Solve Russell paradox

[lemgruber]

Dears Friends,


looks like that:

the confusion starts of definition of set, subset and element.
And the problem desapear not call subset when the set be inside of other set,
in this moment him don't be a subset, but is realy a only element of this set.
Elements being only propertys of a set, never subset.

Aplied, and you see, a set what belongs a self is not a set in this condition, this is a only a element a property of other set.

cool don't you think!

Regards,

Lucio Marcos Lemgruber and Company

 

[lemgruber]

solve russell paradox

This regards, need more explicit from my part to you, so, going more slowly:
The paradox force a non existence of a universal set, because him be a member of set,
what I saying is what hapened is this elements be properties of a set, belongs a him, not
right say a set belongs a yourself set, be same say a properties belongs a properties,
sets be sets, elements be elements, even subset when in this position not a subset, just be elements our properties
of a real set.
I hope be more clear in this time, and apologize by terrific wright.

thanks friends

Lucio Marcos Lemgruber and company

 

[HallsofIvy]

I really don't understand what your point is. Sadly, I find your English very difficult to understand. Also you titled this "Solve Russell Paradox". If you know what the Russell Paradox (also called the "Russell-Zermelo paradox") is, then you know that it cannot be "solved" in ordinary "naïve set theory". It showed that a new, more sophisticated, understanding of the basic idea of "sets" was necessary and led to a "theory of collections" which included the usual concept of "set" as a specific type of collection.

The usual statement of the Russell-Zermelo paradox is this: In naïve set theory we define a set to be any collection (in the usual English definition) of objects. As long as it is possible to clearly define a set (that is, give a rule by which we can determine whether or not any given object is in the set) then the set exists. And, since sets themselves are objects, we can defined sets that contain other sets. So, for example, since it is possible, by that definition, to determine whether or not an object is a set, we can define the "set of all sets" and that set exists. And, of course, since that set is itself a set, it contains itself.

So we see that it is possible for a set to contain itself. Knowing that it is possible for a set to contain itself, although most set don't, we can define the "set of all sets that do NOT contain themselves". Now, the question is, "Does this set contain itself or not?"

If it does NOT contain itself the it is a "set that does NOT contain itself" so fits the definition of thing that should be in it! That is a contradiction. On the other hand, if it does contain itself, it contradicts that definition, again a contradiction.

 

[lemgruber]

solve russell paradox

HallsofIvy


First of all, I like ask apologize to bad english, not my language, if I do that, its because I can achieve a people like you master, if I not to do that, not heard the best mens.
Mr. already now, I be intuitive line, I now what they saying about this type of thinking, but I liked e fight for him, until the end.

the problem: "set of all sets" give a contradiction ancient a russell paradox. The set of all the set, not be a set, because we afirm what all the sets before was used. So, him as a type of supraset or other thing, and this, going out of a ****( sorry by language) paradox.

I ask a you master, if you could analize this idea, his is only in begin, could say if I go a read or stop whith this.

thanks

Lucio