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/sci/ - Science & Math


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12463560 No.12463560 [Reply] [Original] [archived.moe]

>you are just using a different axiom system
Don't you realize the whole point of these axiom systems? Look at the history of set theory and the axiomatic approach to mathematics. The whole reason mathematicians needed it is because nobody understood what the fuck they were doing when they were spouting about the completed infinite sets, the real numbers. Rudin even has a whole video about how set theory came about in an attempt to hide the ambiguities involved in real analysis
https://www.youtube.com/watch?v=hBcWRZMP6xs
The infinitard cope is so strong that they genuinely thought basing the whole subject on a completely undefined notion of a "set" was a good idea and logically sound mathematics.
The same with different kinds of logics. Intuitionism, constructivism etc. all came about because of incredulity in each other's approach to the completed infinite.
If you ground your mathematics in reality, all of these issues completely disappear. All of the different logic systems converge to one actual logic based in reality, the questions become definite questions corresponding to states of being in actual reality, there is no longer the need to believe in some axiomatic dogma like axioms of set theory, you can pick whatever axiomatic system you want and actually PROVE using logic that the system is consistent, but why would you need to, when it's already clear what you're talking about since your math is actually GROUNDED in reality.
Do you think anyone would open Wildberger's book on trigonometry and have a question about what kind of axiomatic system he's using? There's no need to, because it's already clear what he's talking about in the book. The propositions he states doesn't ask you to do infinite amount of work or consider some sorts of unimaginable, indescribable numbers like you see in analysis. They're about rational numbers, which you can write down and calculate with.
(1/2)

>> No.12463562

>>12463560
(2/2)
Also funny to see the infinitard cope is so strong that they ask questions like "well what do you mean by a natural/rational number", as if this question is in ANY way comparable to "what is this completed infinite", which Godel proved is actually IMPOSSIBLE TO DEFINE! You can point out any one of the multiple equivalent definitions/implementations of these numbers and they will turn into the most ardent philosophers when it comes to stuff you can actually touch and compute. Their questioning leads questions like "But how do you know reality is even real?". The infinitard concludes, because his brain was so muddled by the infinitist nonsense that he came to doubt his own reality, he is warranted to believe whatever nonsense he fancies. In particular, he is warranted to believe in the completed infinite and to call anyone advocating a logically sound approach to mathematics a crank. Truly an amazing mind.

>> No.12463581

real numbers = points on the number line
where's the problem

>> No.12463594

>>12463581
It might be that all points on the number line turn out to be rational.

>> No.12463598

>>12463581
Also as far as Euclidean constructions go, for geometry it's enough to work in the "field of algebraic numbers" which is also nonsense but it's way smaller than the reals because it's countable. This just goes to show that your "definition" is inadequate.

>> No.12463603

>>12463594
>>12463598
https://en.wikipedia.org/wiki/File:Pi-unrolled-720.gif

>> No.12463606

>>12463603
Cool animation bro. What are you trying to say though?

>> No.12463621

>>12463606
pi is on the number line

>> No.12463633

>>12463621
So you say. How do you actually know the operation of rolling the circle and unwinding its circumference is mathematically meaningful? (it's not)

>> No.12463650

>>12463633
it's like unrolling a carpet, of course it's meaningful

>> No.12463655

>>12463650
But carpet is not a mathematical object and you cannot measure it's length exactly, there will always be ambiguity involved. Similarly, you can put a tape around a circle and measure its length, but it will never be exact.

>> No.12463660

>>12463655
You can't "measure" "2" exactly.

>> No.12463662

>>12463655
why would it not be exact? it won't be a rational multiple of the unit length, but who cares

>> No.12463664
File: 207 KB, 1110x1600, 1569958429044.png [View same] [iqdb] [saucenao] [google] [report]
12463664

Sup everyone
Is this the thread to talk about measuring lengths?

>> No.12463694

>>12463660
2 is not defined as the measurement of any object. It actually has a discrete, proper definition, for example as the string of strokes II.
>>12463662
Well if you just look at the picture and measure the pixels you will get natural numbers. That's probably not what you want.

>> No.12463711

>>12463694
>Well if you just look at the picture and measure the pixels you will get natural numbers. That's probably not what you want.
wtf are you blathering about

>> No.12463713

>>12463694
If you want to define 1 as I, and 2 as II, just define π as O.

>> No.12463719

>>12463711
You posted a gif, which is a discrete pictorial representation of what you think is happening. It consists of pixels, which can be counted. Capish?

>> No.12463724

>>12463713
Ok but you don't want to restrict yourself to just pi, otherwise all you get is a polynomial ring. You want include many more different numbers, and as far as I know there is no genuine way to do it.

>> No.12463732

>>12463719
I know what you mean, I don't know how is it relevant

>> No.12463735

>>12463664
>B1 B2 B3 B4 A1 A2 A3 A4
kys

>> No.12463741

>>12463724
>You want include many more different numbers
Like what?

>> No.12463747

>>12463732
It's relevant because the representation of the process is not actually the process. Just because it looks like a meaningful process doesn't mean it actually is. You'll have to provide an actual mathematical definition of what it means to unroll a circle like that to give you a UNIQUE number.
This is similar to
>>12463664
It looks like they're doing something meaningful and proving that sqrt(2)=2 but looks can be deceiving. The proper mathematical explanation lies in the way you define "length" of a curve, which you can't even always do.

>> No.12463749

>>12463741
Well, don't you want also to include e?

>> No.12463761

>>12463747
dude it's simple geometry, what more is there to define?

>> No.12463771

>>12463749
Sure, let's add e. Problem?

>> No.12463789

>>12463771
>Problem?
Yes. How do you define arithmetic on this object?
>>12463761
Dude even the greeks realized this is not simple geometry. They didn't include such ambiguous and dubious operations for a reason. this is not actually geometry but analysis, which rests on an extremely shaky foundation.
You have to properly define what is a point on the number line. It's not enough to draw a line, denote a zero somewhere and draw a point. There will be an unending list of rational numbers which could all fit the description of being "at that point" with no real pictorial way of distinguishing them.

>> No.12463814

>>12463789
How do you define it on our polynomial ring for O?

>> No.12463834

>>12463814
I don't know how, I don't think you can do it in a meaningful way. e, pi, these are metanumbers, not actual numbers, and any attempt to define arithmetic that includes them and other general metanumbers is doomed to fail.

>> No.12463845

why have there been so many threads about this lad lately?
some pleb just discover him?

>> No.12463847

>>12463834
What is your standard for meaningful?

>> No.12463864

>>12463847
Meaningful = actually refers to something = is a definite question with a definite truth value.
For example, in the current paradigm of ZFC mathematics, CH is not a meaningful question, even though it appeared to be meaningful for a long time. Similarly, the question of whether a given algorithm halts is no meaningful neither in ZFC nor any other recursively axiomatizable theory extending aritmetic.

>> No.12463869

>>12463845
You cannot refute him.

>> No.12463870

>>12463789
even kids understand what lines and points are, lol

>> No.12463878

>>12463869
i just wanna know why there's the buzz now
he's old news

>> No.12463885

>>12463864
No, I mean in terms of your question about defining an arithmetic. What is your standard for meaningful arithmetic?

>> No.12463906

>>12463845
I think its either a response to tooker posting his infinity hat garbage, or someone who saw ababous anti-infinity posts.
Basically some faggit who likes wildbergers math and so has to crusade against other peoples math.
You can tell the guy is a faggot because instead of doing actual wildberger style math and publishing it, he wastes his time shitposting on 4chan.

>inb4 you are also shitposting on 4chan
Yup, I shitpost for the few minutes a day I take a shit. I don't spend hour after hour arguing on 4chan like an impotent mathlet cuck

>> No.12463915

>>12463906
based
wildberger is a neat and wacky dude (I like his projective geometry stuff), this spammer is annoying tho

>> No.12463983

>>12463885
>What is your standard for meaningful arithmetic?
The standard is that questions about arithmetic should correspond to meaningful questions about the real world, not some fairy tale land.
For example, the arithmetic as implemented in any programming language is meaningful.
The question of whether or not 123^45 is divisible by 7 is a definite question with a definite truth value, which can be found by using a computer. The question of "whether or not there are infinities between aleph null and 2^aleph null in size" is not a meaningful question, because it doesn't correspond to anything in the real world with a definite state.

>> No.12464058

>>12461391
>If you really think we reject real numbers just because computers can't handle them then you're a fucking retard.
>>12463983
>For example, the arithmetic as implemented in any programming language is meaningful.
>can be found by using a computer

>> No.12464065

>>12463983
>meaningful questions about the real world
>The question of whether or not 123^45 is divisible by 7
? ? ?
?
?

>> No.12464075

>>12463560
>All of the different logic systems converge to one actual logic based in reality, the questions become definite questions corresponding to states of being in actual reality, there is no longer the need to believe in some axiomatic dogma like axioms of set theory, you can pick whatever axiomatic system you want and actually PROVE using logic that the system is consistent, but why would you need to, when it's already clear what you're talking about since your math is actually GROUNDED in reality.
Except when you actually do this, you converge to real numbers and a theory that's basically ZFC.

>> No.12464091

>>12463664
Wouldn't the shortest path for each step also be the diagonal?

>> No.12464092

I'm so fucking annoyed with these threads. Stop pretending you have discovered something special, you are starting to like like a flat earth retards. You don't like infinity in ZFC axioms ? Ok, there are pretty intuitive axiomatisations which forbid infinite sets and work only with finite sets. Work within this axiomatisation, what's the problem ?
There is (almost) no absolute truth in math, (almost) every statement needs some context to be true or false. Thus you can't say that one theory is "better" than another in any objective way (because statements can't be "more true"). If we take the subjective way of "more intuituvely clear" another question is - what's the math that you can do within your system ? If it's the same math with the same possibilities, sure, you can convince everyone that your approach is better. If the "usual" real numbers system gives more possibilities in doing math which describes the real world pretty well, then your system needs some adjustments.

>> No.12464093

>>12464092
to look like*

>> No.12464099

>>12464058
These two statements are perfectly consistent with each other.
The implementation using a computer is just one way to see that arithmetic with naturals is meaningful and consistent. You can also do it manually with strokes on a blackboard or do it in your head if you have good cognitive skills.
You cannot either of these things with real numbers, even in principle. Not just with a computer, it's actually impossible to compare or calculate the sum of two "real numbers". What's even funnier, is that you can't even add two natural numbers once you view them as part of the "real number" system. This reason, nor any other reasons outlined in this and the other threads, are merely just that "reals are bad because computers can't calculate with them".
>>12464065
The full quote is
>correspond to meaningful questions about the real world
I personally am a platonist. I believe in abstract mathematical concepts like the number 2 or 3. I also believe that "completed infinity" is nonsense.
The question of whether 123^45 is divisible by 7
is definite because there are many equivalent implementations of the natural numbers where you can calculate this and get an answer. For example, you can ask the python to use its implementation of natural numbers to calculate the answer, or use a piece of paper to write it down.
Nothing of the sort is possible about questions concerning the "real numbers".

>> No.12464102

>>12464075
Not even close.
>>12464092
>You don't like infinity in ZFC axioms ? Ok, there are pretty intuitive axiomatisations which forbid infinite sets and work only with finite sets. Work within this axiomatisation, what's the problem ?
Did you not read the OP? I explicitly addressed this point. "Axiomatizations" are a meme whole purpose of which is to hide the inherent ambiguities involved in the infinitist nonsense.
I don't get why people like you get off pretending to know what they're talking about when they haven't even read the thread which explicitly addresses the points they're making.

>> No.12464105

>>12464099
>or do it in your head
great, I'm perfectly fine with reasoning about the reals in my head


>it's actually impossible to compare or calculate the sum of two "real numbers"
read: it's impossible to execute a finite algorithm on a computer which would do it

>> No.12464109
File: 50 KB, 563x564, b9845787a3a10f62bcfa5f126a4b1b3e.jpg [View same] [iqdb] [saucenao] [google] [report]
12464109

>>12464092
Also,
>There is (almost) no absolute truth in math
This is the result of decades of indoctrination with infinitist nonsense. Kek imagine being so confused by the flawed foundations that it makes you give up on absolute truth itself.
And you have the gall to call US the schizos similar to flat-earthers. This is seriously comical.

>> No.12464110

>>12464102
Once more, ZFC WITHOUT infinite sets contains only intuitive axioms : you can take union of sets etc, there is NO "infinitist nonsense", because there is NO infinite sets. In this context there is NO actual infinity, there is nothing to hide.

>> No.12464116

>>12464105
>great, I'm perfectly fine with reasoning about the reals in my head
Great. Please use your powers of infinitist reasoning to calculate pi+e, or at least answer the infinitely easier question of whether or not it's rational. Take your time. I understand that using your infinite gigabrain can take a while.

>> No.12464121

>>12464110
That's all fine and dandy. My point is that there is no reason to care about ZFC or modifications of ZFC taking away infinity, because there are no ambiguities involved. The only reason you need an axiomatic approach is to hide the ambiguities involved in infinitist nonsense.

>> No.12464127

>>12464121
Ok then, don't call it axioms, but answer my question then. What math can you do within your approach ? Will it give the same results ? If you can do *very little* compared to ZF approach (in particular, if you can't do some applied things slightly harder than simple arithmetics), then what's the point ? If you can do the same, but with different results, do these results stay coherent to the real worlds observations ? If yes, then this approach is viable, if not, then there's a problem.

>> No.12464128

>>12464116
pi+e is already "calculated". rationality is an open problem.

>> No.12464131

>>12464127
>What math can you do within your approach ?
Trigonometry, anything needed for game development, simulation of physics, machine learning, engineering, calculus, number theory, polynomials, group theory, algebra, the list goes on and on....
>>12464128
You have "calculated" it but can't tell if the answer is rational. Give me a break.

>> No.12464132

>>12464131
>You have "calculated" it but can't tell if the answer is rational. Give me a break.
problem?

>> No.12464138

>>12464105
>it's actually impossible to compare or calculate the sum of two "real numbers"
>read: it's impossible to execute a finite algorithm on a computer which would do it
Only if you define "compare or calculate" as "find a least common denominator," which is an arbitrary definition.

>> No.12464141

>>12464138
how do you define "calculate" then?

>> No.12464150

>>12464132
Yes. You haven't actually calculated it. You just believe that you did something because you are supposing an axiomatic framework which you try to semantically interpret as ASSUMING that you can add two real numbers, without actually proving it or saying what the answer is. This is a baseless assumption which renders your whole "arithmetic" an absolute joke. It also completely ruins the arithmetic of algebraic objects you claim are inside the "real numbers" because suddenly you can no longer calculate what a sum of two natural numbers is, nor what a sum of two rational numbers is. The best you can do is to say "it was assumed that it can be done". What an absolute joke.

>> No.12464151

>>12464131
Well, if you can do the same calculus with the same power of it's tools, nice, what can I say. Now formalize these domains within your theory and it will be viable.
Also, if there is no "infinity nonsense" in your approach, there should not be indecidable statements. What are the answers to the problems that are indecidable in the "usual" approach in your approach ?

>> No.12464153

>>12464141
Code golf works for me.

>> No.12464158

>>12464151
>Now formalize these domains within your theory and it will be viable
How many times do I have to explain to you that formalization is completely useless when you have actual semantics. Formalization is only needed when you don't have a clue what you're talking about.
>Also, if there is no "infinity nonsense" in your approach, there should not be indecidable statements.
Correct.
>What are the answers to the problems that are indecidable in the "usual" approach in your approach ?
Which problem in particular? In the standard framework of axiomatic mathematics a lot of them are completely meaningless. You need to reinterpret them using actual mathematics to make them meaningful. Do you have any example of an open problem you would like an answer to?

>> No.12464165

>>12464150
>without actually proving it or saying what the answer is
the answer is "the equivalence class of a_n = sum_{k=0}^n 1/k! + 4*(-1)^k/(2k+1)"

>suddenly you can no longer calculate what a sum of two natural numbers is, nor what a sum of two rational numbers is
false

>> No.12464176

>>12464165
>the answer is "the equivalence class of a_n = sum_{k=0}^n 1/k! + 4*(-1)^k/(2k+1)"
What you did is took the expression you think "defines" pi and the expression for e, and performed a string manipulation. You haven't actually calculated anything, as evidenced by the fact that you can't even answer such a simple question as whether or not the number you got is rational.
This is the whole "basis" of real numbers. Talk a lot, philosophize, without actually being able to write anything down or calculate the stuff. You just "assume it can be done".

>> No.12464182

>>12464165
>>suddenly you can no longer calculate what a sum of two natural numbers is, nor what a sum of two rational numbers is
>false
If I give you an explicit definition of two natural numbers as real numbers, ask you to sum them and give me the answer as a decimal expression, would you be able to do it?

>> No.12464183

>>12464158
Ok then, but you can't go that far with pure semantics. Applied math needs real calculations etc. You can't solve a differential equation to apply it in physics just by using semantics (or is predicting approximate behaviour of a physical system is that semantic to you, that you can just think of it and it comes to your head?).

Give me the answers to these statements then (the ones that can be semantically formulated). There are plenty of pretty "semantic" problems that are undecidable. If you accept the natural numbers, then look up number theory problems. If you think that natural numbers are also an infinity nonsense, then look up some game problems such as game of life indecidability (hope these are not an infinity nonsense for you).

>> No.12464191

>>12464183
>Applied math needs real calculations etc
No it doesn't. None of the math that is actually applied to the real world needs the reals. The most they need is floating point arithmetic.
>If you think that natural numbers are also an infinity nonsense
The natural numbers are perfectly fine, as evidence by us being able to do calculations with them and get useful and wonderful results.
It's the talking about the "set of natural numbers" as a completed whole that is nonsensical.
You mention some categories of problems, but would you perhaps like to give me an explicit problem?

>> No.12464192

{8/(3π)-e, 8/(35π)+e, 8/(99π)-e/2, 8/(195π)+e/6, 8/(323π)-e/24...} = 0

>> No.12464201

>>12464191
Sorry, by "real calculations" I meant real calculations in the direct sense of this phrase, not referring to the real as "real number calculations". Thus my question was : how do you solve an diff. eq. within your approach ? Numerical methods ? But how to measure and justify the calculation error ?

About the concrete problems, do you accept, for example game of life problem and mortal matrix problem ? I find them pretty semantic and "without infinitary nonsense".

>> No.12464207

>>12464176
I don't understand what you want me to do
>>12464182
sure, but make sure you define them by a constant sequence

>> No.12464212

>>12464201
>Numerical methods ? But how to measure and justify the calculation error ?
Yes, numerical methods or symbolic manipulation, like you do in modern mathematics without ever thinking about doing infinite amount of work.
There are obviously some issues to work out because the common justifications for these operations invoke infinities, but the fact that they still give useful and calculable result gives me a lot of confidence that you can make it rigorous finite mathematics, just like people were able to do with a lot of different useful areas that were once thought to have required the completed infinite.
>About the concrete problems, do you accept, for example game of life problem and mortal matrix problem ?
I looked up the game of life problem and if I'm understanding it correctly it's equivalent to (or reduces to) solving the halting problem. In that case, I don't think the problem is meaningful because it relies on the notion of a unique completed infinite set of true natural numbers. There might be such a set, platonically speaking, but in my view Godel destroyed any hope of us ever actually appreciating what the set actually is so even if you do believe in such a unique true completed infinity, the question will still be effectively meaningless as in there is no way for us finite human beings to appreciate what the question is or how you would answer it.

>> No.12464223
File: 119 KB, 836x327, robinson.png [View same] [iqdb] [saucenao] [google] [report]
12464223

>>12464207
I'm simply demonstrating with this example that "real arithmetic" is nonsense. It's impossible to do, even in principle. The notions involved are too ambiguous, and this example demonstrates this well.
Of course you can't calculate the answer of pi+e because these concepts are all meaningless nonsense to begin with.
>sure, but make sure you define them by a constant sequence
Yeah that was what I expected you to answer. You are allowed to provide a general real number by an arithmetic algorithm yet whenever you do that you lose any notion of arithmetic, even on natural numbers. Most of the open problems in pure mathematics can be restated as the sum of natural numbers when viewed as real numbers. This is what I mean when I say the real numbers ruin everything. You can't even add two natural numbers anymore. When you start considering the real numbers as the most general set encompassing the rationals and naturals you lose any sense of what's actually going on, and resort to the endless sea of "let's assume" "suppose it can be done", "we haven't proved it can't be done!". This is seriously embarrassing.

>> No.12464231

>>12464212
Well, if you can justify all the numerical methods without the actual infinity and without the arguments like "I think it's going to work and thus it will", your theory is pretty viable. But at the same time I don't really see much motivation, as you can not pursue 100% semantics in math, even on the level of basic arithmetics. The statement "5+8=2+11" is pretty far from being 100% semantically clear until you try to justify it by imagining "if I take 5 apples and 8 apples and 2 apples and 11 apples it'll be the same" which is based on our everyday expirience and thus is far from "pure semantics". Even if Godel destroyed your hopes in everything past basic arithmetics, then Critique of Pure Reason by Kant should destroy your last hopes as well.

>> No.12464242

>>12464231
I don't think you're being entirely honest there. Sure, there is a sense in which "can anything really be known" philosophically, you can think about these issues. But I think you get a much clearer picture if you simply look at the real world. In the real world, nobody actually finds the statement 5+8 = 2+ 11 ambiguous. Everyone understands what it means, and everyone recognizes it as true. Finite mathematics is regularly used by people to get actual results. Nothing of the sort is the case with completed infinite objects that pure mathematicians like to considered. No infinities are actually used in the real world and the ambiguities are actually there to the point where a lot of smart, well-educated people, even some geniuses in mathematics have recognized the deep problems coming from the consideration of the completed infinite. And it's not even a recent phenomenon, Aristotle out of all people has written about the distinction between the potential and actual infinite, arguing that the latter is impossible. To argue that the ambiguities involved in finite math are in any way comparable in their relevance and logical soundness is in my opinion being a little bit dishonest.

>> No.12464246

>>12464223
you've yet to explain what you mean by "answer to pi+e"

>> No.12464252

>>12464246
It is commonly said that the real numbers form a field, which is a type of algebraic structure in which, among other things, you are supposed to be able to add two objects to get an answer.
It's also supposed that there are numbers called pi and e in this algebraic system. It is very natural to ask, given the claims about the possibility of arithmetic, what does their sum e+pi evaluate to.

>> No.12464256

>>12464252
Again, your misgivings about "evaluating" e+π are entirely based on a circular definition>>12464138

>> No.12464262

>>12464252
it evaluates to pi+e. it's like asking what's the answer to x^2+1 in some polynomial ring. it's x^2+1.

>> No.12464282

>>12464252
>>12464262
This. What do you want it to evaluate to?

>> No.12464288

>>12464242
If I really want to be an annoying phylosophist, I can ask you "do you know that 5+8=11+2 when you are born?". But I will not, because I do not really see a point in asking such deep philosophical questions to the detriment of usefullness of math.
By following the same reasoning : for people who do applied maths, your approach is pretty useful if it does not reduce the power of math tools used in everyday life; for people who do abstract math touching the actual infinity and thus pretty far from any applications, why should we care about the "humaneness" of introduced notions ?
Thus I don't really see a debate : one approach does not make the other wrong, just less intuitive.

>> No.12464293

>>12464288
wtf is with my spelling
philosopher*

>> No.12464349

>>12464282
You can play the same game with rational numbers, too.
>What does e+π evaluate to? e+π
What does 2/3 evaluate to? 2/3

>> No.12464371

>>12464256
>>12464262
>>12464282
>>12464349
This goes back to the fact that the "real numbers" don't have a canonical form nor is there any implementation where you can actually write down and show me what a real number is.
What you do is suppose as an (unproven) axiom that you CAN add two real numbers, but when I give you two specific real numbers you ask "what do you mean by adding them?", "What do you want to evaluate it to?", or simply repeat my question of pi+e back to me.
This is nothing like the game with rational numbers which DO actually exist and on which you actually CAN perform arithmetic. There is no need to take it as an axiom "you can add two rational numbers together", because you can just do it. If a schoolchild is asked to calculate 1/3 + 2/7 he knows what he's meant to do, he doesn't just repeat the question back to you or say "what do you mean by add them?", or say "It is assumed that it can be done". This illustrates one of the aspects of the fundamental difference between the reals, a made up fairy tale system that doesn't work and systems that do like rational numbers or natural numbers.

>> No.12464403

>>12464288
It's not the "humaneness" that we should care about (I'm actually not even sure what that means) but rather how logically sound our theory is. We want to know that what we're saying is meaningful, we don't want to be simply shuffling meaningless formulas around with evidence-free faith that the formula "0=1" cannot be proven from such manipulations, and pretend that the formulas have any semantics behind them.
I do think that some limited amount of infinitist tools can be good to study in mathematics, to investigate what kind of results could be out there that you may later try to verify using finite mathematics. For example, the fundamental theorem of algebra being proven again and again with infinitist tools suggest that there might be something going on here, and we should try to prove it using finite tools. Surprisingly, nobody has been able to do it yet.
Now the problem in my opinion is that mathematicians care too little about the logical soundness of their theories. If you tell them the status of finite fundamental theorem of algebra, they would act confused and ask who cares? It is known that much of the mathematics that was once thought to have require infinities can be actually understood in a finite, and hence much more clearer and logically sound, way. There needs to be a program which brings as many of these results to light as possible. After all, mathematics is a very cool and interesting subject. The state of it now to my mind is something like the state of italian algebraic geometry before they started to be "rigorous", where implicit assumptions and leaps of logic are thrown around carelessly. People recognized that what was done was actually interesting, even though a lot of it was very logically questionable, and tried to recover it with tools they regarded as actually rigorous. The same effort needs to happen to the whole of mathematics, this time with genuinely rigorous finitistic tools.

>> No.12464408

>>12464371
Evaluate 2/7

>> No.12464413

>>12464408
It's already evaluated in its proper canonical form as the ratio of two coprime integers. Do you want me to demonstrate that 2 and 7 are coprime?
Here it is: use the Euclidean algorithm:
gcd(2,7)=gcd(2,7 - 2*3)=gcd(2,1)=1

>> No.12464467

>>12464413
Why are you satisfied by that inevaluable canonical form, but unsatisfied by the other inevaluable canonical form?

>> No.12464477

>>12464467
The "real numbers" don't have any canonical forms.

>> No.12464484

>>12464403
Well, I agree that reformulating the math without actual infinities would be a nice thing. Proving the fundamental theorem of algebra with purely algebraic semantic notions is even nicer. At the same time, it's ONE OF many problems in math. Therefore the question asked in my first post holds : why tf are u spamming these threads like a bunch of retards ?

>> No.12464486

>>12464477
The canonical form for e+π is e+π.

>> No.12464491

>>12464371
tldr; real numbers don't have a cannonical form. so?

>> No.12464530

>>12464486
Interesting. And what is the canonical form of a general rational number p/q?

>> No.12464554

>>12464371
>(unproven) axiom
should we tell him?

>> No.12464558

>>12464554
That Vader is Luke's father?

>> No.12464559

>>12464554
In modern mathematics the word axiom is ambiguous and can be interpreted in different ways in different situations, which is why I felt the need to clarify the use of the word.
For example, it is said that the set of nonzero rational numbers under multiplications satisfy the axioms of a group. But these axioms are proven, it is not just assumed that they hold true.

>> No.12464565

>>12464486
There's actually a unique symbol for e + pi. It's called D. It's exactly the length of the average penis in inches. So e + pi evaluates to D

>> No.12464572

>>12464559
>these axioms are proven
then they aren't axioms dumdum

>> No.12464573

>>12464530
The canonical form of p/q is p/q, 600/π^2 percent of the time.

>> No.12464602

>>12464371
>This is nothing like the game with rational numbers which DO actually exist
they don't though

>> No.12464651

>>12464565
Yes, the special case of a polynomial cock ring.

>> No.12464699
File: 94 KB, 694x437, 104787656_3294711467235256_1030822319958753628_n.jpg [View same] [iqdb] [saucenao] [google] [report]
12464699

>>12463834
"metanumbers" LOL

>> No.12464706

>>12464699
What's so funny?

>> No.12464708

>>12464706
>metanumbers
>numbers which "dont" (((exist)))
>natural and rational numbers
>numbers which "do" (((exist)))

>> No.12464715

>>12464708
Metanumbers are not numbers, that's the whole point. And they do exist.

>> No.12464717

PRAISE!

>> No.12464718

>>12464715
>metanumbers are not numbers
maybe you should just make a new term instead of using "numbers". Numbers are already a well defined concept in which irrationals ARE numbers.
If you want to call them flooflams and metaflooflams, feel free

>> No.12464720

>>12464718
I'm going to stick with calling them "metanumbers" for now, thanks.

>> No.12464723

>>12464720
no problem. the rest of as are gonna stick with knowing youre a retard, buddyboy :)

>> No.12465188

>>12464530
>>12464573
I think you missed this. I'm curious how you would express (or think about) the probability that any two integers p,q are coprime. Is it a concept you simply wouldn't be able to consider or investigate?

>> No.12465211

>>12465188
>I'm curious how you would express (or think about) the probability that any two integers p,q are coprime. Is it a concept you simply wouldn't be able to consider or investigate?
First of all don't you mean 6/pi^2?
Second of, all the notion of probability that any two integers p,q are comprime is not really well-defined even in standard infinitary mathematics, because you have to provide the distribution that you're considering.

>> No.12465278

>>12465211
>6/pi^2
Yes, a.k.a. "600/π^2 percent."
>in standard infinitary mathematics
No, I'm curious to what extent the concept can even be considered from your point of view, if at all.

>> No.12465305

>>12465278
>Yes, a.k.a. "600/π^2 percent."
Ah, you're right, my bad.
>No, I'm curious to what extent the concept can even be considered from your point of view, if at all.
Well it general it seems that whatever way you are going to define it it will involve some kind of limit of natural numbers, n getting arbitrarily high. Such a definition will necessarily have to be formulated in doing infinite amount of work, and this I would be a meaningless proposition (there might be some meaningful ideas in the proof though).
If on the other hand you formulate it as some kind of explicit estimate for any n, like you have some arithmetical expression in terms of n and explicit bounds of how many coprime numbers there are up to n, that would be a meaningful proposition, it would actually give you meaningful information that you can use and understand.

>> No.12465348

>>12464718
The term "meta-number" already implies that they are not numbers, but something BEYOND numbers. The term is fine.

>> No.12465432
File: 1.01 MB, 2128x5320, 1600163454508.jpg [View same] [iqdb] [saucenao] [google] [report]
12465432

>>12465348
How do you people sleep at night, making a complete idiot out of yourselves in such a shameless fashion during the day.

>> No.12465484

>>12465432
Harry Gindi approach

>> No.12465561

>>12464176
By definition:
2=1+1
3=1+1+1
4=1+1+1+1 and so on.
Isn't 3+4=7 the result of mere string manipulation? Is there a problem with string manipulations? How can you have a stroke in a chalkboard that is not a string?

>> No.12465583

>>12464158
>>12464131
I have a finite and meanignful problem so you should be able to solve it:
Hadamard's maximal determinant problem. https://en.wikipedia.org/wiki/Hadamard%27s_maximal_determinant_problem

>> No.12465594

>>12465484
lmao

>> No.12466132

>>12465583
Unless you're restricting to a particular dimension, it's not at all clear what the problem is asking because it seems to involve quantification over the naturals n that represent the size of matrices, and as we know in general universal arithmetic quantification is meaningless.
>>12465561
You are correct. But in one case the actual implementation of natural numbers is as strings, so your manipulation of these strings corresponds to manipulation of actual natural numbers. Nothing of the sort is possible with real numbers. The expressions anon wrote are not any kind of implementation of the reals, they will readily admit themselves that such an implementation cannot exist due to cardinality consideration (another nonsensical concept in my opinion). This means that by their string manipulations they're not actually computing wtih real numbers. If they actually did this, they would be able to get the answer, and in particular say whether or not it's rational.

>> No.12466354
File: 60 KB, 1019x330, wildberger-maimon1.jpg [View same] [iqdb] [saucenao] [google] [report]
12466354

>>12463560
I'm beginning to suspect he actively censors discussions in the comments of his videos: There was a heated discussion with ron maimon in the comments on one of his videos which was really awesome to read, but none of ron's comments are there anymore. I don't know if njw removed them intentionally, but I really hope that's not the case. I've loved wildberger ever since /sci/ introduced me to him.

>> No.12466468

>>12464559
You need to distinguish between synthetic and analytic theories.

>> No.12466476

>>12466132
>in general universal arithmetic quantification is meaningless.
Tell that to the alternate sign matrix conjecture https://arxiv.org/abs/math/9407211

>> No.12467733

>>12466354
Due to the larger clip posted in the other thread, I now think it's more likely that this Ron Maimon troll later realized he'd been btfo and nuked his own comments out of embarrassment.

>> No.12467898

>>12467733
Surely not? It would be rather uncharacteristic of Maimon.

>> No.12468011

>>12463562
>"what is this completed infinite", which Godel proved is actually IMPOSSIBLE TO DEFINE!
Where is this proof?

>> No.12468732

>>12468011
Look up any textbook on mathematical logic. The proof is contained in Godel's first incompleteness theorem. The statement of the theorem assumes you believe the notion of consistency of a theory is meaningful and also that you believe in the ideal set of natural numbers (because its proof uses numbers too big to be ever realizable in any of the common implementations of natural numbers). It states that
For any definition (recursive axiomatization) of the set of natural numbers (completed infinite) that you have, there will always be at least two different ways to extend this definition into a new consistent definition that answers arithmetical questions differently. Also if we ignore the size of the numbers involved, the question it answers differently is one of the simplest kinds of questions, i.e. it's in the form of "some algorithm X halts". This conclusively demonstrates that no definition of natural numbers effectively captures the concept (assuming the concept is a meaningful thing in the first place, which I strongly believe is not).
A pretty short exposition to the incompleteness theorems and their implications can be found in the first chapter of Girard's book "Proof Theory and Logical Complexity, vol 1". Note that he is very casual (as are most mathematicians) about using arithmetic concepts divorced from reality in his proofs (his metamathematics is infinitistic). It's still worth reading though.

>> No.12468742

>>12466476
>>in general
The alternate sign matrix conjecture is definitely meaningful. All I'm saying is that you have to be careful in formulating a question, because just because it looks like it's meaningful, doesn't mean that it is, and this trap cannot even be avoided for general Pi_1 questions.

>> No.12469155

>>12464718
Didn’t Eudoxus solve this shit with quantities, ratios, and magnitudes?

>> No.12469222

>>12468742
Well. Then show if the Hadamard's problem is meaningful or not.

>> No.12469539

>>12463560
Brothers and Sisters of the ONE TRUE FINITE FAITH!

PRAISE THE HOLY BURGER!

Amen.

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