/sci/ - Science & Math

[Anonymous No.12493136]

This terrifies, unnerves, induces anxiety in, and causes psychotic breaks in infinitist schizos

[Anonymous No.12493212]

>>12493136
I don't read books. I just browse /sci/ for the funnies. I don't know half this math autism you guys post about.

[Thales - harem king No.12493220]

>>12493212
Let's destroy civilization.

[Anonymous No.12494843]

>>12493212
Based

[Anonymous No.12494855]

>>12493212
Same, I unironically only post here to call out the retard scientism cultists with bitch tits and make fun of them

[Anonymous No.12494915]

How can one man inspire such as asspain in infini-tards?

[Anonymous No.12495140]

>>12494915
All praise the HOLY BURGER!

He will send those GOD CURSED INFINITY LOVING SODOMITES STRAIGHT TO HELL!

Amen.

[Anonymous No.12496141]

>>12494915
Because retards who don't understand math continuously spout his bullshit on a Cambodian treeclimbing forum that we frequent.

[Anonymous No.12496152]

>>12496141
What in math don't you think we understand?

[Anonymous No.12496184]

>>12493212
fpbp
math is for losers

[Anonymous No.12496278]

>>12496152
Set theory.

[Anonymous No.12496300]

>>12496278
What about set theory don't you think we understand?

[Anonymous No.12496306]

>>12496278
>durr muh cope theory
literally disproven.
do ZFCucks really?
go cope somewhere else.

[Anonymous No.12496316]

>>12496306
>literally disproven.
Show the disproof.
>>12496300
>What about set theory don't you think we understand?
The whole lot.

[Anonymous No.12496330]

>>12496316
Explain what specifically we don't understand about set theory and how specifically it's relevant to the finitist arguments.

[Anonymous No.12496339]

>>12496316
>The whole lot.
cope. just because you don't like something doesn't mean that it's wrong.

[Anonymous No.12496451]

This machine kills fascists.

[Anonymous No.12496517]

>>12496339
You're an idiot. No one denies that finite math is wrong. The finitists/WIldspergs are the ones who claim that math involving infinities is wrong simply because they don't like it.
>>12496330
That you cannot formulate math without some arbitrary assumptions. To my understanding, no one following Wildberger's way of thought seems to accept that it is arbitrary. They seem to think that there is ought to be some inherent physical properties to pure math. That is fine in and of itself if you accept that it is just one point of view, but they regard it as god-given truth, and argue that any other formulation is simply incorrect despite never providing a rigorous argument against.

[Anonymous No.12496543]

>>12494915
>eleven?
>*smirks*
>*shows both hands*
>I only have ten fingers, I'm pretty sure that such a thing does not exist.

[Anonymous No.12496565]

That episode where Nelson posted the paper on the inconsistency of PA and Terence Tao finds an error on it is actually online, with the two interacting, in the nlab blog page

https://golem.ph.utexas.edu/category/2011/09/the_inconsistency_of_arithmeti.html#c039547

iirc Nelson was actually the logic Prof of Tao.

From my understanding, to his death he was quite sure to be able to prove that some computational complexity argument about PA would actually not work out since to express them you need PA and they say something about (recursively defined) numbers that you don't have available yet, at the stage about which you make arguments. Something like that.

[Anonymous No.12496569]

>>12493212
Daily reminder that even though this is called the Science & Math board the name is /sci/ for a reason.

[Anonymous No.12496645]

>>12496517
>The finitists/WIldspergs are the ones who claim that math involving infinities is wrong simply because they don't like it.
well the reason we claim it is wrong is because the only reason you can do math with infinities is because you just assumed you can with the axiom of infinity.
your reasoning is completely tautological; you wanted to be able to manipulate infinite objects (e.g. real numbers), and there was nothing suggesting this was even remotely possible/reasonable.
as a result, you just assumed away your problems by just stating that an infinite set exists and therefore you can do an infinite number of operations.
so it isn't just about finitists not liking it; it's that you claimed something you wanted to be true was actually true by fiat, and then you dismiss all questions about infinities by saying that the axiom of infinity is an axiom so it can't be wrong (since it's an initial assumption that you made). you essentially moved any questions regarding reasoning in foundations/definitions from mathematics to philosophy because you changed the definition of an axiom from "a fundamental fact" to "something I'll just assume."
so in summary, you just assume you can do random bullshit and then, because that bullshit is completely indefensible (other than the fact that you wanted to be able to imagine you could do an infinite number of things), you claim that anyone who questions you is out of line because there are different types of mathematics depending on your initial assumptions. you've essentially just mathematically enshrined wishful thinking.

[Anonymous No.12496672]

>>12496645
>there was nothing suggesting this was even remotely possible/reasonable
Unless you can write down the largest number, there absolutely is.
>you claim that anyone who questions you is out of line
Because you still have not written down the largest number.
>you've essentially just mathematically enshrined wishful thinking.
Yes. Math is literally just wishful thinking. Believing different suggests you have little experience in math.

[Anonymous No.12496707]

>>12496645
Not the guy you're replying to, but almost every infinity that anyone refers to has a finite definition. Variants on a decimal consisting of nines that don't end. Or a continued fraction consisting of ones that don't end. It actually makes more sense, almost always, to assume a thing doesn't change than to be afraid that it might.
In other words, allowing a thing to be "infinite" is almost always much, much simpler than forcing that thing to be arbitrarily finite.
The "arbitrarily" part is what uses up memory exponentially.
In other words, infinitism is almost always more finite than arbitrary finitism.

[Anonymous No.12496710]

>>12496672
>Unless you can write down the largest number, there absolutely is.
>Because you still have not written down the largest number.
To a sane person, this suggests that there is not a largest number. Or in other words, the sequence of natural numbers is unending. It does not at all suggest that you can collect all the natural numbers together as some object and manipulate that infinite amount of information. you just wanted that to be true so you willed it into existence by just stating it.

>Yes. Math is literally just wishful thinking. Believing different suggests you have little experience in math.
exactly; today mathematics is wishful thinking because of the axiom of infinity. it wasn't wishful thinking before though. it became wishful thinking just because you wanted to assume convenient things and as a result, you had to change what the definition of an axiom was.

[Anonymous No.12496740]

>>12496707
i think you are confusing finitism with ultrafinitism (correct me if I'm wrong).
>but almost every infinity that anyone refers to has a finite definition
a finitist is okay with this. for example, a finitist would be okay with 1/3 = 0.(3). Even though the decimal expansion if "fully written out" would be infinite, the finitist view would be that the decimal expansion is unending. as a result, an "infinite object" (the 0.(3)) has been given a completely finite description (namely the 0.(3) or even more simply, the 1/3).
Ultrafinitism on the other hand would be what I think you would refer as "arbitrary finitism". They would say something like TREE(3) is not a number, but rather an expression. A finitist would still be perfectly fine with TREE(3).
So the problem isn't that there can be unending sequences of things (at least to a finitist), but rather that unending sequence of things is some collected together (e.g. in an infinite set) and then manipulations are done on that infinite set (which would involve an infinite amount of work).

[Anonymous No.12496756]

>>12496710
It was, see e.g. Euler, Galois, Euclid, Gauss, Archimedes, Lagrange, Poincare, Newton, etc. All of them used wishful thinking before pure math was even a thing. Pure math is a relatively recent comeuppance, basically invented for the sole purpose of finding a way to formulate math in a logically correct way. Infinite math had already existed for a long time, and to deny that the work of all of those contributors is valid is complete arrogance.
The idea that you can collect all of the (abstract) objects that satisfy a particular property is not unusual, and to say that such an idea cannot be assumed requires at least as much reasoning as to say that such an idea can be assumed. You fail to give such reasoning, even though it should be easier than giving reasoning for the opposite (since all you need to do is provide a contradiction).

[Anonymous No.12496765]

>>12496756
Sorry for the confusion but "it was" refers to your statement "it wasn't wishful thinking before"

[Anonymous No.12496773]

>>12496710
>Or in other words, the sequence of natural numbers is unending.
Not the person you're arguing with, but if you think that "the sequence of natural numbers" is a meaningful thing to talk about, then why do you have a problem with "the set of natural numbers"?

[Anonymous No.12496795]

>>12493136
Those who acknowledge the infinite have no problem with the finite. Finitists are the ones with a problem.

[Anonymous No.12496803]

>>12496740
Again, and we may be agreeing now, if we are manipulating two infinite sets both of which are finitely defined in the manner we agree on, the result must be finite; moreover, that manipulation is almost always far easier to calculate (and even think about) than a manipulation of two arbitrarily large, finite sets. Indeed, the complexity of the latter to the former is surely O(2^n).
Which collections of "infinities" are you decrying as particularly onerous to manipulate?

[Anonymous No.12496810]

Seems like this thread isn't even about Predicative Arithmetic at all, wtf.

[Anonymous No.12496839]

>>12496810
All mathematics threads on /sci/ are entirely about the ideas of the board's two resident cranks, anon. No other topics can be discussed here.

[Anonymous No.12496851]

>>12496756
>Infinite math had already existed for a long time
No, people have wanted infinite math to be true for a long time. That is not the same as saying it has existed. The reason is exactly what you mentioned: they all used wishful thinking. But the difference is that they all knew that something was wrong because their wishful thinking wasn't formalized. Archimedes used a bracketing procedure that, "if continued to infinity", would yield pi; but he never said that the ratio of the circumference to the diameter was actually some number. Newton clearly did not have a rigorously formalized notion of an infinitesimal. Gauss famously rejected completed infinities.They operated under wishful thinking but the difference is that they recognized it for what it was: wishful thinking. They probably thought a more rigorous foundation would replace their relatively informal methods.
Then, at the beginning of the 20th century, the debate was resolved by just assuming the answer, namely that if you just assume you can do an infinite amount of work, a lot of your troubles with integrals and limits just goes away since you can just assume that you can take an infinite sum or continue some procedure to infinity and these actually yield results.
>to deny that the work of all of those contributors is valid is complete arrogance.
I don't deny their work. I deny the resolution that's been provided, namely just assuming the axiom of infinity.
>The idea that you can collect all of the (abstract) objects that satisfy a particular property is not unusual,
It is pretty unusual when you consider you had to make it an axiom in the first place when the number of objects is unending.
As an example, Euclid's theorem is commonly stated as saying there are an infinite number of primes. This is not his exact statement though because he was not comfortable with collecting an infinite number of things together, his actual statement was that any finite collection of primes is incomplete.

[Anonymous No.12496879]

>>12496517
>That you cannot formulate math without some arbitrary assumptions
Everyone already understands this. The need for assumptions is obvious because you can't keep explaining terms in terms of other terms ad infinitum: you need to stop somewhere. However, asserting that you need some assumptions is different from asserting that you must have an formal axiomatic system without any semantics, as is done with mathematics today.
I'm sure Wildberger allows for abstract concepts that don't necessarily directly correspond to reality. You cannot be a mathematician without being a Platonist to some extent. To recognize the validity of the concept of a number, you need to abstract away from all and any concrete implementations to recognize the abstract aspect common to all of them, which is necessarily nonphysical. That's perfectly acceptable. What is not acceptable, is having your mathematics based on concepts which are completely meaningless, even in the abstract sense, as is done with set theory today.
Wildberger simply prefers mathematics to be meaningful.

[Anonymous No.12496880]

>>12496773
It's the fact that you group together all of these objects. In other words, there is a fundamental difference between stating that a_n = n = 1, 2, 3, ... and N = {1, 2, 3, ...}. This is why you needed to make the axiom of infinity an axiom in the first place. The first is saying that there is a procedure by which you can list as many natural numbers as you want. The second is saying that you have collected all of the natural numbers together and you are now planning on manipulating that object.

>>12496803
>Which collections of "infinities" are you decrying as particularly onerous to manipulate?
Well, it's any infinite collection. I am okay with describing an unending sequence of things (like a_n = n). What this is means is that there is a procedure by which you can produce as many natural numbers as you would like. The amount you produce however will never be complete.
What I am not okay with is [1, 2, 3, ...] (the sequence of all natural numbers) or N (the set of all natural numbers).
These constructions are only valid through the axiom of infinity because you need to assume that you can do the infinite amount of work to collect all the natural numbers and then the infinite amount of work to manipulate these objects.

[Anonymous No.12496883]

>>12496851
Okay then. Why are you dissatisfied with just agreeing to disagree? It is clear that neither of us has a good reason as to whether or not we should assume the axiom of infinity, otherwise we'd have said it by now. I don't understand why you are so intent on abolishing essentially a third of all mathematics. No one is forcing you to accept it or to even think about it. They just want to study such things, so what's the problem?
>inb4 wasted resources
Analysis has been more useful in applications than any finite math.

[Anonymous No.12496899]

>>12496672
>Unless you can write down the largest number, there absolutely is.
You misunderstand the position of finitism/ultrafinitism. No infinitist/ultrafinitist thinks there's a largest number. We all recognize the validity of adding 1 to get a bigger number.
What is at question here is the validity of the completed infinite: putting "all the numbers" into a single completed object, whatever that means, and then trying to manipulate it. This is highly questionable.
>Math is literally just wishful thinking
When did math change from being a precise subject in which people reason starting from basic undeniable truths to reach interesting conclusions to being "literally just wishful thinking"?
If you are really OK with math being "literally just wishful thinking" I think you need to do some reevaluation.

[Anonymous No.12496922]

>>12496707
>Not the guy you're replying to, but almost every infinity that anyone refers to has a finite definition
This is actually not true, by Godel's incompleteness theorems. Whatever finite definition you have of the completed infinite, you will always be able to consistently extend it into two mutually incompatible definitions of the completed infinite that disagree. I.e. no finite definition will properly define the completed infinite.
>Variants on a decimal consisting of nines that don't end. Or a continued fraction consisting of ones that don't end.
These particular examples are fine, they do have finite descriptions and they each could be accommodated into a certain logically rigorous theory. The fact is, most "real numbers" are not like that at all. They don't even have a finite description.
>In other words, allowing a thing to be "infinite" is almost always much, much simpler
This is very true. That's one of the attractive features of dealing with the completed infinite, it allows people not to actually consider what they're talking about and get away with lazy, degenerate tricks. A lot of troubles disappear when you can just assume away your inability to complete infinite tasks. However, this comes at a huge cost of losing semantics and rigor.

[Anonymous No.12496941]

>>12496899
Why? Precisely what is questionable about it? You've been saying it's questionable, it's highly problematic, there are many inconsistencies and paradoxes, but you have not given any answer that isn't entirely vague.

[Anonymous No.12496944]

>>12496880
>In other words, there is a fundamental difference between stating that a_n = n = 1, 2, 3, ... and N = {1, 2, 3, ...}.
What is that difference? If "S = the sequence of numbers produced by a_n = n" is a meaningful algebraic notion that can be manipulated (it can be point-by-point equal to some other sequence, for example), why is "the collection of objects that occur in the sequence S" not an equally meaningful algebraic notion?

[Anonymous No.12496965]

>>12496851
>their wishful thinking wasn't formalized.
Friendly reminder that we did math for thousands of years before we started doing foundations.

[Anonymous No.12497009]

>>12496880
But if the work required to define a set as “infinite” is finite, then all of the “manipulations” you’re concerned about would also be finite.
What I’m asking is how do you define the sets you’re worried about?

[Anonymous No.12497010]

>>12496883
>Why are you dissatisfied with just agreeing to disagree?
It's a point of principle. Yes, people assuming the axiom of infinity is doing me no harm and people are free to continue using it, but that does not mean it should be the orthodoxy or the preferred way of doing things. The reason it is the orthodoxy is because it made a lot of things much more convenient; for example that limits always converge to something. But to "achieve" this, we had to assume our goal; if we can do an infinite amount of work, then of course we can consider the "full" infinite decimal expansion of a real number so of course we can construct real numbers. This is a simplification of course, but the point still stands that the axiom of infinity is basically a convenient shortcut that everyone wanted to be true so they just assumed it.

>>12496944
S as a whole is not meaningful. You are considering the entire sequence S as an object. If you have some expression that produces terms of S, then you can manipulate those finite expressions to perform arithmetic on sequences, but S itself in standard theory, is modeled with a choice function, which means to manipulate the sequence, you need to do an infinite amount of work.

>>12496965
Yes? It's perfectly fine to think that you have something that works but acknowledge that there's still work to be done. What is not okay is to assume you can do an infinite amount of work and claim you have modeled the continuum.

[Anonymous No.12497012]

>>12496941
Here are a couple of reasons:
- Historically the idea of completed infinite has been hugely problematic. ZFC was not how set theory started. Before ZFC came many attempts to give an infinitist foundation to mathematics and a lot of seemingly intuitive ideas about the completed infinite gave rise to paradoxes and contradictions. ZFC is the result of many many bug patches to frameworks. It might very well be that ZFC is contradictory as well, and we just haven't found the contradiction like we did for previous attempts.
- In the process of patching up that gave rise to ZFC, one of the patches at the core of ZFC was to get rid of semantics altogether. "set" is left undefined and all that mathematics reduces to is the formal manipulation of meaningless symbols, according to modern foundations. This is unacceptable, not least because it goes against the common understanding that mathematics is meaningful.
- There's no evidence that propositions about the completed infinite have definite truth value, and in fact there is evidence to the contrary. Godel's theorem says that whatever finite description you have of the completed infinite, you can always extend it to a more precise description which answers questions about the completed infinite differently. -- ---
...

[Anonymous No.12497016]

>>12497012
...
- For every such undecidable, meaningless infinitist proposition about arithmetic, set theory allows you to form a "definite" natural number which is 1 if the proposition is true and 0 if the proposition is false, and according modern mathematics this is an explicit definition of a natural number. This ruins our understanding of small natural numbers as something definite that can be calculated with by polluting them with infinitist imaginary nonsense numbers which we can never even approach.
- A lot of propositions that were previously thought to involve the completed infinite turned out to have a finite, and hence much more rigorous and meaningful semantics. Infinitist nonsense is a lazy cope that deflects from what's actually going on.

[Anonymous No.12497079]

>>12497016
You seem to be unduly preoccupied with the impact of things that may or may not exist. We don’t even know if √2 is normal. That doesn’t refute the general concept of a right triangle.

[Anonymous No.12497112]

>>12497009
See >>12497010
In some specific cases, a sequence can be described in finite terms. As an example, if a_n = n, and b_n = n + 1, then a_n * b_n = n * (n + 1) = n^2 + n.
This is perfectly fine since I have manipulated the symbols that represent the ability to generated an unending sequence of terms. I am not doing anything explicitly term-by-term since in this case, I have a general expression for the n-th term which allows me to circumvent the infinite amount of work.
However, this is not actually what a sequence is according to standard terminology. Sequences in general are modeled with choice functions, which means that if you want to manipulate them, you are forced to go term by term and do an infinite amount of work.
Also, more generally, if we consider S = [1, 2, 3, ...], which would be *all* the terms generated by the sequence a_n, you are trying to capture an unending process by just putting brackets or braces around the terms and claiming this is okay because of axiomatics.

[Anonymous No.12497134]

>>12497112
So your cavil about infinity is the Vitali cavil?

[Anonymous No.12497946]

Galileo already noted the bijective map [math]n \mapsto n^{2}[/math]

[Anonymous No.12498365]

>>12494855
Based

[Anonymous No.12498644]

>>12497946
Yeah, and?