/sci/ - Science & Math

[Anonymous No.12392268]

What's the most chad subfield of mathematics and why is it set theory?

[Anonymous No.12392275]

>>12392268
If set theory is such a chad field, let me ask you a question. What is a set?
>inb4 autistic screetching

[Anonymous No.12392281]

>>12392268
I like set theory, but it's really not that chad-like
There are only a handful of things which are interesting that fall cleanly under set theory, like the continuum hypothesis or large cardinals.
The rest of set theory just provides the tools for more interesting fields.
Like you wouldn't sit down and do research on the english (latin) alphabet, but you may find the idea that the letter thorn was removed from the alphabet, but the most interesting part of the alphabet is its applications in language. Any other alphabet would do just as well

[Anonymous No.12392283]

>>12392275
It doesn't matter what a set is.

[Anonymous No.12392285]

>>12392275
>inb4 autistic screetching
You're the one screetching.
"set" is a word use to speak of the terms in set theory. That theory has axioms reflecting, more or less well, the intuitions about collections. More or less because it's inevitably used to conceptualize non-finite sets.
If you formalize what a proof is to the extent that you do formal logic, and set up group theory in this logic (as opposed to defining a group as set together with an operation), then a group "is" also just what the axioms characterize it as.

That's a nice enough formalist definition. If you define it in terms of something else, then you could play this smartypants question also with whatever that something else, so it's questionable what this rhetoric achieves.

[Anonymous No.12392289]

>>12392275
A set is a mathematical object, which can contain other mathematical objects. In set theory with ur-elements, each mathematical object is either an ur-element or a set. In pure set theory, all mathematical objects are sets.

[Anonymous No.12392290]

>>12392275
sets to math are what pic related is to biology

[Anonymous No.12392300]

>>12392268
algebra

[Anonymous No.12392302]

>>12392283
Your whole "chad" subfield rests on an undefined notion LOL. The absolute state of set theorists.
>>12392285
>"set" is a word use to speak of the terms in set theory.
Yeah no shit. The question is what do the terms refer to.
>then a group "is" also just what the axioms characterize it as.
Nobody would buy that unless you explain what you're talking about. If you're just give a set of axioms nobody would care unless you explain what they apply to.
>If you define it in terms of something else, then you could play this smartypants question also with whatever that something else
This is a massive cope. You can define natural numbers, rationals perfectly well. For example, rationals as a string of strokes on a whiteboard, integers as naturals with a sign, rationals as appropriate pairs of integers and so on. It's clear, precise and actually explains what we're talking about. You could ask what a series of strokes on a blackboard is and I can show you.
Nothing of the sort has been done with sets. Nobody knows what a "set" is. Can you show me a set? No. Can you compute with sets? No.

[Anonymous No.12392307]

>>12392289
>A set is a mathematical object
Ok and what mathematical object is it? Please clearly define what a set is for me so I can understand.

[Anonymous No.12392309]

>>12392302
> For example, rationals as a string of strokes on a whiteboard,
Oh great, its the wildberger schizo

[Anonymous No.12392311]

>>12392309
How am I a schizo? Don't just namecall, explain how I am wrong. (protip: I'm not).

[Anonymous No.12392329]

[Anonymous No.12392337]

[Anonymous No.12392339]

>>12392307
An object is a material thing
A mathematical object is an immaterial thing such as a number. I have never seen a number in nature. I have seen an apple, and another similar apple, and yet another similar apple, and denoted those apple with an idea "3".
Similarly I could have "3" bananas. 3 is a non-material object.

Similarly, I can say those apples form a collection, or a set of apples. And those bananas form a set of bananas. I could ask about a set of numbers, a collection of numbers. A set of only mathematical objects is a mathematical object. I can ask about a set of sets of mathematical objects for example.

I use the notation {apple} to denote a set with an apple in it, i use {3} to denote a set with the number 3 in it. I use {{3}} to denote the set containing the set containing 3.

If you don't have a problem with taking a collection of objects and assigning an abstract idea to that collection (numbers) then you don't have a problem with sets either; you're just LARPing

[Anonymous No.12392348]

>>12392339
I can see a number. I can write it down, compute with them. I can either represent them by strokes on a whiteboard, or by a string of digits. How do I do the same for sets? How do I write them down and compute with them?

[Anonymous No.12392365]

>>12392348
You can see the representation of a number as a series of strokes on a whiteboard. But you can't see an actual number, just a representation of it.
I can write down a set. In fact I've already done it. {{},{{}}} is a set. It is a series of strokes on a whiteboard.
You do math (or "compute") with them in a different way from arithmetic. Pure geometry doesnt use arithmetic. Pure set theory doesnt use arithmetic.

>or by a string of digits
obviously you can represent digits with digits

[Anonymous No.12392368]

>>12392365
I can define numbers in terms of these representations so that it's clear for everyone what I actually mean. Now how do you define a set?

[Anonymous No.12392380]

>>12392368
I do it the same way as you define numbers.
{} is an empty set. {{}} is a set containing an empty set. if we have urelements (ie numbers) then I can say, the set of even naturals less than 10 which is {2,4,6,8}. Simple and clear

[Anonymous No.12392384]

>>12392380
>I do it the same way as you define numbers.
How? Surely not as a series of strokes. So how do you define sets that's in any way similar to how I can define natural numbers?

[Anonymous No.12392389]

>>12392384
Do you not see these characters here? {2,4,6,8}
These are a series of strokes.

[Anonymous No.12392401]

>>12392389
So is ||||||||||||||||||||||||||||||||| a set? How do you write the union of it and {2,4,6,8}?

[Anonymous No.12392408]

>>12392401
||||||||||||||||||||||||||||||||| is not a set, and it is not a number.
Each of those lines occupies a unique position in space, and so each line is not equal to any other of those lines. All you are representing there is a line, and a different unequal line, and another different and unequal line, and so on.

[Anonymous No.12392410]

>>12392408
>All you are representing there is a line, and a different unequal line, and another different and unequal line, and so on.
i.e. a string of strokes.

[Anonymous No.12392423]

>>12392410
If you are saying each physical stroke is the same as a different physical stroke, then you are confused.

I have an apple in my bedroom. I have an apple in my kitchen. They are not the same apple, so they are unequal.

You have one stroke here | and a different stroke here |. They are not the same stroke, they are unequal. There is only ever ONE of a particular physical object.
An electron in my fridge is not equal to an electron in my car. Since they are not the same object

[Anonymous No.12392446]

>>12392423
>You have one stroke here | and a different stroke here |
They're both strokes. And together they form a string of strokes.

[Anonymous No.12392447]

>>12392275
>What is a set?
Shut up and calculate.

[Anonymous No.12392453]

>>12392447
Ok please tell me how I can calculate with sets.

[Anonymous No.12392459]

>>12392302
>rationals as a string of strokes on a whiteboard
>integers as naturals with a sign
>rationals as appropriate pairs of integers
>reals as appropriate sequences of rationals
WAIT NONONONO THAT'S TOO FAR MAN

[Anonymous No.12392462]

>>12392446
You misunderstand
I could have a 2 year old called george, and a friend who is 30 called george. I would not put them together and say they are two of the same thing.

I call | a stroke and | a stroke, but they are not the same thing. I simply need names to refer to them by.

I could as easily say I have a | here called fred and a | here called george, to explicitly show their similar names dont make the the same object.

I cant say I have two of the same object if only one of that object exists. At best you have shown only that 1 exists

[Anonymous No.12392463]

>>12392459
>reals as appropriate sequences of rationals
What is a sequence? How do I write it down? You do understand that I'm unable to write down infintiely many things, so what do I write down? How do I represent a general sequence?

[Anonymous No.12392466]

>>12392462
>I call | a stroke and | a stroke, but they are not the same thing
Never claimed they were, nor do I need them to be. Both strokes, as you agree. Put together, they form a string of strokes.

[Anonymous No.12392468]

>>12392463
holy shit this is comedy gold

[Anonymous No.12392470]

>>12392468
What's so funny?

[Anonymous No.12392473]

>>12392466
Yes there is a stroke and a stroke, but there are not "two" of anything. You cant simply represent a number by a series of strokes

[Anonymous No.12392475]

>>12392453
>Ok please tell me how I can calculate with sets.
Are you that retarded?
https://ejcim2017.sciencesconf.org/data/pages/slides_realiz.pdf

[Anonymous No.12392480]

>>12392475
What is this?

[Anonymous No.12392490]

>>12392480
Something that your mediocre brain is seemingly unable to fathom. Most comments in this thread are utterly retarded. If one has to explain ZF by mentioning bananas, they should rather put them up their ass instead of shitposting about something that is clearly out of their reach.

[Anonymous No.12392493]

>>12392490
Why did you reply to me with that link if you think my brain is unable to fathom it?

[Anonymous No.12392498]

>>12392490
>explain ZF with bananas
ZF doesnt contain ur-elements ya retard

[Anonymous No.12392511]

>>12392493
To give you an opportunity to show the world you were retarded.

>>12392498
You are proving my point. What the hell do bananas have to do with ur-elements? Also, stop being a German shill, they are properly called atoms.

[Anonymous No.12392517]

>>12392348
>How do I write them down and compute with them?
Just use those bro: ()

[Anonymous No.12392518]

What quality does a "string" of strokes have that a "set" of strokes doesn't?

[Anonymous No.12392521]

>>12392511
>An urelement or ur-element (from the German prefix ur-, 'primordial') is an object that is not a set, but that may be an element of a set.

How about you tell me why bananas having nothing to do with ur-elements kiddo

[Anonymous No.12392562]

>>12392518
What do you mean by a set of strokes?

[Anonymous No.12392568]

>>12392521
>How about you tell me why bananas having nothing to do with ur-elements kiddo

Ur-elements (and sets for that matter) are a formal concept defined in whatever logical system of your liking.

Bananas are real objects that you can put up your ass.

Can you put a ur-element up your ass? No, because they do not pertain to the same universe of discourse. Ergo, they are unrelated.

[Anonymous No.12392569]

>>12392511
>>12392521

[Anonymous No.12392576]

>>12392562
what do you mean by string of strokes?

[Anonymous No.12392579]

>>12392568
>>12392568
Wrong KIDDO, see pic related, then take an urelement and go hang yourself

[Anonymous No.12392586]

>>12392579
Claiming to be a Platonist does not excuse your retardation.

[Anonymous No.12392589]

>>12392579
>>12392568
Holmes, Randall, 1998. Elementary Set Theory with a Universal Set

[Anonymous No.12392593]

>>12392586
>shifting the goalposts
it's okay to admit youre wrong, sonny-boyo, adults do it all the time :)

[Anonymous No.12392610]

>>12392576
Do you know what a stroke is? It's |. Put several of these together and this gives you a string of strokes.

[Anonymous No.12392627]

>>12392475
>>12392490
Please compute for me the union of the sets A_n = {rational x: x < sum_i=1^n of n^4 / n! }. I'll wait for an answer.

[Anonymous No.12392634]

>>12392627
Please compute for me the 10^(10^100)th prime number

[Anonymous No.12392731]

>>12392610
Put several of them together and you get a set of strokes

[Anonymous No.12392757]

>>12392634
It doesn't exist (too large).

[Anonymous No.12392785]

>>12392757
>It doesn't exist (too large).
Ahh the finitist delusion
There exists CZF if you are interested, constructivist zermelo fraenkel. That might satiate your autism

[Anonymous No.12392787]

>>12392423
>An electron in my fridge is not equal to an electron in my car. Since they are not the same object
Retard

[Anonymous No.12392789]

>>12392787
ahhh i always enjoy when a worthless human being tries to insult me, it's always funny :)

[Anonymous No.12392882]

>>12392787
>inb4 anon starts spouting nonsense about the one-electron universe

[Anonymous No.12392885]

>>12392785
Why delusion?

[Anonymous No.12393144]

>>12392562
How does the concept of a "string" of strokes differ from the concept of a "set" of strokes?

[Anonymous No.12393169]

>>12393144
Because I understand what is a string of strokes, can see it, but I genuinely have no idea what is meant by a "set" of strokes.

[Anonymous No.12393189]

>>12392275
If number theory is such a chad field, let me ask you a question. What is a number?
>inb4 autistic screetching

[Anonymous No.12393193]

>>12393169
How is it different, though? Like when you "see" a "string" how come you don't "see" a "set"?

[Anonymous No.12393197]

>>12393169
you should learn to construct a sentence correctly before claiming you understand much of anything, desu. Try reading more actual books and less set theory.

[Anonymous No.12393203]

>>12393193
It isn't different the anon just doesn't like the idea of infinite sets so he's retroactively attempting to figure out an argument to explain why set theory isn't valid.

[Anonymous No.12393210]

>>12393189
Depends on the kind of number. A natural number? That's a string of strokes. Or you can view it equivalently as a string of digits 0,1,2,3,4,5,6,7,8,9.
>>12393193
If you just mean a collection of written strokes, sure that's the same thing. That is, if you're using the word "set" in a colloquial sense. However, most mathematicians don't use it in the colloquial sense, for them set is some mysterious magical object. In the latter case, I have no idea what is meant by a "set" of strokes because I have no idea what mathematicians mean by the word "set": they never explain it!

[Anonymous No.12393216]

>>12393193
>>12393203
>>12393210
For example, I have no idea what you mean if you said an "uncountable set of strokes". If you're talking about sets of something, assuming we're talking maths, you are usually allowed to take them to be uncountable. I have no idea what that means, that's why I'm wary of using the word "set" when describing a string of strokes.

[Anonymous No.12393225]

>>12393210
Is there also a math sense for "string"? Are you using string colloquially in the same way?

[Anonymous No.12393236]

>>12393216
What about an "uncountable string of strokes"?
Are you saying a "string" couldn't be "uncountable" because you "see" it as one dimensional, in a sense?
But a "set" could have more than one dimension so that's why you can't "see" it in the same way?

[Anonymous No.12393285]

>>12393236
>>12393225
guys...
the anon doesn't have an argument other than grasping at any straws that lets him hold onto his precious finitism

[Anonymous No.12393357]

>>12393225
>Is there also a math sense for "string"?
No, it's not a math term. It's an actual real life term which means an actual string of actual strokes.
>What about an "uncountable string of strokes"?
That doesn't make any sense to me. If you show me a string of strokes, I can count it.
>Are you saying a "string" couldn't be "uncountable" because you "see" it as one dimensional, in a sense?
||||
That's a string of strokes. You can count it: one, two, three, four. I have genuinely no idea what you mean by an "uncountable" string of strokes. Maybe if you explained what you meant I would understand.
>But a "set" could have more than one dimension so that's why you can't "see" it in the same way?
If you write down a description of a set then I can see the description. However sets are not defined as any descriptions, or any writings of any kind, or anything really. They are left completely undefined. It is just assumed that in our descriptions and mathematical manipulations, the objects we are actually manipulating are these "sets". It's a fairy tale concept with no connection to reality. You cannot computationally implement sets or operations with them.

>>12393285
Cope. If people scrutinizing my description of a natural number as a string of strokes payed 0.0001% as much scrutiny to the notion of a "set" they would quickly realize that it's complete nonsense.
>>12393285
You are implying that I have faith in some notions that modern mathematicians would never accept or view as too extraordinary, that I need to hold onto. In reality, I am merely skeptical of the current mathematical dogma of these "infinite sets" that nobody can see, nor write down, nor compute with. Everything I believe about what exist and what you can do with maths a typical mathematician agrees with. I am merely much more modest with what I assert to exist.

[Anonymous No.12393430]

>>12393357
So you're using the word "string" colloquially, but not the word "set"? I really don't understand what you think the difference is.
And you've just said that "uncountable set of strokes" and "uncountable string of strokes" both don't make sense. You don't seem to have the slightest idea why you don't like the word set but do like the word string.
What you're saying doesn't make any sense at all. You're just a word hater? Lol what?

[Anonymous No.12393435]

>>12392268
Based and probability based geometry pilled.

[Anonymous No.12393448]

>>12393430
Mathematicians don't use the word "set" in the colloquial sense. Some collections are not "sets" to them, contradicting the colloquial use. For example, there is no set of all topological space, but there is a set of all real function f:R->R. There is no set of all groups but there is a set of all real numbers. Sets need to satisfy the axioms of ZF(C).
A set of strokes in the colloquial sense is too vague. Does the set need to be written? Or can the set of strokes be completely abstract, existing only in our imagination? Can the set have infinite elements? The answers to all these questions are nonobvious, unless you specify that we're talking about concrete sets of strokes that are written down somewhere. The latter definition is acceptable to me, although I still prefer a string of strokes because it indicates that they're written in a string and not just scattered around somewhere.

[Anonymous No.12393464]

>>12393448
>I still prefer a string of strokes because it indicates that they're written in a string and not just scattered around somewhere
So exactly what I had imagined, and asked, about "seeing" a "string" as "one dimensional"?

[Anonymous No.12393481]

>>12393464
If that's what you meant, then sure.

[Anonymous No.12393495]

>>12393481
>If that's what you meant
Lol. What possible difference do you see? I think you're just being silly and obstinate to make some point in a roundabout way that you don't quite know how to make directly.

[Anonymous No.12393504]

>>12393495
When I think of one dimensional things I think of lines and curves as 1d manifolds, not strings of strokes which live in 2d space. That's probably why the confusion arose.

[Anonymous No.12393518]

>>12393504
Oh okay, no, I imagined that maybe you see the strokes all lining up in one direction in a "string" but maybe having no such neat line in a "set." Was I imagining correctly?

[Anonymous No.12393523]

>>12393518
Here was approximately what I was imagining. "Set" doesn't imply any order.

[Anonymous No.12393540]

>>12393357
>Everything I believe about what exist and what you can do with maths a typical mathematician agrees with
Yup I agree with you on that point about finitism

But to say YOU can't imagine something, and therefore it doesn't exist, is pretty grandiose
As if you are the arbiter of what can or cannot exist, some kind of god.

I don't know any intelligent person who is interested in mathematics and thinks the axioms are god given. Some people like to do math in finitist frameworks, others like to do it in infinitist frameworks. Atleast one of them is wrong.

[Anonymous No.12393545]

>>12393523
There is a way to order elements using set theory.
If you've ever seen the coordinate system (x,y,z) they are ordered by nested sets (x,y,z) = { {x}, {x,y}, {x,y,z} }
Whatever those x y and z are, if they are urelements or other sets

[Anonymous No.12393550]

>>12393523
Okay, that makes sense. I understand the difference you're seeing now.

[Anonymous No.12393552]

>>12393540
If the finitist framework is wrong, then there's no hope for the infinitists.
>But to say YOU can't imagine something, and therefore it doesn't exist, is pretty grandiose
That's never been my argument.
>>12393545
I meant if you're talking about an actual set of strokes written on the board, that doesn't imply the strokes need to be neatly ordered in a string. That's why I use the word string. The sets I and the other anon were talking about here are completely unrelated to set theory.

[Anonymous No.12393557]

>>12392268
Logic.

[Anonymous No.12393558]

>>12392268
Almost nobody does set theory in math departments anymore.

[Anonymous No.12393587]

>>12392268
computation

[Anonymous No.12393609]

>>12393552
>>12393552
>If the finitist framework is wrong, then there's no hope for the infinitists.

You may not know this, there are theorems which are provable in ZF which are not provable in ZFC. So it may be that the axiom that allows infinite sets corrects some defect that finitist set theory has.
So its not necessarily the case that if finitism is wrong then infinitism is wrong.

>>12393552
>I meant if you're talking about an actual set of strokes written on the board, that doesn't imply the strokes need to be neatly ordered in a string.
In this case, a string is a set of strokes.
You could represent that string as an ordered n-tuple if you wanted.

Take ||||||||||. Assume each stroke is unique, then we assign it a number in its place, so we can uniquely identify it, which becomes 123456789. Which is the same as counting the place of each stroke. Then a string is equal to the ordered n-tuple (1,2,3,4,5,6,7,8,9)
If I had:
||||||
|||||||||
||||||

Three strings of strokes. I could have the set of all those strokes, or i could one set per string, and the set of those 3 strings.

A set is actually pretty well defined as an abstraction from the real-world version, but they dont teach much about bolzano or cantor.

Generally they teach children about venn diagrams, which is pretty much what a set is.
The set of all men. The set of all Greeks. The set of all Greek men is the intersection in a venn diagram. Pretty simple stuff

[Anonymous No.12393621]

>>12393609
>You may not know this, there are theorems which are provable in ZF which are not provable in ZFC

[Anonymous No.12393624]

>>12393210
>A natural number? That's a string of strokes.
Show me a number.

[Anonymous No.12393625]

>>12393624
||||||||

[Anonymous No.12393639]

>>12393210
Show me a complex number.

[Anonymous No.12393647]

>>12393639
To do that, I would need to be able to show you a real number. But nobody has ever explained how to do that.

[Anonymous No.12393655]

>>12393621
Is that a picture of yourself when you realized you were a brainlet?
Avatarfagging is a bannable offense my newfriend :)

[Anonymous No.12393661]

>>12393655
Every theorem that's provable in ZF is also provable in ZFC, retard.

[Anonymous No.12393665]

>>12393661
you're absolutely wrong, you faggot

[Anonymous No.12393672]

>>12393665
Give one example of a theorem provable in ZF but not in ZFC.

[Anonymous No.12393682]

>>12393665
>>12393609
Absolute moron. Any proof in ZF is also a proof in ZFC since all the axioms of ZF are also axioms of ZFC.

[Anonymous No.12393740]

>>12393682
>>12393672
There is a non-existence result in ZF, but in ZFC you cannot prove the non-existence

[Anonymous No.12393758]

>>12393740
The theorem here is that there is a model of ZF in which there are no non-continuous solutions. The theorem is true both in ZF and ZFC.
Just like in ZF, in ZFC you can also construct models of ZF which do not satisfy choice and in which there are no non-continuous solutions.
tl:dr you're wrong. ZF doesn't imply nonexistence. ZF, just as ZFC, implies existence of models of ZF without any noncontinuous solution.

[Anonymous No.12393784]

>>12393758
>You can construct models of ZF in ZFC
okay?
The axiom of choice itself guarantees the existence of those solutions within models of ZFC

I said
>it may be that the axiom that allows infinite sets corrects some defect that finitist set theory has.
Which means I'm talking about the effects of adding a new axiom.
I'm not talking about modelling ZF in ZF and modelling ZF in ZFC.
I'm talking about the difference between ZF and ZFC

[Anonymous No.12393792]

>>12393740
I think the subtlety here that's confusing you is that the the theorem here is not that in ZF implies there cannot be such functions. That's false, since ZFC implies ZF, and if ZF implied the nonexistence, then so would ZFC, but we know ZFC implies the existence of such functions, so we get a contradiction.
The theorem here is that ZF doesn't allow you to CONSTRUCT such a functions. The axioms of ZF are simply insufficient to construct them. That doesn't mean that there aren't any though. Also the theorem is not "you cannot construct such a function" in ZF. It's rather that "with ZF alone you cannot construct such a function", which is completely different, and as a theorem it's true both with ZF and ZFC.

[Anonymous No.12393805]

>>12393784
All theorems that are true in finitistic mathematics remain true in ZFC.
>Which means I'm talking about the effects of adding a new axiom.
They cannot change any status of the theorem. If a theorem is proven true, it will remain proven true with the added axioms. If it was proven false, it will remain false with the new axioms.
Your assertion that
>there are theorems which are provable in ZF which are not provable in ZFC
Is plainly wrong. Any theorem that is provable in some axiomatic system is also provable in any consistent extension.

[Anonymous No.12393810]

>>12393784
You said
>there are theorems which are provable in ZF which are not provable in ZFC
In the pic that you posted, what do you think is the statement of the theorem that you think is provable in ZF but not in ZFC?

[Anonymous No.12393837]

>>12393805
>proof of infinite primes
>take a set of finite primes and prove there is a new prime that exists not in the set
If i do this in your finitism you will tell me that a certain large number does not exist
which is what you did here >>12392757
>It doesn't exist (too large).
If I say, take a set of all the primes which exist, it will be a finite set. If I say, take the product of the multiple of all these primes + 1, you will tell me, that number doesn't exist because it is too large
In which case you can prove that there are a finite amount of primes.

Whereas in an infinitist framework I can prove there are not finite primes.

[Anonymous No.12393875]

>>12393810
I’m not that poster but obviously their statement is something like
“the existence of non continuous solutions is decidable”

[Anonymous No.12393887]

>>12393875
And you take this to be the example of a statement that's provable in ZF but not ZFC? You're retarded.

[Anonymous No.12393888]

>>12393810
I’m not that poster but obviously their statement is something like
“the existence of non continuous solutions is undecidable”

[Anonymous No.12393892]

>>12393888
>>12393887

[Anonymous No.12393896]

>>12393837
Saying that such and such number doesn't exist is not a theorem of my framework but rather a metamathematical statement about the domain of discourse.

[Anonymous No.12393897]

>>12393887
it’s obvious what i was writing you ducking imbecile

[Anonymous No.12393906]

>>12393892
yes, idiot

[Anonymous No.12393907]

>>12393897
If >>12393888 is your correction then you're still wrong, retard.

[Anonymous No.12393916]

>>12393888
>>12393906
How fucking retarded must you be to not understand that ANY PROOF that's valid in ZF is ALSO VALID in ZFC!?

[Anonymous No.12393920]

>>12393896
If your framework is finitist and it can't decide whether there are finite primes or not, it sounds like your framework has a defect :^)

[Anonymous No.12393929]

>>12393907
>>12393916
Are non continuous solutions decidable in ZF?
LMFAO retards

[Anonymous No.12393950]

>>12393929
>>there are theorems which are provable in ZF which are not provable in ZFC
>example of the theorem: "the existence of non continuous solutions is undecidable"

[Anonymous No.12393973]

>>12393950
Idgaf about ZF or ZFC, moron.
If you can prove that X is true under axioms ABC and that X is false under axioms ABD, you’ve proven that X is undecidable under axioms AB.
Fucking absolute moron.

[Anonymous No.12394089]

>>12393973
Anon stated there are theorems which are provable in ZF which are not provable in ZFC. Your example theorem is "the existence of non continuous solutions is undecidable". You're clearly retarded.
>If you can prove that X is true under axioms ABC and that X is false under axioms ABD, you’ve proven that X is undecidable under axioms AB.
Nobody contested that. This is however irrelevant to our discussion.

[Anonymous No.12394118]

>>12394089
Lmfao, I just owned your sorry retard ass with preK level logic, and all you can do is keep repeating my simple statement that proves you’re an idiot who didn’t think this through, and call me a retard for proving that you’re an idiot.
Keep howling at the moon, moron.

[Anonymous No.12394790]

>>12392423>>12392789
>>12392882
>>12392882

>An electron in my fridge is not equal to an electron in my car. Since they are not the same object
there is no proof of this btw, not even theory says they are different entities but with the same characteristic. that's s because in theory, there is only one wave function for the electron for the whole universe.

or rather, it's what happens when subhumans like atheists take scientific models for reality.

[Anonymous No.12394793]

>>12392423 >>12392789
>>12392882
>>12392882

>An electron in my fridge is not equal to an electron in my car. Since they are not the same object
there is no proof of this btw, not even theory says they are ''different entities but with the same characteristic''. that's because in theory, there is only one wave function in the model for the electron for the whole universe.

or rather, it's what happens when subhumans like atheists take scientific models for reality.

[Anonymous No.12395306]

>>12394118
Mate, what happened here is that you got your shit pushed in, said something irrelevant to save face and when it didn't work, you covered your ears and started shouting "I'm right" over and over.

[Anonymous No.12395443]

>>12395306
That’s literally you describing yourself in your own post you sad stupid retard.

[Anonymous No.12395876]

>>12392268
Set theory is on the way out. It cannot encapsulate more and more of modern mathematics.

[Anonymous No.12395895]

>>12393973
Proving that X is undecidable under axioms AB is not the same as proving in AB that "X is undecidable". The set of provable theorems in axioms AB is a subset of theorems in ABC. You're retarded.

[Anonymous No.12395900]

>>12395876
Give examples.

[Anonymous No.12395921]

>>12395895
>Proving that X is undecidable under axioms AB is not the same as proving in AB that "X is undecidable"
LMFAO imbecile

[Anonymous No.12395933]

>>12395921
Why is it so hard for retards like you to realize that ANY PROOF THAT WORKS in an axiom system AB IS ALSO A PROOF IN ABC. ADDING NEW AXIOMS ONLY ADDS THEOREMS, AND DOESNT TAKE AWAY ANY.
I swear to God you're genuinely the dumbest poster I've interacted with all week.

[Anonymous No.12395939]

>>12395933
You literally wrote this sentence, you are the single dumbest poster in the history of this website lmao fucking idiot.
>Proving that X is undecidable under axioms AB is not the same as proving in AB that "X is undecidable"

[Anonymous No.12395948]

>>12395939
Saying "X is undecidable" doesn't even make sense without specifying the axiomatic structure. "ZF doesn't decide AC" is a theorem both in ZF and ZFC. Any statement that is a theorem in ZF is also a theorem in ZFC. I can't believe how hard it is for you to grasp this extremely simple idea.
Think of it like this:
You have a proof some proposition on ZF. Then all the axioms of ZF you use are ALSO axioms of ZFC or ZF+A where A is any new axiom. That means the extended axiomatic framework ALSO proves the same proposition.
That means that your statement that you so wish to be true that
> there are theorems which are provable in ZF which are not provable in ZFC
IS FALSE.

[Anonymous No.12396001]

>>12395948
>your statement that you so wish to be true that
> there are theorems which are provable in ZF which are not provable in ZFC
I NEVER SAID THIS YOU FUCKING IDIOT

I don't give a flying fuck about ZF or ZFC. I replied to a question about an image someone had posted.
The simple logical fact is that I'm correct, and you're an IDIOT.

You are trying to defend this statement:
>Proving that X is undecidable under axioms AB is not the same as proving in AB that "X is undecidable"
Which literally reduces to P is not the same as "P"
LMFAOOOO
You are lower than pond scum, and you should literally shove your keyboard up your ass until this thread archives.

[Anonymous No.12396086]

>>12392268
Nonlinear dynamics

[Anonymous No.12396292]

>>12393740
Lmao, absolute brainlet getting absolutely confused because he can't tell apart the object set theory from the background set theory.
Someone tell him about Skolem's paradox. His brain will explode.

[Anonymous No.12396767]

>>12395948
>"ZF doesn't decide AC"
HOLY FUCK
I'm glad I came back to check the thread again, sorry I missed this the first time.
You really are the dumbest motherfucker in the history of this website lmfao.

Your argument against
>If you can prove that X is true under axioms ABC and that X is false under axioms ABD, you’ve proven that X is undecidable under axioms AB.
is literally
"AB doesn't decide C"

LMFAO LMFAO LMFAO
I take it back, please feel free remove the keyboard from your ass and keep posting.
This is gold.

[Anonymous No.12396875]

[math]\xi \in \emptyset[/math]

Troubling, isn't it?

[Anonymous No.12396931]

>>12396875
Who needs god when you have the empty set?

[Anonymous No.12396944]

>>12396875
oh is that my main man Zarathustra?

[Anonymous No.12397165]

>>12392302
>string of strokes on a whiteboard
You again?

[Anonymous No.12397185]

>>12392268
Type theory. Sets need to go.

[Anonymous No.12397204]

>>12397185
You can still do set theory in type theory, and vice-versa.