# non axiomatic set theorem

#### lemgruber

Hello Brothers,

I'm a brazilian admirator of math and philosofy, my english is very poor, because I ask apologize antecipated.
I whish yours opinion about a theorem, if I must go on, or forget about. let see:

Became G a set of total possible of existence, in the form:

{x e G/ x property of a total possible of existence}

think existence in all levels.

Theorem: First cause

"If set G is not a subset of nine other existent set, what import to say, him is self cause, so him is perfect, and finite."

Prove for contradiction: G is not a subset, but is imperfect. So must exist least one element what is not a property of G,
became possible a existence of a set compound by elements of G and a least one element, so G became a subset. Absurd(contradiction).

in other hand, let see: the set G is perfect, but is a subset of another set. but if G is all possible of existence, a set what a contain G do no property
elements , because this not have existence of ents what sustain this set. Absurd(contradiction).

Q.E.D.

if theorem is true, let say what set exist, is cause by yourself and perfect e finite. I know what this prove seems very simple, but if is true, another consequences of him, maybe not be so simple.

thanks antecipated,

Atenciously,

Lucio Marcos Lemgruber

#### v8archie

Math Team
It's difficult to understand, but appear to start by assuming that a set G exists, such that everything is a member of G.

This is a problem because the power set of G (the set that contains all subsets of G) cannot be a member of G unless G is empty.

So either G is empty and thus nothing exists (can the empty set exist if nothing exists?) or G does not exist.

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#### lemgruber

Dear Mr.,

I think understood what you say, but if is true, only exist subset, never set
complete, high? what we doing whith concept of perfection, doesn't exist either?

Mr. you was a first persona a aswer my thread, I glad and I hope our dialogue continue for a long time, its a honor for me.

thanks

Lucio

#### v8archie

Math Team
I see no reason why perfection must exist except as an abstract ideal. I just believe in what the logic shows.

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#### lemgruber

I be try construct a argument, not yet ready, because this paradox ( I gues you
use the Russell paradox) destroy a ideia, even abstract of perfection.
joing whith me in the this journey.

thanks to much for suport my inocence.

Lucio

#### lemgruber

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

#### v8archie

Math Team
I'm afraid that doesn't help.

The elements of the power set of G are the subsets of G. There is no reason why an element should be a set in its own right, and this is the case here.

1 person

#### lemgruber

Archie,

can you help whith the theorem now? him is valid? the proofs be right?

lucio

#### v8archie

Math Team
Not really. Your set G doesn't exist, so you can't have a theorem about it.

#### lemgruber

Archie,

if G be a power set of all subsets of possible of the existence.

what you think?

the paradox disappear. and the proofs seems as same of other try.

Lucio

Power sets
Main article: Power set
The power set of a set S is the set of all subsets of S. Note that the power set contains S itself and the empty set because these are both subsets of S. For example, the power set of the set {1, 2, 3} is {{1, 2, 3}, {1, 2}, {1, 3}, {2, 3}, {1}, {2}, {3}, âˆ…}. The power set of a set S is usually written as P(S).

The power set of a finite set with n elements has 2n elements. This relationship is one of the reasons for the terminology power set[citation needed]. For example, the set {1, 2, 3} contains three elements, and the power set shown above contains 23 = 8 elements.

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