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

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

>b-but, muh axiom of infinity!
Are you really going to base an entire field of study on some bullshit Cantor pulled out of his ass when he didn't prepare any lecture notes? You might as well make the statement "A Sasquatch exists" an axiom in biology. It is truly indefensible.

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

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

Is Wildbro the Terry Davis of mathematics

Is Wildberger being persecuted by CIA niggers?

Prove the diagonal exists

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.

That depends. Are we CIA niggers?

this

>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.

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

>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.

>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."

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

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

A compiler? An entire OS, more like.

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

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

Model reality by approximation.

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

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.

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

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?

He's more of the Alex Jones of mathematics

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.

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?

>tax dollars
opinion discarded

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

>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!"

>Banach-Tarski
ZF is inconsistent.

Math ain't an empirical science ya goof

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.

>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.

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

Math is not biology you twerp so stop drawing equivalences.

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

Something that you can see.

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

Literally retard tier response.

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

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.

This guy isn't me 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.

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

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

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

>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.

>"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.

Do you mean constructivists or intuitionists?

>
>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.

who are you responding to, ya dangus

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?

to

>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?

this is bait

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

>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.

>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.

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.

>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.

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

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

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

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.

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

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

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.

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.

people actually think infinity is a problem
kek

"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?

>my rustles have been jimmied

yeah "not finite"

Who are you quoting?

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

>thinks green text is for quoting only

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

Who said this? Why are you quoting it?

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.

>being this much of a newfag

>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.

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.

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

>ultrafinite
Is there a proper definition of this term?
>meme

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

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

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?

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.

>meme
maymay

>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."

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 or

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

...

That's a limitation of mathematics then.

>/r/eddit/

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.

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

>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.

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.

>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