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 December 27th, 2014, 04:51 PM #11 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,649 Thanks: 2630 Math Focus: Mainly analysis and algebra 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). Thanks from lemgruber Last edited by skipjack; January 11th, 2015 at 04:35 PM.
 December 27th, 2014, 06:34 PM #12 Senior Member   Joined: Dec 2014 From: Brazil Posts: 203 Thanks: 1 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
 December 27th, 2014, 06:48 PM #13 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,649 Thanks: 2630 Math Focus: Mainly analysis and algebra 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. Thanks from lemgruber
 December 27th, 2014, 07:33 PM #14 Senior Member   Joined: Dec 2014 From: Brazil Posts: 203 Thanks: 1 non axiomatic set theorem o mais engraÃ§ado Ã© que eu entendo relativamente bem o que vocÃª escrever em espanhol, mas nÃ£o tenho a minima ideia de como escrever em espanhol. Ã© capaz que se eu tentar escrever em espanhol vou passar mais vexame ainda. Obrigado, amigo pela paciencia e compreensÃ£o LucioÂ´
 December 28th, 2014, 01:07 PM #15 Senior Member   Joined: Dec 2014 From: Brazil Posts: 203 Thanks: 1 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
December 28th, 2014, 01:47 PM   #16
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 Originally Posted by lemgruber 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.

 December 28th, 2014, 02:20 PM #17 Senior Member   Joined: Dec 2014 From: Brazil Posts: 203 Thanks: 1 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.
December 28th, 2014, 02:51 PM   #18
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 Originally Posted by lemgruber 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"?

 December 28th, 2014, 04:02 PM #19 Senior Member   Joined: Dec 2014 From: Brazil Posts: 203 Thanks: 1 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.
 December 28th, 2014, 07:24 PM #20 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 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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