paradox arises.

I think I'm getting too old for this crap. I still haven't figured out how many angels can dance on the head of a pin.

Well, I have. But I don't know how to phrase it mathematically.

Set belongs to the Franklin Mint Civil War chess set.

did they move to Canada, too?

A combination of the love for the powerhouse CFL and the pursuit of the all mighty Canadian dollar.