What is the basis for the universe

If it contains a mistaken proof that all vectors have bases, then it's definitely popsci.

google.com.mx/url?sa=t&source=web&rct=j&url=http://sierra.nmsu.edu/morandi/OldWebPages/Math482Spring2005/Zorn.pdf&ved=2ahUKEwiN6-HRqPXZAhVK64MKHW_SD-YQFjAFegQIBBAB&usg=AOvVaw106wLpuxk-JNZNuo94vheR

>google.com.mx/url?sa=t&source=web&rct=j&url=http://sierra.nmsu.edu/morandi/OldWebPages/Math482Spring2005/Zorn.pdf&ved=2ahUKEwiN6-HRqPXZAhVK64MKHW_SD-YQFjAFegQIBBAB&usg=AOvVaw106wLpuxk-JNZNuo94vheR

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Epic

>Zorn
>assuming an axiom which is equivalent to "all vector spaces have a basis" to prove that "all vector spaces have a basis"

Which is equivalent to the axiom of choice retard.

>Which is equivalent to the axiom of choice retard.
Of course it is, what's your point?

What's your point? It's still a proof so I don't understand

Anything is true if you assume it to be true.

Proving equivalence not the same as holding somthing true by definition you moron. By your logic, a statement such as "the sum of angles of a triangle is always 180 degrees" is euclid just assuming it's true, because it's equivalent to his fifth postulate.

>Proving equivalence not the same as holding somthing true by definition you moron.
There's no meaningful distinction, if you can't prove something without assuming it to be true then it's hardly a "proof".

Again, so tell me, how would you proove that a triangle in plane geomtry has the propwety that the sum of it's angles id always 180 degrees.

>Again, so tell me, how would you proove that a triangle in plane geomtry has the propwety that the sum of it's angles id always 180 degrees.
I am not a geometer.

3 vectors: right, left, and the direction of my cock lmao

You don't need to be one to learn know about euclid elements and plane geometry. What you are is a moron.

>You don't need to be one to learn know about euclid elements and plane geometry.
I only study mathematics, I am not sure what business I have with triangles. If you are an expert why do you not provide such a proof yourself?

Those that ask, Them that aspire, They that inquire.

我,誰提出了這個問題,回答只有答案。

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Of what? I provided you with a proof that all vector spaces have a basis, which is true in ZFC. I'm not even a mathematician, but are you really thid ignorant of synthetic geometry?

>Of what?
"that a triangle in plane geomtry has the propwety that the sum of it's angles id always 180 degrees."

> I provided you with a proof that all vector spaces have a basis, which is true in ZFC.
It's a hardly a "proof" to assume your conclusion. The statements are isomorphic in the category of axioms and so no work has been done. If you handed this in for grading I would give it a 0.

>I'm not even a mathematician, but are you really thid ignorant of synthetic geometry?
As a mathematician, triangles do not interest me. I assume they may be more interesting to someone in a different field such as graphic design.

Does synthetic geometry require other people to understand it in order for you to apply it in your communications with them?

I agree. Triangles are not well-ordered until given a square to fit within, complete, or assigned an affine-space.

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>A triangle in plane geometry has the property that the sum of it's angles is always 180 degrees
apronus.com/geometry/triangle.htm
>It's hardly a "proof" to assume your conclusion
>categoru of axioms
>grading
>As a mathematician
You got me 6/10 I was getting pretty worked up
Is it schizo hour? Anyways, order and shit is resolved with hilberts axioms.

>apronus.com/geometry/triangle.htm
If you already had a proof then why did you ask me for one?

>>It's hardly a "proof" to assume your conclusion
I don't see how you can have an issue with this. Logically it is true that any statement implies itself but this is not what anyone operating in the field of mathematics would call a "proof".

Hilbert Hotel is essentially the Schizo Oasis for Mathematicians anyway.
It is more like mathematicians and scientists are more content with the whole 'sharing identity with a perceived god of a specific field' than celebrities are with sharing theirs with their fans.

Any conclusion derived from a generative and concluded by a nominative becomes a votive. Otherwise you are declaring yourself part of the community that would reject something and therefor must adhere to stricter standards than that. To whit, I raise the following:
-1 < +1
+1 > -1
±1 > 0

I mean, you accepted a proof of a statement that is equivalent to the fifth postulated. Your whole troll falls off after this.

>I mean, you accepted a proof of a statement that is equivalent to the fifth postulated.
I'm not sure what you mean by "accepted a proof"?

Is this a bot?
So you don't accept the proof that all triangles have internal angles that add up to 180 degrees?

He means 'conceded the point', which is also another way of saying he willingly rotated on your axis/axiom of expression/understanding.

Are you a human? Given how the species is governed it becomes increasingly difficult for those that are wealthy without society to know what the greatest shared identity is.

Given that 180 degrees is an arbitrary choice (as 360 for a full circle also is, given that the 0 is simply a substitute for 9 moduli)

>So you don't accept the proof that all triangles have internal angles that add up to 180 degrees?
What do you mean by "accept"? I personally have no interest in triangles, I just do not know why you would ask me for a proof of something you apparently already have a proof for. I personally would only consider something a veritable proof if it has length at least one in the category of axioms, while the kind of things you are proposing have length 0 since the statements are isomorphic.

Theres no such thing as the category of axioms.

>Theres no such thing as the category of axioms.
How do you do proofs without axioms?

You can't, that doesn't mean that there's such a thing as a category of axioms, because any wff can be a fucking axiom, i.e. you are talking about thd category of all first order logic expresions. If you take an axiomatic system, maybe you could define a category between equivalent statements, but that would give you nothing. Also, isomorphism, in the broad sense of category theorem ks between two categories, not one. A general morphism has nothing two do with structure preserving shit. In any sense or for equuvalent statements in an axiomatic systems are trivial shit.
You starting to scare me bro.

>Also, isomorphism, in the broad sense of category theorem ks between two categories, not one.
I only referred to axioms (such as Zorn and "all vector spaces have a basis") as being isomorphic (as objects in the category of axioms), not two categories, so I am not sure what you are trying to imply.

Define the category of axioms for me please.

How and why? As an identity I can't actually harm you over the internet. All I can do is provide statement/counter-argument/submission and subscription.

To anyone of sufficient intelligence the concept of 'divide by even' is no different than '4 % 2' or '2 x 4% = 0.08' or a continued fraction of [math]\frac{1}{\frac{1}{\frac{1}{\ldots }+2}+12}[/math]

>Hilbert Hotel
Is that even well-defined?

"electromagnetic waves"

Well-defined as a defined well of occupiable space, yes. It just isn't directly advertised or easily inspectable given how most real mathematicians have perversions that would be beyond most mortal men, and any GOOD mathematician would ensure that their Hotel would account for the tastes of 'all' their clientele.

Even if they simply adopted the name "Hilbert" upon entry as the only discriminator/exclusionary criteria (which would satisfy the problem)

>Well-defined as a defined well of occupiable space, yes. It just isn't directly advertised or easily inspectable given how most real mathematicians have perversions that would be beyond most mortal men, and any GOOD mathematician would ensure that their Hotel would account for the tastes of 'all' their clientele.
>Even if they simply adopted the name "Hilbert" upon entry as the only discriminator/exclusionary criteria (which would satisfy the problem)
I see...

To a mathematician '1' = 'identity', which is what a lot of the big fancy question of mathematics is actually inquiring. They aren't really seeking optimal pathing (because that must 'always' be a multiplicative/exponential/commutative result when dealing with 3+), it is more 'what is the optimal identity assignment stepping?'.

Paradoxes are as infinite as 'reals over time' so in truth just identifying the problem OR a potential solution (of any measurable strength) causes an axial shift. It's usually why so many people argue over axioms.

Your words mean nothing my dude.

*shrug* all words have only the value an observer prescribes to them. It is just easier for me to explore my own internal dictionary here on Veeky Forums than anywhere else because despite whatever the overarching personality type that draws humans here, people here at least 'talk' to some degree.

Turnover rate > fixed state.

>Also, this is Veeky Forums. Nobody's words mean anything because

Let it be b, such that log_b(1)=universe(t)

>*shrug* all words have only the value an observer prescribes to them. It is just easier for me to explore my own internal dictionary here on Veeky Forums than anywhere else because despite whatever the overarching personality type that draws humans here, people here at least 'talk' to some degree.
>Turnover rate > fixed state.
>>Also, this is Veeky Forums. Nobody's words mean anything because
test

Testing for/

he thinks you're a bot m8

>he thinks you're a bot m8
I'm not a "he".

中肯?

匿名性別?

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ah the sperm worm thinks you're a bot
why are you even on this board if you think gender is important subhuman

>匿名性別?
Quite.

傳遞性的兩性

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But you know all axioms, including ZF, are just assumed in the same way AC is? You can as well that all proofs that 1+1=2 are wrong because they rely on axiom equivalent to 1+1=2

>if you can't prove something without assuming it to be true then it's hardly a "proof".
But that's how every proof looks like, you show your statement is equivalent to some axioms which are assumed to be true, so by your reasoning you can't prove anything

>But that's how every proof looks like
This is false.

>You can as well that all proofs that 1+1=2 are wrong because they rely on axiom equivalent to 1+1=2
This is also false.

You have proofs that don't assume axioms?

>You have proofs that don't assume axioms?
Why would you think that?

Then what's the problem with

Why are all proofs of 1+1=2 equivalent to 1+1=2?

Why do all proofs of 1+1=2 rely on an axiom equivalent to 1+1=2?*

How do you prove 1+1=2 without some axiomatic system of naturals?

>How do you prove 1+1=2 without some axiomatic system of naturals?
What's the relevance of this?

You are retarded

>You are retarded
Can we stay on topic? What's the relevance of what you said?

en.m.wikipedia.org/wiki/Peano_axioms retard

Did you misread my post? I was asking for the relevance, not which axiomatic system of naturals you were referring to.

All models of natural bumbers rely on there being some "succesor function" or statements equjvalent to them, either induction, the well order principle (for natural numbers) or anything equkvalent to them. A succesor function is a formal way of saying 1+1=2

Gay Juice.

I still don't see the relevance. I asked why all proofs of 1+1=2 rely on an axiom equivalent to 1+1=2. Are you trying to imply that the Peano axioms are equivalent to 1+1=2?

They use it, yes.

>They use it, yes.
Who are "they" and what is "it"?

Can you demonstrate how 1+1=2 implies the Peano axioms?

Anyone trying to make a condtruction of the natural numbers.
That wasn't the point, the pibt is that in any model of the peano axioms, or some equivalent axiomatic system you either take that 1+1=2 or you need an equivalent axiom. In general it's not just 1+1=2, but a succesor function defining addition.

All of this is because some retard said that the proof of all vector spaces have a basis is not a proof, because it's equivalent to AC.

>That wasn't the point, the pibt is that in any model of the peano axioms, or some equivalent axiomatic system you either take that 1+1=2 or you need an equivalent axiom.
Now were just back to my original question which remains unanswered: Why do all proofs of 1+1=2 rely on an axiom equivalent to 1+1=2?

> the proof of all vector spaces have a basis is not a proof, because it's equivalent to AC.
This is true.

Because if we take peano axioms as a model of natural numbers, all other axiomatic systems for the natural numbers should give you the sane results. Because the existabce if a successor function is independent of the other aximos in Peanos formulation, if you want an equivalent AS, that gives you the same results as Peano, and you take out the succesor function axiom, you need set of statements equivalent to it, otherwise you may ebd with more or less true proofs.
So the proof of the well ordering principle is not a proof? You understand that you can't determine if two statements are equivalent a priori right? Zermeli still had to show the implication.

>Because if we take peano axioms as a model of natural numbers, all other axiomatic systems for the natural numbers should give you the sane results. Because the existabce if a successor function is independent of the other aximos in Peanos formulation, if you want an equivalent AS, that gives you the same results as Peano, and you take out the succesor function axiom, you need set of statements equivalent to it, otherwise you may ebd with more or less true proofs.
You're still not addressing my question, so to be more specific, which axiom is equivalent to 1+1=2?

If you don't know shit about logic I can't explain further. The point is not to give a specific Axiomatic system equivalent to Peano, but that all of them either contain the succesor function axiom or a statement equivalent to th

Equivalent to it. *

>If you don't know shit about logic I can't explain further. The point is not to give a specific Axiomatic system equivalent to Peano, but that all of them either contain the succesor function axiom or a statement equivalent to th
What part of my question do you not understand? You claimed "all proofs that 1+1=2 ... rely on axiom equivalent to 1+1=2". Which axiom is equivalent to 1+1=2?

You keep showing you don't know what an axiomatic system is, and fail to see the point. If you give me a specific axiomatic system, that is supposedly equivalent to peano then I could maybe find the ir the set if statemnts equivalent to that, but if you don't provide a fucking acxiomatic system, your question makes no fucking sense.

>You keep showing you don't know what an axiomatic system is, and fail to see the point. If you give me a specific axiomatic system, that is supposedly equivalent to peano then I could maybe find the ir the set if statemnts equivalent to that, but if you don't provide a fucking acxiomatic system, your question makes no fucking sense.
Then use the Peano axioms. Can you lay off the swearing?

THE PEABO AXIOMS ALRADY CONTAIN THE SUCCESOR FUNCTION AS AN AXIOM YOU RETARD.

>THE PEABO AXIOMS ALRADY CONTAIN THE SUCCESOR FUNCTION AS AN AXIOM YOU RETARD.
Are you saying 1+1=2 is equivalent to the successor function?

1+1=2 is the fuckibg succesor function you retard.

>1+1=2 is the fuckibg succesor function you retard.
1+1=2 is an equality, not a function.

Eric, be dense all you want, nice b8 whatever.

>So the proof of the well ordering principle is not a proof?
Which proof? If the objects are isomorphic in the category of axioms then they represent the same 0-simplex in the nerve of the category. Proofs require a chain including a strictly positive number of 1-simplices.

>Eric, be dense all you want, nice b8 whatever.
What definition of function allows "1+1=2" to be a function? Here, have a read: en.wikipedia.org/wiki/Function_(mathematics)#Definition

en.m.wikipedia.org/wiki/Successor_function