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December 27th, 2014, 04:51 PM   #11
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No it doesn't, because G also has a power set - the set of all possible subsets of G. There is no paradox here. Only a statement that there is no largest set, because whatever set you pick, I can pick it's power set which is bigger.

I understand that the existence of power sets is an axiom (in ZFC) so in principle one could deny this assertion and create a system in which not all sets have a power set (I don't think you could manage to make any sensible system in no sets have a power set, unless you were to do something such as disallow sets to be members of another set - although such an approach is likely to serious reduce the abilities of your system).
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December 27th, 2014, 06:34 PM   #12
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non axiomatic set theorem

Archie,


my intention is realy, became a set more largest of all, be the first cause of all, I need to prove him, the philosofy lost credibility because not demonstrate yours foudments, and the proof needs be a formalist.
In philosofy exist a first cause, call being, I must reduct him in notation of set theory(understand now my problem.).
first version of theorem be wrong because the definition the set, as set o all sets, leaves a contradiction in russell paradox.
Rest two more aproachs, first of all, proof a russell paradox in reality caused, for the assumption what exist a set of all other sets, and demonstrate what a happenig before is a contradiction, because a set of other all sets doesn't exist, because al sets be in using, not have possibility for another set. The problem is a definition of ent. this is one way.
the other possibility is use a definition of power set,

save me, don't give up of me.

I need your help!

attenciously,

Lucio
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December 27th, 2014, 06:48 PM   #13
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Are you able to write that in Spanish? I don't know Portuguese and I'm having trouble understanding your English.

I'm also not a set theorist, so I don't know how much I'll be able to do.
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December 27th, 2014, 07:33 PM   #14
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non axiomatic set theorem

o mais engraçado é que eu entendo relativamente bem o que você escrever em espanhol, mas não tenho a minima ideia de como escrever em espanhol.
é capaz que se eu tentar escrever em espanhol vou passar mais vexame ainda.


Obrigado, amigo pela paciencia e compreensão


Lucio´
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December 28th, 2014, 01:07 PM   #15
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non axiomatic set theorem

Archie,

I like you rewiew a possibilitie of a powerset of G, in acord whith definition what a copy of wikipedia and post above, be a set wha I looking for.


Lucio
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December 28th, 2014, 01:47 PM   #16
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Quote:
Originally Posted by lemgruber View Post
I like you rewiew a possibilitie of a powerset of G, in acord whith definition what a copy of wikipedia and post above, be a set wha I looking for.
I'm sure he already understands the definition of a powerset, but it's not even clear if your G is well-defined.
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December 28th, 2014, 02:20 PM   #17
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non axiomatic set theorem

Realy, I must modify my definition of G, let see:

G is formed for all subsets possible of G whith a property:
possibilitie of existence.

so:

G:{x e G/x propertie of possibilitie of existence}

I not be able to say if this set is well defined, or not.
I say possibilitie of existence an very ample sense, even mathematic sense.

can you help me?

thanks anteciped

Lucio

Last edited by lemgruber; December 28th, 2014 at 02:23 PM.
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December 28th, 2014, 02:51 PM   #18
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Quote:
Originally Posted by lemgruber View Post
G is formed for all subsets possible of G whith a property:
possibilitie of existence.

so:

G:{x e G/x propertie of possibilitie of existence}
1. It looks like you're using G in the definition of G. Is that your intent?
2. Is e supposed to be $\in$?
3. What thing has this property -- x, G/x, or something else?
4. What is G/x? Is is $\{g/x:\ g\in G\}$ or $G\setminus\{x\}$ or something else entirely?
5. What is "possibilitie of existence"?
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December 28th, 2014, 04:02 PM   #19
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non axiomatic set theorem

the answer to two first questions is "yes".
to question 3, sorry, the string correct is "|",

the question of existence, deserve a better explanation:

I don't know if talk about my true objective whith this theorem, the philosofy be treatise like a non science because can't demonstrate yours metaphisics concepts. for exemple, Sartre, is a simple poetry, when confront a formalist demonstration.
I think what a philosofy like a science. the first concept in usual metaphisics, is "being", but beyond don't be demonstred, make be a possibilitie of dialetc, our better saying, open a possibilitie a existence of opositives. to escape of this error, I retry a one concept before, or, a possibilitie of being, because not can oposity in the rest, only "impossibilitie of existence", and "impossibilitie of existence" even can be put in a set , because don't suport a existence of a ent, like a set. You see. the first cause not be a negative cause in our side. Remenber God is a jelous(sorry by joke).

one more time, I ask apologize by the horror english, thanks by patience
and I hope your help my dear friend, in ardue task.

Lucio

Last edited by lemgruber; December 28th, 2014 at 04:47 PM.
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December 28th, 2014, 07:24 PM   #20
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OK. So let $f(x)$ be a predicate meaning "$x$ has the property of possibility of existence" (whatever that means). Then $G$ is some set satisfying
$$
G=\{x\in G:\ f(x)\}
$$
that is, $f(x)$ is true for all $x\in G$. To put it another way: define $\mathcal{G}$ as the (possibly proper) class of all $x$ such that $f(x)$ is true. Then $G\subseteq\mathcal{G}.$

To actually understand this I'd need to know what $f(x)$ is (what "possibility of existence" is) and to know which members of $\mathcal{G}$ are actually in $G$.
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