December 27th, 2014, 04:51 PM  #11 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,675 Thanks: 2655 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). 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: 7,675 Thanks: 2655 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. 
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 
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  
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  
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  Quote:
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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