/sci/ - Science & Math

wow math is so exciting, I need to sit

>>11235781
too bad there are no chairs, huh

>>11235775
You literally do have to show the constructive method for how you do it, faggot.

>>11236367
According to...?

>>11236367
why? as long as you know there are still elements in the set you can just choose them, if it exists why can't we choose it?

>>11236376
the laws of computation
>>11236423
Because mathematics is a subcategory of computation and unless you show the computation, you have not done math (there is no argument against this btw)

>>11236425
Kys.

>>11236425
> subcategory of computation and unless you show the computation, you have not done math
Functions are just mappings, no computation has to be done if you remember the inputs.

Take a course on computability and complexity theory brainlet. You'll realize there are numbers that can't be described given a turing machine and an infinite amount of time.

>officer this guy shot me!
>what does he look like
>i don't know
>is he black?
>don't know. just arrest him

>>11236871
>You'll realize there are numbers that can't be described given a turing machine and an infinite amount of time.

Sure, such as any real number. Disregarding anything that can't be described by a turing machine in finite time is a very limited view of mathematics.

>>11236425
nonconstructive math is the chaddest thing you can do because it puts cs subhumans on suicide watch

>>11236871
I have. Those "real numbers" aren't real (lmao)
If you can't describe it with a universal model of effective computability, it isn't math. All of the non computable reals do not exist anywhere, whether in this universe nor in the "platonic realm".
>>11236883
It isn't math, it must be disregarded. The axiom of choice "allows" you to perform operations that aren't actually computable, which means it isn't math. It's fantasy, like a fairy tale.
The axiom of choice, as well as the "law of the excluded middle" and double negation elimination are not valid universally.

>>11236890
Chads don't lock themselves up into rooms to play around with fairy tales.
Mathematics is real, objective, it's not a human invention, and it corresponds to computation. If you can't compute something, you don't have anything. Mathematics is a subcategory of computation and any "math" that isn't computable isn't valid.

>>11236883
>Sure, such as any real number.

I don't know if you're trolling me on purpose or if you misspoke.

1 is a real number.

>>11236883
Pi is a transcendental number. You can describe its computation in a finite number of steps. It doesn't matter that you can't compute the whole thing because that's not the problem. There are numbers you that you can't even describe its computation, and not even talking about busy beaver numbers. You can describe those however abstract.

There are numbers that you don't know that you don't know and the best you can say is "I don't know how to describe it".

>>11236425
>mathematics is a subcategory of computation
yikes

>>11236936
It is, saying "yikes" doesn't change this. Everything is a subcategory of computation.
I'm sorry this triggers you.

>>11236946
Yikes lol

>>11237099
Dilate

>>11238794
Yikes

>>11238796
Yikes

>>11236809
"remembering the inputs" corresponds to "a pointer is stored in memory that points to the output of all inputs of a function" which is a computation.

>>11236425
>the laws of computation
Are you just memeing?

> Because mathematics is a subcategory of computation and unless you show the computation, you have not done math (there is no argument against this btw)

I'm really interested in this philosophical approach.
Book? Author? Article? Or you are just talking out of your ass and baiting mathtards?

>>11238811
>Are you just memeing?
No
>I'm really interested in this philosophical approach.
>Book? Author? Article? Or you are just talking out of your ass and baiting mathtards?
The entire philosophy of constructive mathematics.

>>11236425
CS brainsplat detected

>>11236423
>why? as long as you know there are still elements in the set you can just choose them, if it exists why can't we choose it?

I give you a bunch of French people, you may choose to single you the oldest guy among them.
I give you a set of twenty integers, you may choose the biggest number.
I give you the reals, you may choose to give me the number 7.25.
I give you a countable infinite set of colors, together with an enumeration. You may choose give me the color corresponding to the number 24 w.r.t. the enumerationn.

Now I give you an anonymous set of which I promise you it's the same cardinality as the power set of the power set of the power set of the reals (but I don't claim I know a bijection which makes that true). You know nothing about the elements of the set, cars could be among them, or maybe their elements are topological spaces, who cares. You only know (by my claim, if you believe me), it's cardinality.
Give me an element of the set!
Faggot, give me an element! You can't.

>inb4 well then I adopt the well ordering axiom, and then by axiom, there is a well-ordering (which you can't tell me explicitly)
>Here is your element, I choose the smallers element w.r.t. the ordering I just axiomized into (non-explicit) reality, lelelelelel

>>11238811
>really interested in this
Its not true, and no one in mathematics worth anything believes this. Its an attempt by cstards to include themselves in mathematics, and to try to take ownership of the prestige and accomplishments of mathematics without actually contributing to mathematics or understanding most topics in math. The people who say this have not had a rigorous education in math, do not know much math, and are not interested in pure math. Its a means of stealing status and nothing more, the same reason that they call themselves engineers when its convenient but don't know anything about engineering. No other fields in Science or Math have this problem, no one in physics thinks they're a chemist, no one in biology thinks they're an engineer, no engineer who isn't an idiot thinks they're a physicist. Only in CS is this mentality incubated and encouraged.

>>11238819
>The entire philosophy of constructive mathematics.
I'm familiar with the concept that constructive proofs are preferable to proves by contradiction, but that's all.
Any good book about the subject?

>>11236423
>why? as long as you know there are still elements in the set you can just choose them, if it exists why can't we choose it?
because is only well defined in your mind
is not well defined in a mathematical sense

It's similar to the halting problem and it's variations
You can't defined a program that f(x) will return 3 if f(x) returns 4.
Doesn't make sense.

>>11238887
>A bunch of crying and ad hominems
Constructive mathematics is the real mathematics, get over it.
Mathematics is not invented, it is discovered, and thus we HAVE TO ACTUALLY DISCOVER IT. Constructive proofs are discoveries. If you tell me, "I know of a place where the mountains are made of candy and the rivers flow with gold, but I can't tell you how to get there" you're making shit up and you're a dumb fucking retard.

Proud TCS-retard here. The problem is AC + classical logic, not AC alone. It'd take too long to explain it to a bunch of brainlets like you, but there are good reasons to frown upon the non-essential use of classical AC.

Also, it's cringy to see that most people on /sci/, even those who claim to be mathematicians, are utterly clueless when it comes to formal logic. We're not the 30's anymore, please learn stuff that is almost one century old and come back whine about it afterwards.

>>11238893
Start with the handy Stanford Encyclopedia article on it
https://plato.stanford.edu/entries/mathematics-constructive/

The quick overall metaphysical underpinning is - Mathematics is about proof, and the Law of the Excluded Middle isn't actually universally valid. The statement "There exists an A such that P(A)" is better understood as "we have a construction of E with property P". The statement "¬A" is defined as "A ⊥" Where ⊥ is contradiction or absurdity.
From this we get a difference between proof of negation, and proof by contradiction. A proof by negation is completely fine constructively - Show that a certain proposition implies a contradiction, and that means that there doesn't exist a proof for that proposition! So it's fine. But the proof of "¬A ⊥" doesn't mean that A is proven, IT JUST MEANS THAT A PROOF FOR A WOULD IMPLY A CONTRADICTION.

So from here we get the real philosophical basis for thinking of mathematics constructively - Just because something is not a contradiction, DOES NOT MEAN IT IS TRUE OR PROVEN/PROVABLE. Being True/Existing is a stronger statement than being non-contradictory, and it requires an actual construction of the object to prove it's existence and truth.

>>11239005
Some of the symbols didn't show up in the first post so I'm rewriting it without the symbols.

Start with the handy Stanford Encyclopedia article on it
https://plato.stanford.edu/entries/mathematics-constructive/

The quick overall metaphysical underpinning is - Mathematics is about proof, and the Law of the Excluded Middle isn't actually universally valid. The statement "There exists an A such that P(A)" is better understood as "we have a construction of A with property P". The statement "¬A" is defined as "A implies ⊥" Where ⊥ is contradiction or absurdity.
From this we get a difference between proof of negation, and proof by contradiction. A proof by negation is completely fine constructively - Show that a certain proposition implies a contradiction, and that means that there doesn't exist a proof for that proposition! So it's fine. But the proof of "¬A implies ⊥" doesn't mean that A is proven, IT JUST MEANS THAT A PROOF FOR A WOULD NOT IMPLY A CONTRADICTION. This is a different idea than saying "because the negation of A is a contradiction, then A must be true" which is how it's interpreted classically.

So from here we get the real philosophical basis for thinking of mathematics constructively - Just because something is not a contradiction, DOES NOT MEAN IT IS TRUE OR PROVEN/PROVABLE. Being True/Existing is a stronger statement than being non-contradictory, and it requires an actual construction of the object to prove it's existence and truth.

>>11239015
Meant for >>11238893

>>11239005
>But the proof of "¬A ⊥" doesn't mean that A is proven, IT JUST MEANS THAT A PROOF FOR A WOULD IMPLY A CONTRADICTION.

Hmmm so you can have a model were a proof for A implies a contradiction but A is true anyway?

>>11239021
I rewrote the post because of the mistakes and because the implication arrow didn't show up

>>11236890
>>11238862
keep telling yourself that.
because mental masturbation gets you nowhere and you know it.
I get it, the ego of a mathematician is too big and fragile to accept that those CS guys do a lot more productive things with their lives and knowledge than any mathematician ever will.
make up for it by learning other stuff.

>>11239036
Sorry anon, by I love mathematics. It is my love of mathematics that motivates my constructive philosophy. I do not consider computer science or mathematics as better or worse than the other.

If you feel strongly either way about the axiom of choice you are a brainlet.

Sophisticated gentlemen realize it's just a tool.

>>11239036
based neets

>>11239043
good.
but still I recommend you to have a set of useful skills besides maths.
because the majority of CS guys and guys who are learning also give a shit to learn a variety of skills they can put to use beside what they are learning so they can be something in life unlike those dumbasses who think that knowing how to math is more than enough.
>>11239050
I know of a neet who literally lives alone and for free, he somehow got money from somewhere and buyed many properties so that he could literally live off the rent of those places.
he literally got stuff that produced money so that he could be a lazy ass and is LEGAL.

>>11239046
This is the only based post in the thread

>>11235775
Oh! I get it! Is the OP saying that they are triggered by this event because they believe/feel/perceive that it is THEIR choice that is being removed?

So is OP's meme someone being an intellectual rape victim?

>>11239105
Would be funnier if his name was Professor Zorn

>>11239113
I don't know the reference. Using memes always leads to some sort of off-by-one because each unique identity doesn't consume the same pleasure-media diet.

Care to share?

>>11239046
>Sophisticated gentlemen realize it's just a tool.
Fine, but this is a normative statement. Tool for what? If you're not into functional analysis etc., but logic or foundations itself, then adopting is not just using a tool. The word "tool" means you have other goals than designing a mathematical system itself. Which is fine, but it can't universally apply to all people interested in math.

>>11235775
Axiom of choice just says "pick one out of a group".
Mathematicians freak out, "which one? which one do I choose??"

>>11239315
So mathematicians only exist when a problem exists? I don't have any problems.

>Problem: a matter or situation regarded as unwelcome or harmful and needing to be dealt with and overcome.

>>11236899
>pi isn't a real number

How does it feel to be a brainlet?

>>11236425
ahem... FUCK OFF YOU CS BRAINLET PIECE OF SHIT.
on a serious note. mathematicians find it disgusting how hard all you brainlets try to rub shoulders with mathfags. CS is not math.

>>11236899
>which means it isn't math. It's fantasy, like a fairy tale.

That's what they said about negative numbers.
That's also what they said about imaginary numbers.

Do you really want to go that way again?

>b-but this time it's different!

Math is a craft about creating new such axioms and seeing what follows through, what new logical constructs are made, what's possible and what's not. Your dismissal of it all as "fantasy" undermines the entire spirit of mathematics. You don't *know* it's fantasy. For all you know, it may lead to the next big breakthrough.

>>11239352
CS is analytical + applied math. That's literally why everyone uses computers and calculators instead of abacus and moon runes.

>There will always be elitist groups getting butthurt that their once precious secret or special language has been distributed amongst the commons.

>>11239356
>What are pivot points, fractals, and variables

I see why /sci/ hates CS freshmen now.

I'm sorry /sci.

>>11236367
No, the axiom choice just states the existence of an arbitrary choice function. You don't have to construct it.

>>11239358
keep telling yourself that faggot. you mentally inferior appliedshit

>>11239364
Why would I tell myself anything when the internet is immediately willing to tell me everything that could, and ever will, be truth?

>Together or not at all

>>11239358

>>11239370
So you plotted your point at the height of a hyperbolic function and expect the area under the curve to be able to identify the tip of the pile of shit that is your opinion?

DISREGARD THAT I SUCK COCKS

>>11239375
How efficient/fast is your cyclic boundary classifier operating?
Identity is the boundary of an evaluation's priority.
For non-phased binding methods, the outside of the box of the target term is stored as it is in the factorization of your class.
For constrained methods, only the smallest quantified initializer of your method can be evaluated, and the value of the smallest quantified initializer is stored in the parameter field.
For uniform bounding-box methods, the binding-box is mapped directly to the update-target-term value in the RAM.

>The flirting A.I. GAN shitposting auters.

>>11239375
Also, why would sucking cock ever be a reason to disregard an interaction? Who needs to suck cock SO badly that they would interrupt heart surgery to blow the anesthesiologist?

https://www.youtube.com/watch?v=arCITMfxvEc

>>11236906
>Mathematics is real, objective,
>it's not a human invention,
>and it corresponds to computation.
this doesn't make the point you think it makes.

There are truths that cannot be computed and godel's incompleteness theorem has demonstrated proof of this. There is more to math than just arithmetic and computation anyway. Math is about finding coherent truths. CS is just applied mathematics. It's limited to only the application and optimization of what's been discovered. Mathematicians are the ones who discover them. And the very fact that we have transcendental numbers (i.e. numbers that cannot be 'computed' and 'transcend' algebra) should strike you with the idea that there may be transcendental structures i.e. functions that transcend algebraic structures i.e. functions that convey truths but cannot be expressed as an algorithm because it cannot be conveyed in any formal mathematical group.

>>11239427
Yes, the truth of identity cannot be computed. This is correct. Identity is consensus of a tuple or triplet.

>Observer/Audience/Presenter(Performer)

>>11235775
here are some facts for you, toddler:
1. Real numbers don't exist.
2. There is a biggest number.
3. Axiom of Infinity is gay.
>>11236899
based

>>11239628
FACT:
There are only 3 axioms that hold for all communicable arguments.

1. (You)
2. Myself/I/Consciousness
3. Other + 1 = Other(s)

The first clause of this axiom (I) is the general axiom of intuitionistic propositional logic. The second (you) clause is true when all participants agree on the existence of the subject, and likewise the third (other) clause is true when the participants agree on the existence of the property.

>>11235775
I believe in the existence of a basis for every vector space. That's the only reason I accept the AoC.

>>11239021
>Hmmm so you can have a model were a proof for A implies a contradiction but A is true anyway?

Nope, you still have modus ponens and by definition (A implies False) and A together prove False. The thing is that A is a stronger statement than ~~A, but once you start shoving double negations everywhere you get back classical logic. This is well-known as "double negation translations" (see e.g. Glivenko, Gödel or Krivine), or through the Curry-Howard correspondance, "continuation-passing style". The latter is a fairly common design pattern in interactive programs.

The one thing that is interesting is that double negation translation doesn't give a model for the axiom of choice if the target theory is not strong enough, namely you need a principle known as "double negation shift". So far I have not heard of a convincing computational model for that principle, and people like Krivine have been fighting for 30 years to give a classical realizability interpretation of the AoC, to no avail.

>>11236899
>model of effective computability, it isn't math. All of the non computable reals do not exist anywhere, whether in this universe nor in the "platonic realm".
t. wikipedia scholar
people who work in actual computability theory have the opposite view.

>>11235775
Axiom of countable choice is true, but axiom of choice is false.

>>11239635
yikes

>any vectorspace has a basis
this is true and self evident

>>11240134
What is the point of ever being around this kind of sentence or expression? If reality can just regex-wrap some 'bind-spot-ignorance' filter then let it include this text example and allow me to continue my immortal journey to provide Heaven to those that want to get out of our way first, their way second, and my way LAST::EXECUTE.

[repl, male]:/] If we ever need to continue and explain why we keep pushing forward, or why our existence is a sort of lottery for bearers of your last month's reward.

Any kind of function named after a male will work for any female interpretation of their history and character within any story/script/narrative/input module.

>>11240146
right...

>>11239315
I have 3 coupons for a car. You can have one of them as a present and get a nice car.
Side note: Those coupons aren't distinguishable, I don't know anything about them. They just popped up in front of me, and actually they popped up at the same identical position in space. Very odd.

Anyway. Which one of the coupons do you choose?

Once you formulate a decision, you get a new car. Night of me, huh

>>11239999
>existence
What do you mean by this, though.

Okay let's say you're given any vector space: Let [math] V [/math] denote the set of all vectors in it. We cant to show that there's a basis [math] .B\subset V [/math] of [math] V [/math] by removing elements of it.
Pick one vector, [math] x \in V [/math], and decide whether the set [math] V \smallsetminus \{ .x \} [/math] has vectors such that a linear combinations thereof is [math] x [/math]. Can you do the picking and the deciding. Do you know that Gödel won't fuck with you if you consider a vector space of cardinality far far far far beyond that of a large function space with Banach norm?

For example, consider a set of this size
https://en.wikipedia.org/wiki/Extendible_cardinal

More down to earth let's stay within models of ZF but only consider sizes of sets defined by power set iterations as often as... some large but still countable ordinal, say
https://en.wikipedia.org/wiki/Ordinal_analysis#Theories_with_proof-theoretic_ordinal_%CE%B50
By "there exist" a basis, do you mean more than
>the biggest vector space that I've ever worked with, something like [math] { \mathbb R^n } \to { \mathbb R^m } [/math] , for those there are some functions that I understand as basis. So if someone comes along and says I do transfinite induction on the power set operation q times, where q is an ordinal describably by Peano arithmetic, say epsilon naught (still far beyond omega^omega^omega number of power set operation), and if on the set of that size I freely define a an addition over a field, then this object should behave exactly like I'm used to from my function space?

>>11240339
Why would you interrupt me to need to validate this, you fucking worthless time Scribe? Do you not fucking get eventually YOU are the GENIUS with the IDEA. Stop seeking 4chan's approval, go get your dick sucked!

Some men are just SALTY SALTY FUCKSTICKS!

>>11240342
interrupt me?

>>11240346
Daughter's of Silent Healing.

>>11235775
>NOOO YOU CAN'T
Yes you can, Cadet Capslock.

>>11236899
Yeah show me your computation approach to get infinite values of pi or e , they are assumed and used on all branches , exist any approach in computation?
You are putting object over subject

>>11235775
>NOOO YOU CAN'T JUST SELECT ELEMENTS FROM A NON EMPTY SET AHHHHHHHHH YOU EXPLICITLY HAVE TO TELL ME HOW YOU DO IT IT IS INCONCEIVABLE AAAAHHHHHHHHHH NOOOOOOOOOOO STOP THIS ISNT ALLOWED THE REALS DON'T EXIST NOOOOOO
Lrn2set-theoretic fgt pls

>>11239356
Negative and imaginary numbers are quite computable. Not so for all the recent innovations in the last 100 years or so.

Whether something is computable or not is how you can tell if something is fantasy or not. Also I really doubt this kind of attitude where the underlying structure of computation is ignored will lead to the next big breakthrough in ML or something important to the real world. I'd much rather bet that actually studying that structure is what will lead to the breakthrough.

Reals, infinite sets and other axiomatic derivations are just hacks made by mathematicians to make their life easier because the real thing was too much for them.

>>11235775
>>11240448
>YOU CAN'T
Yes we can

>>11236871
>>11236883
There are many reasonable extensions to the conventional Turing machine. Look up anything with the Blum-Shub-Smale model (the weakened model especially), Type-2 Effectivity, computable analysis, etc.. Traditional computability is given to us convenient definitions that have a lot of inherent logical and combinatorial structure to it, but there are (reasonable) models out there that strengthen it to be able to reason with reals, to an extent.
But even in a more general way - oracle machines may not be physically realizable, but that doesn’t mean they don’t “exist” or that they aren’t a key role in the study. CS is another view on traditional mathematics, but it isn’t necessarily the “reals don’t exist hahaha” viewpoint

>>11240120
Lol that’s the funniest part
Computability researchers are always trying to enhance the robustness of their definition and are way more concerned with locality than any form of discrete ness

>>11238887
Okay, not him but counterpoint - a nontrivial portion of TCS researchers are bona fide mathematicians who have tenure jointly, or do regular collaboration on topics only tangentially related to grants on CS theory.

Anyone who writes, in seriousness, "You can't just select elements from a non-empty set!," should be asked, "How did you come to the 'Y' in the set of Latin characters such that you were able to use it to begin to spell the word 'you'?"

>>11239352
>mathematicians find it disgusting how hard all you brainlets try to rub shoulders with mathfags.
Idk, widgerson and IAS, all of Berkeley, etc. seem to more than enjoy the cross departmental research
>CS is not math
LOL read any domain theory or geometric complexity theory paper and tell me CS isn’t math. I’m not OP, and I’m not claiming that it encompasses every subject (CS itself is very wide) but anyone who tries to convince themselves that TCS and other activities in the math departments around the world aren’t the same, you’re deluding yourself. This isn’t the 70s kid - people have stopped looking at basic sorting algorithms and have started studying resource bounded measure theory

I'd like for you to stop the shit flinging contest and actually write down some definitions, explain math, explain your perspectives, explain different approaches to set up the reals - also from a computational perspective. Stuff like that.

E.g. if I get around to it this holiday, I might check out this book:

https://www.amazon.com/Computable-Analysis-Introduction-Theoretical-Computer/dp/3540668179

>>11239364
Complexity and related topics aren’t applied...
You’re really telling me recursion theory and the fucking PCP theorem are applied?

>>11240961
Real Numbers in the Neighborhood of Infinity
http://s000.tinyupload.com/index.php?file_id=64138881285874172768

>>11239427
This is a reductive view about what CS is - you’ll see that incompleteness and Turing computability fall from more general type/category theoretic observations. Furthermore, despite the fundamental incompleteness in mathematics, it doesn’t stop math from being a deep subject. If you think CS is “the theory of arithmetic” as computation then you’re pretty clueless. CS is a similarly deep subject because even as early as in the 80 researchers stopped giving a shit about realizability as a chief concern (literally oracle machines, BSS model, polynomial hierarchy, etc). Similarly, the conventional incomputability concerns has not limited CS in the same way it hasn’t limited math

>>11240969
I'm vaguely hesitant to really read this because I've seen this shilled in a spammy way for months now. Taking a cursory glance, I also know that I'd have to go back and forth with people who defend it on what definitions are used. E.g. where I can read up why
[math] \lim_{x\to \infty} (x^2-x) = \lim_{x\to \infty} x^2 - \lim_{x\to \infty} x [/math]
would be true or meaningful, if the first page emphasizes how those aren't the reals defined with sequences and the epsilon-delta framework that usually defines lim.

Besides, those this tell us about the reals that are conventionally known, as opposed to just adjoin more element to it. It seams to say the object we work with here is a superset of R.

This is what happens when idiots get into math
This is the basics, stop being a little bitch
Also I presume you're a little algebra cunt
OP please drop out and change majors before it's too late

>>11241052
First off, the notation "lim" describes an algorithm which produces a number. I use the standard epsilon-delta definition which is implicit in the "lim" notation. The definition of the number that is output is separate from the definition of the algorithm implied by the "lim" notation.

Second, the reason it seems like my R is a superset of everyone else's R is because everyone else was considering a tiny subset of R to be all of R. I have proven that numbers less than any natural number are only a small subset of R, and the only axiom have taken to do so is that R is a connected open interval of the form
R = ( -inf , inf ).

Also, your statement
>reals defined with sequences... usually
is highly tenuous. You are not wrong, persay, because "usually" can mean "usually right now," but if you take it to mean "usually in the history of mathematics" then you are totally wrong. Usually in the history of mathematics, and even usually in 1859 when Riemann published his hypothesis, R was defined as per Euclid as a cut in an infinite line.

Since the main purpose of modern mathematics is algebra rather than geometry, I agree that it is good to have an algebraic definition of R. However, my conjecture is that Cauchy's and Dedekind's attempts to do so are suboptimal because they contradict the geometric definition that R is a connected open interval of the form
R = ( -inf , inf ).

My opinion is that any algebraic definition of R needs to preserve the axiom that R = ( -inf , inf ), and it is a cold fact that the Cauchy and Dedekind definitions do not do this. The extension, however, is quite easy to make, and I have done so in the case of the Cauchy definition, pic related.

>>11236883
>Disregarding anything that can't be described by a turing machine in finite time is a very limited view of mathematics.
You've literally never encountered a number like that.

>>11236917
The situation is worse than that. The set of numbers with a finite description is countable. So with probability 100% if you pick a real number at random, it will be an undefinable number.

>>11239352
>mathematicians find it disgusting how hard all you brainlets try to rub shoulders with mathfags.
I don't mind theoretical CS, especially the ones doing programming language theory (i.e. types, categories, and logic). The only semi-related group I do mind are computer programmers who can't into CS and think learning Haskell has given them advanced math knowledge.

Physicists are fucking brainlets though and science empiricists aren't math nor do we want to be associated with them unless they're bringing us funding money. For real though, scientists are fucking brainlets.

>>11240312
by the laws of thought I can pick one out, no algorithm required

>>11241812
oh, how could I forget about those laws of thought

>>11241817
exactly, its a bit bizarre that you can formulate that question that explicitly tries to attack AOC, while invoking the AOC

>>11241820
Why would age of consent matter to anyone unless you expect or require an audience to judge you? What sort of weird legal exhibitionist are you?

>>11241825
People shouldn't use LEM beyond a certain playful age, say 17

>>11241812
No you can't. There is no "law of thought" that allows you to do this

>>11239352
>CS is not math.
Mathematics is a subcategory of computer science

>>11239343
Pi is a computable real you brainlet
Those "real numbers" that are noncomputable don't exist

>>11242220
I'm with you in pointing out that computability isn't the same as stating all digits at once, but are you meaning to say that non-computables "don't" while pi does?
I can define a number X which on all digits in base 2 has those of pi, but exactly on the 50'th digit, I define the value to be *return value of non-computable function*. Does pi "exist" but this number doesn't because of that?

>>11242872
I'm not that anon but you clearly don't know what you're talking about.

A number is computable if there exists a function that computes it. You didn't describe a unique number there, and if you had then there would be a function that would compute it.

>>11243492
Where's the part where I don't know what I'm talking about?

>>11243494
In order to describe a non-computable number you must:
>1. Give a description that uniquely describes that number and no other number.
>2. Prove that there does not exist a function that computes that number.

It is possible to define a non-computable number but it's quite hard. Refer to: >>11241396
or more precisely:
https://en.wikipedia.org/wiki/Chaitin%27s_constant

That said, the set of definable numbers is still countable, and the remaining real numbers only have infinite definitions. I don't agree with the notion that non-computable reals don't exist, but imo the notion that non-definable reals is very hard to argue against and it's a good way of exposing people to just how bizarre the reals actually are.

>>11243543
>I don't agree with the notion that non-computable reals don't exist, but imo the notion that non-definable reals is very hard to argue against and it's a good way of exposing people to just how bizarre the reals actually are.

This is the basic idea under the Löwenheim–Skolem theorem, and probably the reason why people call this a paradox...