Is this guy seriously the only non-spooked mathematician in academia

>>9096381
>Is this guy seriously the only non-spooked mathematician in academia right now?
Not counting me that is.

>>9096381
Construct a square with rational side length. What's the length of the diagonal?

>>9096381
Is Wildbro the Terry Davis of mathematics

>>9097016
Is Wildberger being persecuted by CIA niggers?

>>9097007
Prove the diagonal exists

>>9096381
He is just reiterating other's work. He is called an ultrafinitist, there are plenty like him. Their ideas are underdeveloped and if they reduce the utility and expansiveness of mathematics (they generally do) then they should be dismissed immediately as nothing more than a curiousity.

>>9097029
That depends. Are we CIA niggers?

>>9097053
this

>>9096381
>You might as well make the statement "A Sasquatch exists" an axiom in biology. It is truly indefensible.
False equivalence.

Mathematics is under absolutely no obligation to discribe reality, only to be logically consistent.

Biology by definition is the study of certain physical phenomenon.

>>9097053
Can a mod approved bot please auto reply this to every Assurger thread?

>>9097053
>they reduce the utility and expansiveness of mathematics
These things (utility and expansiveness) are not necessarily correlated. Using the Sasquatch example, that axiom allows me to make a lot more statements within biology (they have this type of hair, they interact with the ecosystem this way, etc.) but those statements are no longer connected to reality and in fact do not have utility.

In the same way, the axiom of infinity allows you to make more statements within mathematics, but if if those statements are valueless or contradictory, what's the point? In mathematics today you can make all the statements you want but they're no longer guaranteed to comport with the world or even be self-consistent.

Do you really think people would be happy with their tax dollars going to professors who are just in a a pissing contest to see who can construct the most absurd values?
> Look, guys, I made another infinity!
> You mean, like all those other infinities?
> No, uh...this one is bigger! It's an even bigger infinity than all those other puny infinities!
> But it's just an infinite number, right? Aren't all those other infinities just the same thing?
> Ye--well, just--go read Cantor or something, okay? I've got to use this funding somehow.

>>9097179
>Mathematics is under absolutely no obligation to discribe reality
What is even the point of it, then? Just seeing who can imagine the prettiest house in the clouds? All the engineers and scientists that use mathematical methods are sure relying on math having an "obligation to describe reality."

>>9097293
I would think if a certain mathematical concept was an inadequate description of reality, engineers would not use it.

>>9097016
Terry wrote a fucking compiler
This guy is nowhere near Terry's level

>>9097333
A compiler? An entire OS, more like.

>>9097293
>What is even the point of it, then?
To discover new mathematics.

>>9097293
how new can you be that you think mathematics and by extension mathematicians give 2 shits about "reality" all that matters is logical consistency

>>9097293
Model reality by approximation.

>>9096381
biology doesn't have any axioms
mathematics isn't about describing things that exist

>>9097031
It is the straight line that connects opposite corners.

I think it's less of a jump to claim that the ratio of this length to the side length cannot be written with a finite string than to claim that this intuitively definable length does not exist at all.

>>9096381
What does Wildberger think about the law of the excluded middle?

>>9096381
Let's play a game, we both say a number, the bigger wins, but you must talk before me and if you have the right to us ea formula, i can us a formula too. Who will win? Would this guy win against me? Would Wildberger win? If no, what the fuss with that ultrafinitist BS?

>>9097016
He's more of the Alex Jones of mathematics

>>9097700
Numbers, operations, Turing machine exists (you don't needan "infinite band". You only need a band; all the relevant information is on the table state which is finite btw and whenever a computation terminates, only a finite part of the band is used, sso everything you learn about Turing machine in CS course is legit even in ultrafinitist sick paradigm).
Mathematical proofs are as real as a computer program i.e. they are REAL and provide REAL turuth about claim, see Curry Howard correspondence.

>>9097284

you realize your rejection of an empirical infinity is in fact non empirical and as such is a claim based entirely upon a faith identical to that of Sasquatch believers?

>>9097284
>tax dollars
opinion discarded

>>9098002
just because mathematics can describe real things, that doesn't mean mathematics is about real things
mathematics is the logical exploration of axiomatic assumptions

>>9097700
>mathematics isn't about describing things that exist
And yet, virtually everybody including mathematicians themselves use math in this way in order to justify mathematical study. If you ask any mathematician about why their work is worthwhile to the public they'll say stuff about how math powers engineering, finance, etc. which are actually horrific thoughts if math is, like you say, disconnected from reality.

An even better example is when mathematicians pull stuff like Banach-Tarski out to "wow" laypeople and convince them that conservation of mass don't real. They're using the absurdity of their own results to justify their work, which is completely backwards. If a biologist got up in front of a crowd and told them they have six eyeballs, they would be laughed off the stage, but when a mathematician does the same thing it's like "Amazing! Math is so cool!"

>>9098247
>Banach-Tarski
ZF is inconsistent.

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>>9098247
Math ain't an empirical science ya goof

>>9097957
The fact that someone can conceive of higher and higher numbers does not mean that these numbers are in any way meaningful. They are just that: concepts, and have no bearing on the way we ought to conduct mathematics.

Let's have another contest. I'll imagine a big animal, then you imagine a bigger animal. Should the results of this exercise change how we conduct biology? I should think not. Just imagining a mega-whale the size of Saturn should not in any way change biology on a daily basis because that animal I imagined is not in any way real or study-able. They very fact that I had to imagine, rather than experience, a huge number or animal is proof that it doesn't merit study. It's just intellectual onanism to think "wow, I just made up a really big number in my head, let's all spend a lot of time figuring how this concept can be made logically consistent!"

Just because humans have the ability to imagine something doesn't mean it exists.

>>9098275
>let's all spend a lot of time figuring how this concept can be made logically consistent!
Most "mathematicians" who engage in that sort of stuff couldn't care less about logical consistency.

>>9097948
I believe he referred to it as "Cantor's cumshot."

>>9098275
Math is not biology you twerp so stop drawing equivalences.

>>9098247
>>9098275
>"exist"
What is the precise meaning of this?

>>9098300
Something that you can see.

>>9098311
So if I can write out a so-called "real" number in a certain form does it somehow make it real?

>>9098311
Literally retard tier response.

>I can't see an electron
>Electrons don't exist

>>9098247
the bits you are talking about are the calculations and extra solutions. after the math has been done.
most physicists discovered there theorems by shitting brix when they realise some math guy already did it.

>>9098300

This guy isn't me >>9098311 and is using sloppy language to boot.

"Numbers" are a concept that represent a real-world things. Just like words describe real things ("chair", "person") numbers describe concepts related to counting and geometry, etc. (i.e. "one" chair, "7 billion" people). That's the sense in which a number exist.

And, just like with words, it's possible to write down descriptions of things which do not exist. I could write down the mathematical sentence "2+2=5" but that doesn't stop the fact that in real life if you put "2" of something next to "2" of something else you will always get "4", not "5" of it.

Taking this one step further, I could imagine several "words" (numbers) which I could do "maths" with but these new numbers no longer correspond to reality. Just because I can put a name to the concept of a "unicorn" does not mean that there is actually one hiding out in the woods somewhere. Just because I can write out a symbol for "infinity" does not mean that there are an infinite number of things somewhere in the universe (or that something is infinity units long, etc.).

If I made up a new digit called "blorp" and then couldn't tell you how it represents some concept humans have ever interacted with, I would get lauged at and my digit rightly called pointless. But for some reason it's okay for mathematicians making up "infinity" despite humans never having seen something infinite in either dimension or multiplicity.

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>>9098433
It depends I suppose on what you mean by "infinity". Is there a precise formal definition of this term?

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>>9097007
>diagonal """""lines"""""

>>9098445
Yes, but intuitionists don't actually care about precise definitions.

>>9098445
>Is there a precise formal definition of this term?
You've struck on a major issue with the standard ZFC model of mathematics. There isn't, and can't be, a precise formal definition of "infinity" because something infinite has never been experienced.

This is the same reason there's so much debate over the definition, abilities, and attributes of "God." God can't be precisely defined because no one has or even could experience a being which has infinite power, knowledge etc. The ramifications of what it would mean to really be "omniscient" are so far beyond human conception that it's impossible to discuss sensibly, no less "formally" and "precisely"

In the same way, humanity has not experienced an infinite number of things so the numerical concept of infinity is nearly semantically meaningless. Just putting the infinity symbol on paper already puts us outside the realm of human conception (unlike putting the number "1" down, where I can imagine "1 chair"), and when you start doing stuff like "infinity - infinity = ?" it's just semantically meaningless. It's basically equivalent to asking "what happens when an unstoppable force meets an immovable object?" Two objects beyond human conception are interacting and mathematicians supposedly know the answer, which is nonsensical. In the case of the infinities, they say the answer is the patently absurd -1/12, which is equivalent to the immovable object farting in the other example. It's a total non-sequitur.

>>9098433
>"Numbers" are a concept that represent a real-world things. Just like words describe real things ("chair", "person") numbers describe concepts related to counting and geometry, etc. (i.e. "one" chair, "7 billion" people). That's the sense in which a number exist.
You're just making assertions. Feel free to believe them and do mathematics in whatever way those beliefs lead you to, but don't expect others to. Your assertion that numbers are absolutely concrete things that are only valid if they describe concrete objects is no more logically valid than the converse assertion.

>>9098458
Do you mean constructivists or intuitionists?

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>>>909847
>There isn't, and can't be, a precise formal definition of "infinity"
Then what are you arguing against? I fail to see the point of your posts.

>>9098498
who are you responding to, ya dangus

>>9098471
So what do you mean when you use the word "infinity"? You must have some idea of what it means otherwise how can you refer to it?

>>9098500
to >>9098471

>>9098498
>Then what are you arguing against?
I am arguing against people throwing infinities around willy-nilly and using them as an axiom in their mathematical models. If you don't even have a definition for something, why on earth would you include its existence as an axiom in your system? It's only going to lead to contradictions or difficulty later when you realize that you didn't fully understand what you were declaring, or when people argue about what was even declared in the first place. For an example of this, see Banach-Tarski, where the axiom of choise leads to clearly absurd conclusions. If even the axiom of choice, which seems so innocuous, leads to nonsense so quickly, how much more should we be wary of the implications of infinity, which we cannot even conceive of to begin with?

>>9098471
this is bait

>>9098247
bologna. the math profs i worked with as an undergrad studied what they did because they liked it. same with me
it's always nice to see an instance where my/their work overlaps with reality, but that's not the goal

>>9098503
>You must have some idea of what it means otherwise how can you refer to it?
You are right, I do have some conception of it. I would say that I can refer to the idea (in the sense that the idea exists and it is related to being a number beyond which there are no numbers). But that definition isn't precise enough to do maths with, nor even if it were more "precise" would we be able to do maths with it in any sort of verifiable way. I can refer to the idea of "a unicorn" but that idea is not coherent or defined enough to conduct biology on.

If I posed the problem "what would a leprechaun do to a unicorn?" the only correct answer would be to say that it's a nonsensical problem that relies on having absolute information about two beings who are either nonexistent or barely understood at all (or both). The same is true of the question "what is infinity minus infinity?" but people act like they know the answer to that one despite never having observed anything infinite, no less two interacting infinite things.

>>9098514
>I am arguing against people throwing infinities around
Throwing what around?
>and using them as an axiom in their mathematical models
So there is a formal definition of this "infinity"?
>If you don't even have a definition for something, why on earth would you include its existence as an axiom in your system?
To include it in your system as an axiom you already need to have a formal definition of it. You seem to be pretty new to mathematics.
>It's only going to lead to contradictions
ZF is inconsistent with or without the axiom of "infinity".
>see Banach-Tarski
Irrelevant. ZF is inconsistent and AC simply shouldn't be used.
>If even the axiom of choice, which seems so innocuous
If occult-type garbage like AC seems innocuous to you, you might be retarded.

>>9098514
Banach-Tarski is contradicting himself. To even know how to use the word "infinity" you have a conception of it. Infinity cannot be applied to our physical reality because it is not infinite, but the concept (non-physical) can be, and is, infinite.

>>9098528
>I would say that I can refer to the idea (in the sense that the idea exists and it is related to being a number beyond which there are no numbers).

But infinity is not a number, it is a property of numbers. Numbers are infinite.

>>9098514
Do you believe in the consistency of ZF without the axiom of infinity?

>>9098535
>"Numbers are infinite."
This sounds like retarded pop-sci bullshit. Write out what this means formally.

>>9098535
Sure, fair enough. The words "related to" in my sentence were just there to say I was speaking approximately for the sake of brevity.

>>9098544

There's no such thing as an "end number" because you can always add another, numbers don't suddenly just stop working like they usually do when they're really big.

>>9097284
Math is about stating axioms and creating theorems based off of the those axioms. It is entirely disjoint from ``the world''.

>>9098545
That idea of infinity is what's causing problems, it won't last though.

>>9098549
I realize that, but your posts are retarded pop-sci bullshit. Rewrite them formally or leave this board.

Provide your evidence it's "pop-sci" bullshit? In my opinion, any science studying concepts rather than physical things is bullshit too.

>>9098561
I agree. Soon people will begin to realize they've bit off more than they can chew with all this "infinity" stuff and concentrate on a more comprehensible and utilitarian mathematical system.

>>9098561
people actually think infinity is a problem
kek

>>9098581
"Numbers are infinite" is mathematically meaningless. So is "There's no such thing as an "end number" because you can always add another, numbers don't suddenly just stop working like they usually do when they're really big". It's now clear that you are just a mathematically illiterate eng*neer.

What is this "infinity" stuff people keep talking about? Is there a definition of it?

>>9098587
>my rustles have been jimmied

>>9098589
yeah "not finite"

>>9098592
Who are you quoting?

friendly reminder that there will never EVER be an actual formal development of so-called ultrafinite """"""""""mathematics""""""""""

>>9098595
>thinks green text is for quoting only

>>9098581
>any science studying concepts rather than physical things is bullshit too.
Black "person" spotted.

>>9098600
Who said this? Why are you quoting it?

>>9098587

It's mathematically meaningless in the sense that infinity is a property rather than a number, but it is a property that mathematics cannot away from.

>>9098600
>being this much of a newfag

>>9098604
>but it is a property that mathematics cannot away from.
I couldn't care less about that, I'm just asking that poster to rewrite his posts in a non-reddit non-pop-sci manner.

So has Wildberger just completely given up proofs by induction since he won't use infinity? Or does he make 'finite induction' proofs, where he determines a statement holds only for a finite range of numbers? Because that would be retarded.

>>9098587
Looks like your ankles have been rankled, my friend.

Have you been reading too many math papers again? C'mon, man, that's bad for your eyes! You need to get out in the world. Ride a bike, work in a machine shop, learn welding. There's a beautiful, real, and practical world waiting for you out there. Get your head out of the clouds and lose the theoretical weight that's holding you back.

>>9098606
not him but the "who are you quoting" meme has never been funny

>>9098596
>ultrafinite
Is there a proper definition of this term?
>>9098615
>meme
>>>/r/eddit/

>>9098603
>Who said this? Why are you quoting it? Why did father never love me?

>>9098617
usually "there is a largest natural number" or "exponentation is not total"

>>9098609
I am that poster you are referring to. I'm failing to see why it needs to be written formally for it to be a property of numbers?

>>9098611
have done most of the things you mentioned. Good thing you don't have to be a braindead eng*neer such as yourself to do that.

>>9098617
>meme
maymay

>>9098604
>it is a property that mathematics cannot away from
Finally! someone brings up the TRUE definition of infinity. "That property that mathematics cannot away from."

>>9098623
It's mathematically meaningless unless there is a formalization of it you can refer to. There currently doesn't appear to be one, so you have to define it before using it.
Pop-sci garbage and word games belong on either >>>/lit/ or >>>/r/eddit/

>>9098618
I don't understand what you're saying. Where is this quote from?

>>9098626
>>>/r/eddit/

>>9098629
That's a limitation of mathematics then.

>>9098641
>/r/eddit/
>>>/r/eddit

>>9098643
Not being filled with word games and reddit-pop-sci garbage is in no way a limitation.
The inability of mathematically illiterate retards to make pop-sci garbage statements without being ridiculed is also in no way a limitation.

>>9098629
[math]\inf := \vert \mathbb{N} \vert[/math]
Happy now?

>>9098532
>Throwing what around?
Elsewhere in this thread I literally said that infinity was poorly defined. Now you are trying to insult me by implying that "infinity" is poorly defined. No shit, dude, I agree, and that's part of the problem of why infinities shouldn't be lurking around in the axioms and planting the seeds of inconsistency.

>>9098654
Not until you specify the language this is written in. You would also need to show that all of the symbols used here are well defined.

>>9098657
>I literally said that infinity was poorly defined
I think it's simply not defined. But that doesn't make the concept itself invalid, nor does it lead to any contradictions.
Answer my question, do you believe ZF without the axiom of infinity to be consistent?
>infinit"ies".
>planting the seeds of inconsistency.
Another case of reddit-pop-sci "understanding" of "mathematics". Refrain from posting here.

ya'll niggas need constructive type theory

>>9098652
Numbers cannot exist without without the property of infinity. They also cannot exist without the property of "nothing" or zero as mathematicians like to call it. Zero isn't a number either, it represents the lack of a number, a property which all numbers also have.

>>9098654
This is better:

The set of infinite sets := [math]\{X: \vert X\vert \geq \vert \mathbb{N}\vert\}[/math]

>>9098672
>Numbers
What is your non-standard definition "numbers"? What is the "property" of having "infinity" or "being infinite"? Is there a particular number which is "infinite"?
>Zero isn't a number either, it represents the lack of a number
This is just gibberish with no mathematical meaning.

>>9098665
>Not until you specify the language this is written in. You would also need to show that all of the symbols used here are well defined.
Well, that could be only be done if you have a metatheory specifying the metatheroy specifying the language this is written in. But then you'd need another metatheory specifying that language, and another...
So no.

>>9098671
Most of them can be shown to be equiconsistent with ZF or some other similar system. Which means they are probably inconsistent.

>>9098684
>Well, that could be only be done if you have a metatheory specifying the metatheroy specifying the language this is written in.
Mathematically illiterate pop-sci reddit retards aren't welcome here. Simply refrain from posting.

>>9098688
This isn't well defined. Semantically vacuous gibberish. Please formalize this.

>>9098692
I don't understand what you're saying. It doesn't sound rigorous, whatever it is.

>>9098665
>>9098677
ITT: angry grad student who got his shit blown out and so needs to demand arcane terminology to salvage credibility

sorry you got rejected by that nursing student, dude, it happens. I'm sure there are a few girls in the engineering department that will be impressed with how far you shoved your set theory textbook up your ass.

>>9098694
This isn't formal enough. This is metametamathematically meaningless.

>>9098673
>infinite sets
It is not clear that there are any sets that are not finite.

>>9098698
>grad student
I don't have a formal education in mathematics, didn't even read past this point.
>>9098700
I don't understand what you're saying. It doesn't sound rigorous, whatever it is.

>>9098701
>What is a definition?

>>9098705
Where does that post say "What is a definition?"?

>>9098703
>I don't understand what you're saying. It doesn't sound rigorous, whatever it is.
Good, but could you now formalize this metametametamathematically please? I can't make any sense of this.

>>9098708
I don't understand what you're saying. It doesn't sound rigorous, whatever it is.

>>9098707
>Where does that post say "What is a definition?"?
On the line above this line.

>>9098703
> I haven't even gone to school but I demand that everyone else on 4chan have a PhD!
> also I don't know how greentexting works, can anyone help with that?

>>9098710
Could you now formalize this metametametametamathematically please? I can't make any sense of this.

>>9098711
It doesn't seem to.
>>9098712
Knowing basic logic doesn't require a PhD. If you can't rigorously formulate basic mathematical ideas, you're subhuman and you shouldn't be using this board.

>>9098714
I don't understand what you're saying. It doesn't sound rigorous, whatever it is.

>>9098715
>Knowing basic logic doesn't require a PhD. If you can't rigorously formulate basic mathematical ideas, you're subhuman and you shouldn't be using this board.
And anon admits to nobody's surprise that he's been LARPing all this time.

>>9098717
Are a black "person" by any chance? You do sound like one indeed.

>>9098720
How do I grammar? Me no PhD.

>>9096381
The what now? What did I miss?

>>9098722
You've already asked this question before. Stop being stupid and shut up.

>>9098712
It's okay anon, not everyone is capable of understanding freshman level math. It's especially true when it comes to your kind of people.

>>9098717
Listen, just because I don't have a PhD doesn't mean I don't know any math! I'll let you know that I have watched AND MEMORIZED every single Numberphile video. I've read the wikipedia pages for Calculus, Linear Algebra as well as the first few paragraphs of Discrete Mathematics. None of it made any sense to me, and that's when I discovered Wildberger's Youtube channel, where I finally saw that none of this made any sense not because I'm bad at math, but rather because it's all fundamentally senseless. So fuck off brainlet. Only real mathematicians are allowed on my favorite anime image board.

>>9097031
In what sense?

>>9098732
>>9098734
Black eng*neer spotted.

>>9098732
Bruh, you realize that he is arguing against Wildberger, right? Keep up with the fucking thread or get out. You're just confusing everyone.

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>>9097031

>>9098738
It's a negro, of course it doesn't realize that.

ITT:
LARPers are contained within a thread. The rest of /sci/ rejoices.

>>9098738
I was, you're not following.

>>9098749
You weren't, I am following.

>>9098749
Sorry, I'll leave the thread.

>>9098754
This is adorable.

>>9098752
Sorry, I'm not. Silly me.

>>9098749
Have you been mainlining bong water, my dude?

>>9098761
What is this retro slang? I can't seem to understand it.

>>9098685
>Which means they are probably inconsistent
Source: your ass

And anyway, it's not about equiconsistency, it's about having a FoM that is well-grounded philosophically

>>9098677
Numbers are just a logical way of separating infinity into set parts. Zero is the logical opposite of infinity, and infinity the logical opposite of zero, and both of these "work" together for the concept of numbers to also "work".

>>9098765
>philosophy
>>>/lit/

>>9098765
>it's not about equiconsistency
That's pretty important since ZF being inconsistent is extremely likely. It's basically established at this point. It's just a matter of time.
>it's about having a FoM that is well-grounded philosophically
I agree, that's definitely something they achieve a lot better than ZF.

>>9098767
What do you precisely mean by "numbers"? What is a "set part"? What is a "logical opposite"? What is "infinity"?
None of these terms seem to mean anything mathematically. Maybe you should discuss this on >>>/lit/?

>>9098769
>ZF being inconsistent is extremely likely
again, you're completely pulling this out of your ass

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>>9098773
Mathematicians are furious at him!
Find out how this stay at home son does math without numbers!

>>9098775
It's pretty insane and unbelievable that there are still people who believe that such an abomination can possibly be consistent.

>>9098785
Hey now. No need to call ZF an abomination.

>>9098783
Yet another reddit pop-sci garbage post. You should seriously reconsider the choices you've made.

>>9098792
>I don't have a PhD, but I'll call people pop-sci redditors
>sometimes, the realization that I'm a pseud keeps me up at night
>inb4 who are you quoting lel

>>9098773

I think you know what I mean by those words.

How can you do mathematics without words?

>>9098796
You don't need a PhD to discuss high-school level mathematics. The very fact that you fail at doing so already means you're barely human.

>>9098797
I'm just that good.

>>9098773
Are you going to answer my questions or what? Simply provide the notation for infinity within a set-theoretical context.

Suck my dick while you're at it. Stop shitting up this board. Some freshman is going to wander into this thread and shank his professor tomorrow when he sees how screwed up the foundations of math are.

>>9098799
kek

>>9098799
> calls people who don't use strict mathematical notation subhuman
> hasn't even used TEX in the thread

hmm...

>>9098799
well meme'd, my friend

>>9098797
>I think you know what I mean by those words.
I honestly have no idea what you mean by any of that, except "number" perhaps. But even that is a non-standard definition, since you claimed "zero" is not a "number".
>How can you do mathematics without words?
I can do mathematics only when the definitions of the words I'm using have been established.
>>9098804
>Are you going to answer my questions or what?
What questions?

>>9098807
My posts never mentioned "notation".

>>9098810
>I can do mathematics only when the definitions of the words I'm using have been established.
I don't know what 'definition' means. Please define it.

>>9098812
I don't understand what you're saying. It doesn't sound rigorous, whatever it is.

>>9098813
Stop pretending you're a computer.

>>9098815
Don't be lazy. Please use proper non-pop-sci terms if you genuinely want to communicate.
I'm not interested in word games. Take them to >>>/lit/

>>9098816
No.

>>9098816
You are the one using word games, dude. Stop projecting. You're refusing to have an actual discussion and just repeating "define futher" over and over. It's an evasion of the issue.

>>9098819
None of the concepts in that post are mathematically meaningful. Which means I can't even begin to discuss them.

What the fuck is going on?
I have not much experience in math. The only proofs I ever did were in geometry and I tried reading a proof for how 1=1 or some shit which made no sense. I've also tried reading about ZFC and can't make sense of that either. Too many symbols I don't understand.

Where is the inconsistency? Has it been proven yet? Where does infinity cause an issue?

I'm not a hater of pure mathematics but I'd like to know what the hell is going on. I'm not dumb but I can't fuckin understand the importance of this crap because I can't find a fuckin starting point.

I also don't understand why it would take anyone more than a few minutes to understand this shit if they did know how to read this.

So I've got a gun pointed to your head and I want you to tell me what this ZFC nigga is going on about. Can you save your life?

Why can't we just accept that we live in a finite universe but use infinity when necessary? We know we can never have a circle with both rational radius and diameter. One of those numbers has to go on infinitesimally. Does that not matter? What are the suggestions of those who hate infinity?

>>9098821
None of the words you're using are mathematically meaningful either. Now what?

>>9098823
>Where is the inconsistency?
It's almost certain that ZF (and thus ZFC) is inconsistent.
>Where does infinity cause an issue?
The issue isn't with the so-called axiom of "infinity".

as far as i am concerned math is a tool

why do autist always argue which hammer, pc, console they want everyone to use.

>>9098823
>Why can't we just accept that we live in a finite universe but use infinity when necessary?
"The unexamined life is not worth shitposting about" - Socrates

>>9098824
That post doesn't make any statements about mathematics. It doesn't have to be mathematically meaningful.

>>9098826
Because they're autists.

>>9098823
>We know we can never have a circle with both rational radius and diameter.
We can. Pretty easily. The so-called "real" numbers can't be shown to exist.

>>9098821
You do realize, of course, that YOU're going to have to bring some mathematical meaning to the table, too, right?

It's a two-way street. You can't just demand that someone else fully define and articulate an entire system before you even contribute anything, and then claim victory when they refuse to allow you to sit on the sidelines.

>>9098826
Because people disagree with your conception of math?

>>9098810

Zero isn't a number, it is used for separation. When you say 1000, you are also saying "one, with the lack of three other potential numbers." Zero is a placeholder for numbers, it is not a number itself.

>>9098838
Oy vey, why are we debating whether zero is a fucking number or not. It's a purely semantic debate of no consequence. The only thing that matters in math are the premises we agree upon. If you want to say zero is not a number, fine. It won't change anything in your system.

Jesus Christ, the fucking autists on this board.

>>9098836
>You do realize, of course, that YOU're going to have to bring some mathematical meaning to the table, too, right?
I'm interested in discussing those concepts, but I simply can't do that when they're gibberish.
>You can't just demand that someone else fully define and articulate an entire system before you even contribute anything
If you want to discuss mathematics, use mathematically meaningful terms or use >>>/lit/ or >>>/r/eddit/ to dicuss pop-sci garbage.
Here is a "good" channel, discuss your crap in the "youtube comments" https://www.youtube.com/user/numberphile

>>9098838
What is meant precisely by a "number" here? What system are you using to encode these "numbers"? What is meant by "zero"?

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>>9098842
>semantic debate of no consequence
>semantic
>of no consequence

>>9098842
>why are we debating whether zero is a fucking number or not
You seem to understand his terminology. Could you define what those terms mean mathematically?

>>9098846
Fuck off, a semantic debate is not a debate about semantics you degenerate OCD autist.

>>9098849
Shut the fuck up.

>>9098842

If you agree zero isn't a number, why do mathematicians use it like one?

>>9098858
Who gives a shit. Zero is how you define it to be you mongoloid.

>>9098843
>What is meant precisely by a "number" here?
When he gives any answer you're inevitably just going to request further and further definitions. "Please define a set." "Please define axiom." It's turtles all the way down, dude. At some point you're going to have to sack up and defend your views, or else descent into a life of nihilism where math is nothing but a tale of sound and fury, told by an innumerate idiot.

>>9098861
Please, don't engage with the autists. It's not good for them.

>>9098861
>When he gives any answer
That doesn't seem likely since the terms he is using are complete gibberish.
>"Please define a set." "Please define axiom."
Those are pretty well established notions which require no further definition as far as this discussion is concerned.

>>9098858
>>9098860
What is a "zero"? What is a "number"?

>>9098867
I told you to shut the fuck up.

>>9098866
So is number, asshole, so just shut the hell up. You're being intentionally dense. Everyone else here knows what a number is but you've sniffed your own farts so much that you forgot first grade math concepts. Then you have the gall to act like having forgotten those concepts somehow makes you smart. You're so smart that you got sucked up into your own asshole and vanished in a poof of nothingness.

>>9098843
>What is meant precisely by a "number" here? What system are you using to encode these "numbers"? What is meant by "zero"?

Maybe you should study linguistics or the philosophy of language. Words are what we use to turn our subjective experience into an objective one.

Hey guys does anyone want to discuss this area of math?
[math]\infty \oplus 0 = \pi^\infty \otimes -\infty ^\infty \otimes \sqrt{2} ^\infty \oplus \mathbb{C}^\infty[/math]

>>9098871
>So is number,
By any standard definition "zero" is a "number".

>>9098875
Please provide that definition.

>>9098875
>"zero"
>"number"
Your use of quotation marks here make you an insufferable faggot.

>>9098877
Write that on a math exam.

>>9098825
>It's almost certain that ZF (and thus ZFC) is inconsistent.
no matter how many times you insist on this, that doesn't make it true

>>9098877
>>9098879
Hey guys. Look at this new cool area of math
[math]\phi ^\infty = \infty + 3 \implies \phi ^\infty(3) = \pi_1(\infty_\infty)[/math]
From which it follows that
[math]
\eta ^\infty(\phi^\infty) \cong 0
[/math]

>>9098886
cool

>>9098886

It's looks complicated so it must be true.

>>9098886
"Wow, amazing! Makes sense to me." -Infinitist

>>9098831
What the fuck does that even mean? If we construct a circle, beginning with the radius and then the circumference with lengths 1-10, we must stop at three before we go past the beginning. So we get lengths .1-1, we stop at 1. Then we get to .04. Then .001 onto infinity. It doesn't matter how many times this is down we'll never create a perfect circle because it would require the ability to manipulate an infinite number of lengths. Perhaps we will reach the plank length and have no smaller length to use but we can still see that the ratio between radius and circumference goes on to infinity.

So what is the response to this? Are we to say there's really no such thing as a circle? I mean that works for me but I think plenty of people need pi y'know. We may be fine with an approximation but that approximation is still one based off an infinite regression

>>9098894
This theorem actually confirms what he is saying.

Theorem: [math] Con(\Pi_\infty^\infty) \implies 0 = 1 \otimes^\infty[/math]
Proof:
By the axiom of infinity the following equation holds.
[math]
\phi(\eta_1...\eta_\infty) = \infty + \pi
[/math]
But by a previous lemma this is just:
[math]
Con(\Pi_\infty) + 3 = \pi
[/math]
Using the axiom of infinity once more gives us the desired result.
[math]
Con(\Pi^\infty_\infty) + 3 = Con(\Pi^\infty_\infty)
[/math]

[math]
\blacksquare
[/math]

this whole thread is proof that foundations should be taught to undergrads

then again, most of these posters are probably engineercucks anyway

>>9098901
I agree. This quick calculation actually confirms what you're saying.
[math]\alpha \otimes \epsilon_\infty = 0 \implies \Phi^\lambda(\infty') = \Psi^\Lambda(\infty)
[/math]

>>9098903
t. buttblasted finitist that doesn't understand mathematics so he thinks the emperor must have no clothes

>>9098903
Does this even mean anything? lol

>>9098903
>>9098899
wtf is this bullshit

This thread is a complete shitshow.

Math is foundationally flawed.

>>9098894
>Are we to say there's really no such thing as a circle?
There is. I can even prove it.
By the axiom of infinity we have:
[math]
\Sigma : \lambda_1 \rightarrow [0 ,\infty^\infty_\infty]
\\
\Sigma(0_\infty) = 1^\infty\\
\Sigma(0^\infty) = 1_\infty
[/math]

And by the axiom of extended infinity we even have the more general statement:

[math]
\Sigma(\pi_\infty) \oplus \sqrt{2}_\infty \cong \mathbb{R}/\mathbb{Z} \cong S^1
[/math]

Which concludes the proof that the circle exists.

>>9098910
It's a simple proof of what he was saying.

>>9098915
130 IQ here, agreed. Let these math aspies worship their god whose name is "Axiom."

>>9097031
>Wildbots will literally deny the existence of triangles in order to justify their bizarre worldview

>>9098932
190 IQ here. You're a brainlet.

>>9098939
define triangle. prove that triangles exist.

triggered much infinicuck?

>>9098949
lol

what the fuck is going on in this thread. Is it trolls trolling trolls or are these pedants serious?

>>9098949
Here is a proof of existence.

Let [math]\Upsilon[/math] denote the "triangle construction".

It immediately follows from the axiom of choice that the following equation holds.
[math]
\pi^\phi = \lambda + \eta \, + \lambda \, + \eta \, ... \, \eta
[/math]

We apply the axiom of infinity transfinitely and obtain the following statement:
[math]
\pi^\phi \wedge^\infty (K(G, \infty) /\ \mathbb{R} * \mathbb{C}) \wedge^\infty \mathbb{N} \wedge^\infty (\mathbb{N} \times \mathbb{N}) = \Pi^\phi(\Upsilon)
[/math]

Yet again we apply the axiom of infinity and we are left with proving:
[math]\forall \alpha \in \Pi^\phi(\Upsilon),\ (\lambda + \eta \, + \lambda \, + \eta \, ... \, \eta) + \infty + \alpha = 0 [/math]
But [math]\Pi^\phi(\Upsilon) = \emptyset[/math] and so we are done.

Since [math]\Pi^\phi(\Upsilon) = \emptyset[/math] is a well-known equivalent of the triangle existence and uniqueness lemma, this completes the proof.
[math]
\blacksquare
[/math]

>>9098964
Just some retards who refuse to believe in infinities.

>>9097007
By the universal property of the square with rational side length its diagonal should be [math]a =\omega^\Delta = H^{i+a}(X, \Delta)[/math] where [math]X [/math] is obviously the square.
I'm not 100% sure though.

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wtf is this thread

>>9099002
what do you mean?

>>9098975
>We apply the axiom of infinity transfinitely and obtain the following statement:
There's a mistake in your proof. It should be [math]\pi[/math] copies of [math]\mathbb{N}[/math] and not just [math]\mathbb{N}\times \mathbb{N}[/math]

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>>9099013
Yeah, my bad.

>>9097700
>biology doesn't have any axioms
It does though?

>>9097333
>Terry wrote a fucking compiler
that's not that impressive desu, sure a lot of work, but an undergrad could make one in a semester
Creating a functioning os from scrach, now that's an other story

>>9098275
Ok let's play a variant then: we pick both *meaningful* numbers, you talk first and the bigger number wins.
same problem.

>>9096381
At least flat earth theory is fun.
But THIS

>>9098975
What field of math is this? Looks like logic.

>>9099260
An occult field.

>>9098825
>It's almost certain that ZF (and thus ZFC) is inconsistent.
So ZFC is consistent in a set of measure zero? :^)))))

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this thread is fucking premium holy shit this is what i needed to start the day

>>9100959
what's it called?

>>9102822
Occult categorical set theory.

>>9098879
Why?

>>9098885
Yes, writing it down doesn't make it true. But it's still true regardless.