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/sci/ - Science & Math

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9395918 No.9395918 [Reply] [Original] [archived.moe]

Lately I've been seeing a lot of anti-infinity autism on this board. Why is this happening? Is this the state of our education system? Will they grow out of it? How can we eradicate the wildburger disease? Discuss.

>> No.9395926
File: 50 KB, 488x398, Religion math.png [View same] [iqdb] [saucenao] [google] [report]


>> No.9395934

My theory is that finitist thought is more attractive to those with a computation background, since computers can only compute up to finite precision, and can only deal with a finite amount of objects, both in memory and in principle. As such, like the physicist or applied mathematician who sees mathematics as a mere language to describe the "real" reality, the computationally-minded person sees in mathematics their own philosophy. This is also the same reason why actual computer scientists are more likely to favour set-theory skepticism, and a denial of classical logic in favour of intuitionistic formulations of formal logic.

As such, since it is more likely that on the internet you will find "computationally-minded people" (whether they are legitimately involved with the theory or are just fanboys of a new edgy kind of mathematics), it is more likely that you will find a finitist than not.

>> No.9395935
File: 5 KB, 211x239, 92d.jpg [View same] [iqdb] [saucenao] [google] [report]

>These are roughly analogous to religion, atheism, and agnosticism.
That is the most retarded analogy I've heard all year.

>> No.9395940

In my opinion consciousness is infinite, but it experiences this reality finitely.

>> No.9395942

No, it's perfectly fine.

>> No.9395947

What a bullshit

>> No.9395951

no it's not

>> No.9395956


>> No.9395994
File: 23 KB, 600x450, 0bb.jpg [View same] [iqdb] [saucenao] [google] [report]


>> No.9395998

>platonism = religion
>finitism = atheism
>formalism = agnosticism

>> No.9396002
File: 38 KB, 640x628, eyeroll.jpg [View same] [iqdb] [saucenao] [google] [report]

>platonism = religion
>finitism = atheism
>formalism = agnosticism
What the fuck.

>> No.9396019

True its a bad analog. I'm religious yet believe in finitism when it comes to math that produces real results. The issue here is that it's sorely implying "believing" infinite sets to work means is similar to "believing" religion to work, when in reality religion produces working results regardless if you "believe" while atheism aka lazy brainletism doesn't give enough shit to actually figure anything out towards the effect of either contradicting believe or supporting it.

>> No.9396026

The fact that, for example, certain weak solutions to the Navier-Stokes equation are unphysical implies that the continuum is in some sense physically real. If the continuum is physically real, then [math] \mathbb{R} [/math] exists beyond mere formalism.

The universe does not obey finitistic mathematics.

>> No.9396027

> finitist thought is more attractive to those with a computation background
/thread, it's comp """sci""" brainlets.

>> No.9396032

Comparing stuff to religion, atheism, etc. is dumb.
Your full of shit, maybe you got lost on your way to humanities department
Totally agree retarded
Get the fuck away from me you dumb finitist, you probably don't actually know what these words mean. Your brainlet mind can't handle words bigger than 2 syllables.

>> No.9396037

Damn, truth hurts, you sticken it to them.

So many people here believe that there opinion has some sort of value when they know nothing of the subject. Don't talk unless you know what your talking about, dont just sprout "math words" in strings without meaning to justify your (meaningless) opinion. Instead maybe read a book. I'm lookin at the finitists here and people like

>> No.9396073

a literally meaningless string of words

>> No.9396076

> there opinion
> your talking about,
> sprout "math words"

>> No.9396088

What are you trying to say? My grammar is bad?This is 4chan, a part of the internet, no one care. You are exactly the kind of people I was talking about, you go on /sci/ to a math topic and correct people on their english instead of maybe learning some math.

>> No.9396099 [DELETED] 
File: 7 KB, 420x420, b36.png [View same] [iqdb] [saucenao] [google] [report]

[math]\infty[/math] is not a number
[math]n \rightarrow \infty[/math] cannot evaluate to a finite answer in finite time
[math]0.\bar{9} < 1.0[/math]
[math]0 \neq 0.\bar{0}1 \ngeq 0.\bar{1}_{base2} \ngeq 0.\bar{9}_{base10} \ngeq 0.\bar{F}_{base16} \neq 1.0[/math]
[math]N \geq 2 \rightarrow \infty; (0.\overline{N-1}_{baseN} < 0.\overline{N}_{base(N+1)})[/math]
[math]X = \sum{N%3=0}^{/infty} 0.(\frac{N}{3})_{baseN} × 3_{base10} = 1.0 \neq 0.\bar{9}[/math]
[math]0.\overline{N-1}_{baseN} = [/math] NaN

>> No.9396102 [DELETED] 
File: 7 KB, 420x420, b36.png [View same] [iqdb] [saucenao] [google] [report]

[math]\infty[/math] is not a number
[math]n \rightarrow \infty[/math] cannot evaluate to a finite answer in finite time
[math]0.\bar{9} < 1.0[/math]
[math]0 \neq 0.\bar{0}1 \ngeq 0.\bar{1}_{base2} \ngeq 0.\bar{9}_{base10} \ngeq 0.\bar{F}_{base16} \neq 1.0[/math]
[math]N \geq 2 \rightarrow \infty; (0.\overline{N-1}_{baseN} < 0.\overline{N}_{base(N+1)})[/math]
[math]X = \sum{N/3=1}^{/infty} 0.(\frac{N}{3})_{baseN} × 3_{base10} = 1.0 \neq 0.\bar{9}[/math]
[math]0.\overline{N-1}_{baseN} = [/math] NaN

>> No.9396108 [DELETED] 
File: 214 KB, 400x399, 1365111121911.png [View same] [iqdb] [saucenao] [google] [report]

[math]\infty[/math] is not a number
[math]n \rightarrow \infty[/math] cannot evaluate to a finite answer in finite time
[math]0.\bar{9} < 1.0[/math]
[math]0 \neq 0.\bar{0}1 \ngeq 0.\bar{1}_{base2} \ngeq 0.\bar{9}_{base10} \ngeq 0.\bar{F}_{base16} \neq 1.0[/math]
[math]N \geq 2 \rightarrow \infty; (0.\overline{N-1}_{baseN} < 0.\overline{N}_{base(N+1)})[/math]
[math]X = \sum_{N/3=1}^{\infty} 0.(\frac{N}{3})_{baseN} × 3_{base10} = 1.0 \neq 0.\bar{9}[/math]
[math]0.\overline{N-1}_{baseN} = [/math] NaN

>> No.9396110

Keep going anon. The irony of your posts is delicious.

>> No.9396113


>> No.9396117
File: 214 KB, 400x399, 1365111121911.png [View same] [iqdb] [saucenao] [google] [report]

[math]\infty[/math] is not a number
[math]n \rightarrow \infty[/math] cannot evaluate to a finite answer in finite time
[math]0.\bar{9} < 1.0[/math]
[math]0 \neq 0.\bar{0}1 \ngeq 0.\bar{1}_{base2} \ngeq 0.\bar{9}_{base10} \ngeq 0.\bar{F}_{base16} \neq 1.0[/math]
[math]N \geq 2 \rightarrow \infty; (0.\overline{N-1}_{baseN} < 0.\overline{N}_{base(N+1)})[/math]
[math]X = \sum_{N mod 3 = 0}^{\infty} 0.(\frac{N}{3})_{baseN} × 3_{base10} = 1.0 \neq 0.\bar{9}[/math]
[math]0.\overline{N-1}_{baseN} = [/math] NaN

>> No.9396146
File: 232 KB, 300x300, 1307889832001.png [View same] [iqdb] [saucenao] [google] [report]

So you're saying the universe has infinite energy?

>> No.9396174

>computers can only deal with a finite amount of things
This isn't really true. If you believe that then humans can't either.
Lazy lists are one kind of way computers deal with the infinite.
A slightly better example is that most theorem proving languages will have a non-finite set construct.

>> No.9396178

Are you making fun of the finitists or actually believe this, thanks for proving my point exactly. You write down a bunch of nonsense to make it seem like you know shit, but you are really just a brainlet. Listen up, heres the key:

0.999... represents the number after "finishing" the sum 0.9+0.09+0.009... (and we can find a scheme for computing this in finite time, though this is not the point: first sum 0.9+0.09 in 1/2 second, then add on 0.009 in the next quarter, then add on 0.0009 in the next eigth etc.).

0.999...9 is always less than 1 if there are a finite amount of 9s but thats not what .999... denotes, it denotes the number that is the limit of that sum, which is 1.

Trying to make sense of the gibberish that is written about 0.999... in different bases:

First note that 0.0...1 is not a thing (unless we are talking about surreals but your brainlet doesn't understand what those are, even then no one defines it as 0.0...1).

While any 2 different bases converge at different "speeds" to 1, that does not mean they can't converge to the same thing, your argument can be used to show that the sequence 1,1,1,1,.. and 3,2,1,1,1,1,... don't converge to the same thing (which is absurd because they both converge to 1 because they both are 1).

As for the other lines of mess, I have no idea what they are supposed to mean.

>> No.9396196

[math]0.\bar{8}[math] must converge towards 0.89 if [math]0.\bar{9}[/math] converges to 1.

The fact of the matter is [math]0.\bar{9}[/math] is simply not a natural number. It can only be crafted using elements of infinite sets of directions, like [math]\sum_{n=1}^{\infty}\frac{9}{10^n}[/math]
And doesnt otherwise naturally occur during normal arithmetic.
[math]0.\bar{3} × 3 = 1.0[/math]
[math]0.\bar{1} × 9 = 1.0[/math]
[math]0.\bar{n}_{base(n+1)} is simply not a real number.

>> No.9396208

[math]0.\bar{8}[/math] must converge to 0.89 if [math]0.\bar{9}[/math] converges to 1.0. Theres no greater number above [math]0.\bar{8}[/math] and less than 0.89 after all.

>> No.9396232

0.889 is less than 0.89
and 0.8889 , 0.88889, 0.888889
so what is the next biggest number past [math]0.\bar{8}[/math]?

0.9 repeating really doesnt equal 1.

>> No.9396278

Seriously how can we define the next biggest number for any repeating decimal, much less [math]0.\bar{9}[/math]?

0.81 is bigger but
0.801 is smaller than 0.81
0.8001 is smaller still
0.80001 is smaller still
0.800001 is even smaller
0.8000001 is there a pattern here?
cause to me it looks like
[math]0.8\bar{0}1[/math] would be the smallest number bigger than 0.8 and less than 0.81, but i guess notation of a significand after the repetition isn't allowed?
so how would it be possible to know that [math]0.\bar{9}[/math] should equal 1? rather, why should it equal 1 in all circumstances, when it is just as easy to say it doesn't even exist at all?

[math]0.\bar{1} + 0.\bar{8} = 1.0[/math]
>this is how the equation actually evaluates
[math]0.\bar{1} + 0.\bar{8} = 0.\bar{9} = 1.0[/math]
>this is how turdburglars evaluate it

[math]0.\bar{1} - 0.\bar{1} = 0[/math]
>this is how everyone evaluates it
[math]0.\bar{1} - 0.\bar{1} = 0.\bar{0}1 = 0[/math]
>but this is somehow too confusing for turdburglars even though its exactly what they do with [math]0.\bar{9} = 1[/math] in bridging a gap with an infinitesimal

convergence is just rounding and dont deny it, so c'mon put away the elementary school math and put on your thinking hat.

>> No.9396280

That is true, and when I first was writing my post I was going to mention this but I forgot. I would say that this is not a true handling of the infinite, it is analogous to the finitist in mathematics, using algebra to conceal infinite objects. For instance, considering the ring Q[sqrt(2)], which can be described in a purely finitist framework, despite what it "really involving" an infinitely precise notion of the "square root of 2", in this way, it is like lazy evaluation.

>> No.9396281

>implying I'm a finitist


>> No.9396295

Your opinion is worth less than the pixels it's written with. This is /sci, not /x, and your vaguely worded mysticism doesn't wash.

>> No.9396311

But all humans do with maths is find finite ways of dealing with the infinite. That's why we use things like limits. I don't see what you want from a "true handling of the infinite" unless you're arguing that it is never really possible.

In the same way a finite human is able to reason about non-finite things such as "the set of natural numbers satisfying predicate p", finite computers can be used to reason about non-finite things. There's nothing we can do with maths that couldn't (theoretically) be done on a computer.

Pretty funny to use Q as your example field since I don't think ultra finitists would believe in it.

>> No.9396443
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>> No.9396444
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>> No.9396447

With the usual ordering of [math]\mathbb{R}[/math]
there is no such thing as "the next biggest number"
Your arguments make no sense whatsoever.

>> No.9396453

>t. butt blasted atheists

>> No.9396462

finity works better with real world measurements where precision is arbitrarily limited by the tools at hand. Beyond that precision, acknowledging that something approaches infinity adds no information so it tends to be as frustratingly useless as things like intelligent design. This seems more of an engineering complaint versus an autistic one.

>> No.9396474

If you suffer from brainletism, then yes. Meaning requires room for thought.

>> No.9396482
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It is a real number, because we sense it as a 1 in the physical world.

>> No.9396485

Define the difference between 0.0...1 and 0 pls

>> No.9396487
File: 68 KB, 800x600, 1513733938675.jpg [View same] [iqdb] [saucenao] [google] [report]

I guess 0.999.... is its own universe, that expands itself to the untangible border 1.

>> No.9396707

0.999... is just a different notation for [math] \lim\limits_{n \to \infty} \sum\limits_{i=1}^{n} \frac{9}{10^i} [/math]. This thing makes sense if and only if the limit actually exists. The limit actually exists and it is 1. 0.999... is not its own thing. It's denoting the limit of that series/sequence. If you want the definition of a limit, see https://en.wikipedia.org/wiki/(%CE%B5,_%CE%B4)-definition_of_limit#Precise_statement_and_related_statements.

Now back to the main topic.

>> No.9396744

*looses zeno's arrow*

>> No.9396768
File: 31 KB, 480x531, 6.jpg [View same] [iqdb] [saucenao] [google] [report]

I've been seeing this on the same finitist threads. How sad that the CS fags don't realize that Math extends far beyond their puny CPUs.

>> No.9396774

>cannot evaluate to a finite answer in finite time
But it can retard. This is basic Calc 1 shit, look up "Limits at Infinity" it'll be in one of the earlier chapters bc of how easy it is to understand.

>assuming [math] 0.\bar{0}1 [/math] exists
fucking disgusting

>> No.9396787

The easiest way to prove that 0.(9) = 1 is to use base 3 you brainlets. In fact the method is pretty general, in that for any rational number with an infinite periodic representation in base x there exists base y in which its representation is finite.

>> No.9396838

Uh no.
For every N modulo 3 limit to infinity, 1/3 in that baseN × 3 easily equates to 1.0.
In base3, 1/3 = 0.1
0.1 + 0.1 = 0.2
0.2 + 0.1 = 1.0

[math]0.\bar{9}[/math] is not a number in base 10, and truthfully [math]0.\overline{N}_{base(N+1)}[/math] is not a valid number in any base. Brainlets think [math]0.\bar{9}[/math] must exist though because [math]0.\bar{3} × 3[/math] seems to evaluate to it, but only cause brainlets dont understand that a number [math]\bar{N}[/math] is not related to a number [math]N[/math].
They incorrectly evaluate [math]0.\bar{3} × 3 = 0.\bar{9}[/math] cause they treat [math]\bar{3}[/math] to mean the same as 3, but with using that logic [math]0.\bar{3} × 4 = 1.\bar{3}2[/math], which having used the same exact logic to get [math]0.\bar{9}[/math], now returns the incorrect answer.

>> No.9396886

>My theory is that finitist thought is more attractive to those with a computation background, since computers can only compute up to finite precision, and can only deal with a finite amount of objects, both in memory and in principle.
A) Most programmers don't know or care much about hardware issues like that. A minority are deeply familiar with both, but everyone else is either hardware or software, and software people are all about abstraction free from physical concerns.
B) Object oriented programming is literally applied Platonism e.g. you instantiate objects that participate in abstract blueprint classes.
C) The limiting factors you brought up aren't unique to computers, they apply to everything else too e.g. human thinking isn't any less limited than artificial computation, both are classically physical cause and effect based functional processes.
So if anything, I would bet the average programmer is way more sympathetic to a framework that uses infinities than one which tries to avoid them.

>> No.9396891
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actually that example was a little wrong too
[math]0.\bar{33} × 4[/math] might evaluate to [math]1.\bar{3}2[/math]

a megabrainlette might see [math]0.\bar{3} × 4 = 1.\bar{2}[/math]

either way, treating [math]\bar{n}[/math] like it's natural number n results in the wrong answer, so [math]0.\bar{9}[/math] as a result from [math]\frac{1}{3}×3[/math] is a wrong answer too.

>> No.9396981

>Lazy lists are one kind of way computers deal with the infinite.
You can't represent an uncountable set as a lazy list.

>> No.9396997

>You can't represent an uncountable set as a lazy list.
natnums = [1..]
You now have the natural numbers in a Haskell list. It'll give you however many elements you need in a give operation through lazy evaluation. And no, it does still count, there are many examples of infinitie set manipulation handled this way in Haskell. It works no matter how much you don't like it.

>> No.9397003

Uncountable, not infinite.

>> No.9397033
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>uncountable set
cslets, everyone

>> No.9397070

But there are other ways to represent uncountable sets.
Lean for example let's you use a set membership predicate to define a set.

>> No.9397076

Doesn't that constrain you to constructible sets?

>> No.9397082
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oh boy the one language designed literally just to do abstract math and reinforce the concept that you're totally not doing something that is worthless.

>> No.9397085

This is why I love Haskell. Its higher barrier to entry helps keep the brainlets out.

>> No.9397129

I'm not sure (haven't done much set theory).
Can you give an example of a non-constructible set?

>> No.9397273

It doesn't matter if infinity is real or not- it isn't useful. Nothing humans have to deal with is infinite. It's just a concept that useless number pushers mess around with all day to no purpose.

And even if it is real, humans- who are finite beings- can't ever comprehend it. People pretend to comprehend infinity but no one can. So once again, it is useless to even talk about infinity.

>> No.9397281
File: 91 KB, 645x729, b90.png [View same] [iqdb] [saucenao] [google] [report]

>It doesn't matter if infinity is real or not- it isn't useful.
>it is useless to even talk about infinity.
>calculus is useless
>analysis is useless
>I'm retarded

>> No.9397288

>People pretend to comprehend infinity but no one can.
Are you fucking autistic? Are you stuck in the 19th century? Mathematicians deal with infinities and prove theorems about them all the time, you worthless sack of shit. Just because YOU are too braindead to understand these concepts doesn't mean everyone else is.

>> No.9397291

Name me one example of a practical usage of the concept of infinity.
A brain with a few billion cells can't comprehend infinity.

>> No.9397295
File: 14 KB, 478x523, d04.png [View same] [iqdb] [saucenao] [google] [report]

>People pretend to comprehend infinity but no one can.

>> No.9397306

>Name me one example of a practical usage of the concept of infinity.
anything involving limits

>> No.9397308

>Name me one example of a practical usage of the concept of infinity.
>Foundation of caculus and analysis

>A brain with a few billion cells can't comprehend infinity.
Holy shit, you're even dumber than I thought.

There are ~100 billion neurons in the human brain. Are you claiming mathematics can't be done with numbers greater than 100 billion, you fucking retard?

>> No.9397312

All of those reside completely in theory and have no practical value. Those don't apply to the physical world.
>There are ~100 billion neurons in the human brain. Are you claiming mathematics can't be done with numbers greater than 100 billion, you fucking retard?
The human mind can't truly comprehend any numbers above 100

>> No.9397315
File: 77 KB, 645x729, 80c.png [View same] [iqdb] [saucenao] [google] [report]

>no practical value

>The human mind can't truly comprehend any numbers above 100
>said unironically

>> No.9397316

>humans- who are finite beings- can't ever comprehend it.
What kind of retarded logic is that?
>humans- who are carbon based beings- can't even comprehend silicon
>humans- who are meat based beings- can't even comprehend plants
>humans- who are bipedal based beings- can't even comprehend wheels
>People pretend to comprehend infinity but no one can.
You don't comprehend what comprehension is.
primes = sieve [2..]
where sieve (p:xs) =
p : sieve [x | x <- xs, x `mod` p /= 0]
Ooooooo I'm using a SPOOKY infinite list, who knows what it means? Surely not us poor finite humans, it must only coincidentally produce the expected results because there's no way any of us could ever actually UNDERSTAND infinity, it just like, goes on forever, man *bong toke*, you can't count to forever, mannnnnnn

>> No.9397321

>The human mind can't truly comprehend any numbers above 100
We are reaching levels of retardation that shouldn't be possible.

>> No.9397323

>We are reaching levels of retardation that shouldn't be possible.
So > Level 100?

>> No.9397326
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>The human mind can't truly comprehend any numbers above 100
lmfao, you can't count to 101?

>> No.9397331

You only think you counted to 101, your mind skips one of the numbers to make it work without you consciously noticing, usually somewhere around the 80-90 range.

>> No.9397335

>lmfao, you can't count to 101?
I can count to it but then I forget the numbers I counted before it as I'm going along- finite memory.

Just think about it, if I try to picture roughly 100 fajitas, for example, I can, but if I go over that it goes all fuzzy and they disappear.

>> No.9397345

>You only think you counted to 101, your mind skips one of the numbers to make it work without you consciously noticing, usually somewhere around the 80-90 range.
Simple question: What is 100 + 100?

>> No.9397348

200, obviously. But I didn't do the sum in my head. I did 2+2 and just added in the zero's

>> No.9397356

You're claiming we can't do mathematics and prove stuff about quantities that are larger than what we can immediately visualize.

So pretty much all of science, physics, chemistry, and biology is useless. OK.

>> No.9397362

Can you not conceive of a situation where it is useful to deal with quantities >100?

If so, you're autistic.

>> No.9397366

If you could easily visualize everything expressible via mathematics there would be no point in having mathematics.

>> No.9397376

Yeah I can see the use, that's where maths comes in I guess. But infinity is different. Not only can't we comprehend it, but it doesn't exist in the finite world of matter we inhabit. Nothing can be done with infinity. It's not just that we can't visualise it, we can't conceive of it at all. We can use maths to conceive of massive numbers, but not infinity, which is a vacuous and nonsensical concept.

>> No.9397395

Let me guess: You're still doing arithmetic and haven't started calculus?

>> No.9397402

>infinity, which is a vacuous and nonsensical concept.

>> No.9397426

>what is a limit

>> No.9397433

It's a load of bullshit that doesn't apply to reality is what it is

>> No.9397435
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>apply to reality

>> No.9397436

>what is a derivative

>> No.9397445

lol ok

>> No.9397547

finitism triggers math autists because it reminds them that their entire field is based on arbitrary axioms that have unintuitive and nonsensical conclusions as a result

>> No.9397550
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Its true i just tried counting to 100 but for some reason i counted 86, 87, 88, 89, 80, which made me go like woah. Took a second to say "90" then start counting again.

>> No.9397558

Calm down Xavier.

>> No.9397573

fucking read a book on the hyper reals in in the
pin kys

>> No.9397582

It's way more autistic to feel the need to introduce a bunch of new axioms just to reinvent the mathematics we already have in a way that doesn't use an idea you dislike.

>> No.9397607 [DELETED] 

[math[0.\bar{9}[math] is a hyperreal

>> No.9397612

[math]0.\bar{9}[/math] is a hyperreal

>> No.9397624

No, it's not. Not in the standard notation.

>> No.9397702

>what is the last 100 years of physics

>> No.9397742

Its afflicted with the same problem as the infitesimal though. If one is, so must also the other.
You might be beginning to realize how retarded math is and how much needs to change to produce real results.

>> No.9397745

Either all of mathematics is wrong because a bunch of brainless retards on 4chan "proved it".

Or the brainless retards are just brainless retards that get triggered when they come across stuff they don't understand properly/don't like.

Sorry but I am siding with my boys Tao, Gauss, Erdos, Hardy, Fermat, Lagrange, Einstein, Euler, Galois, Abel, Russel, Godel, Klein, etc. and not the NJ Wildberger + retarded fags team.

>> No.9397760

ad hominem, you have no proof and anything you can put forth is just an unfalsifiable theory

>> No.9397768

get the fucking jewish doodles out of my math pls i literally exchange the aleph with capital N and bet with capital V whenever i have to write that shit out.

>> No.9397773

Well we have developed an axiomatic system that works and have proven its validity, and the fact that 0.999... = 1 many different ways. The fact that you don't understand why the proof works is your problem, not mine.

If you wat to invent a "finitist axiomatic system" where 0.999... is not 1 go ahead, people like NJ Wildberger are trying to do that but it's not complex enough for any use to come from it. With finitism, we cannot do any sort of physics or even just prove interesting theorems (that are provable otherwise).

The correct side of the arguments has many many proofs, which is why most people know a name like Einstein but not Wildberger. You come in here with your brainlet shit and try to say all of math is wrong, well why don't you have a proof?

And I mean a real proof, not the kind of B.S. that I previously invalidated like

You want to make a theory of math where only numbers up to 100 exist, fine go ahead. But don't disturb a math class when a professor writes the number 101 on the board.

>> No.9397781

Every proof for [math]0.\bar{9}[/math] is literally false and easily contradicted. So far there is only 1 way to artificially construct the number via
[math]\sum_{n=1}^{\infty} \stackrel{+}{=} \frac{9}{10^n}[/math]
It really isn't a number and any other problem that might seem to result [math]0.\bar{9}[/math] actually just returns [math]1.0[/math] where [math]0.\bar{9}[/math] is actually the objectively wrong result earned by misinterpreting the question.

>> No.9397782

>An "unfalsifiable theory"
Brainlet, that's what math is, its proven as in: Not possible to prove false. We aren't experimentally testing numbers to see if they are equal.

You idiots just put together words that sound like they are what smart people use but you don't know what math is, what a limit is, etc.

Read a book.

>> No.9397783

Meant to say any proof for [math]0.\bar{9} = 1[/math] but it works either way considering it isnt a number

>> No.9397787

What the fuck? How would you define 0.9 ...then? If 0.9... is not the given sum of $\frac{9}{10^n}$?

Go ahead, give me a good definition of what the symbol 0.9... denotes.

>> No.9397799

Thats just it though.
[math]0.\bar{9} = /sum_{n=1}{\infty} \stackrel{+}{=} \frac{9}{10^n}[/math]
9/9 = 3/3 = 1.0
[math]0.\bar{8} + 0.\bar{1} = 1.0[/math]
the problem of thinking it exists betond that sum is based on misinterpretation of numbers and thinking [math]0.\bar{9}[/math] occurs more often than it actually does.
For example, [math]0.\bar{3} × 3 = 0.\bar{9}[/math] is a wrong answer, because it misinterprets what [math]\bar{3}[/math] is and the misinterpretations stems from the fact it looks like a normal 3.
If the above solution is supposed to be valid, the same logic applied to the problems and answers of [math]0.\bar{3} × 4 = 1.\bar{2}[/math] or [math]0.\bar{33} × 4 = 1.\bar{3}2[/math] would also be considered valid, even though these answers are plainly wrong. In all three examples, the repeating 3 is treated as a substitute for 3 and presumptiously contatenated. In the old days before anyone knew better, they'd do 1/3 × 3 = 0.999... and think "this makes sense" even though they already know deep down that three thirds is nothing but 1 whole, and I don't think these dingdongs really understood the ramifications of infinite repetition so they just let this shit slide.

>> No.9397813

But the sum exists, it is convergent, and basic grade 10 textbook will tell you how to sum geometric series like this. 0.9... is defined as the given sum, which when evaluated is equal to 1. So we agree?

Using stuff like 0.3...*4 = 1.2.... is clearly incorrect, rather it should be computed as the sum of 0.3...*4 = $\frac{4*3}{10^n}$ which is 4/3

>> No.9397815


>> No.9397817

If [math]0.\bar{9}[/math] converges to 1 in the same exact way an infinitesimal concept like [math]0.\bar{0}1[/math] converges to zero, we are only accepting that [math]0.\bar{9}[/math] is a hyperreal and still not naturally occuring in the similiar scope as the infinitesimal.

>> No.9397820

No, nowhere do hyperreals follow from what has been said. We are accepting that 0.9... is a notation for the sum, nothing more.

>> No.9397822

If infinite is real than it's possible Earth could be flat. Like an infinite plane with antarctica being a barrier to unknown lands. What do you guys think?

>> No.9397825


Obviously you're retarded. It isn't saying that those things are the exact same thing and a person can only believe one of those 3 things. It's saying they have similar belief systems and outlooks towards the subject it is describing.

>> No.9397828


Its analogous with respect to the belief of the existence of infinity/infinite sets. It has nothing to do with you belief in god, its just a tool the writer used to explain the different stances on infinities. You see, many people are familiar with religion, by making a comparison with something familiar it helps people learn unfamiliar concepts.

Platonists believe infinity exists
>Religious people believe god exists

Finitists believe infinity doesnt exist
>Atheists believe god doesn’t exist

Formalists dont know and dont care whether or not infinity exists
>Agnostics dont know and... you get the fucking point

The fact that i had to explain this to you means you need to leave this board.

Seems closer to your IQ. Try there.

>> No.9397861

*drops mic*

>> No.9397875

counting isn't comprehending the quantity 100, you dumb fucks

>> No.9397916
File: 207 KB, 692x960, 1510723646424.jpg [View same] [iqdb] [saucenao] [google] [report]

What is this convergance bullshit we aren't rounding this isnt fuckin 5th grade.

[math]0.\bar{9}[/math] doesn't converge to 1, it converges to even more 9's. The fact 9 is a maximal integer is completely regardless to the fact [math]\bar{N}[/math] is not related to [math]N[/math]
if [math]\sum_{n=2}^{\infty} 0.9 \stackrel{+}{=} \frac{9}{10^{n}} = 0.\bar{9}[/math]
then [math]\sum_{n=2}^{\infty} 0.1 \stackrel{-}{=} \frac{9}{10^{n}} = 0.\bar{0}1[/math]
We cleary have all the information we need from various proofs and tests and all we need to do is consolidate them instead of continuing to pretend [math]0.\bar{9} = 1[/math]

As much as infinity is actually an abstract concept that mathematicians pretend to fully understand, they should also understand that there are different number bases like hexidecimal and that [math]0.F _{16} = 0.9375_{10} > 0.9_{10}[/math] where that every step of
[math]\sum_{n=2}^{\infty} \big( 0.9_{10} \stackrel{+}{=} \frac{9}{10^{n}} \big) < \big( 0.F_{16} \stackrel{+}{=} \frac{F}{10^{n}} \big) [/math]
proves there are numbers greater than [math]0.\bar{9}[/math]
and dont be retarded with
>i-if you mark on a number line every 9th, you'll eventually run out of room and just mark 1.0
cause if you try to do the same with [math]0.\bar{1}[/math] you'll eventually make it to 2.0 of you're that retarded, or dumb enough to say [math]0.\bar{1} = 0.12[/math]
like damn, fuck. 9 is not a special number that gets to play by different rules than all the other numbers.

>> No.9397925

Actually, I haven't seen anything stating 0.9¯ = 2

Do you really think that is how this stuff works?

Technically 0.9¯ is only approachable from infinite sums. There is no "other" knowing of it, except from the blatant assumption that it is different.

I mean, if you want to write it out to prove what you are saying is true, then we can do it that way.

>> No.9397947

Antisemitism is disgusting.

>> No.9397957
File: 7 KB, 420x420, b36.png [View same] [iqdb] [saucenao] [google] [report]

[math]\frac{JewsKilledJesus}{JesusWasSemitic} \approx JewsAreAntisemites[/math]

>> No.9397960
File: 103 KB, 1920x1080, 1488294775841.jpg [View same] [iqdb] [saucenao] [google] [report]

>> No.9397961

Jesus was a white man you fucking SJW.

>> No.9397974

>around the 80-90 range

your IQ has very little to do with this

>> No.9397980

[math] \displaystyle
1 = \left (\frac{15}{16} + \frac{1}{16} \right )
&= \text{0x0.F} + \frac{1}{16} \\
= \text{0x0.F} + \left ( \frac{15}{256} + \frac{1}{256} \right )
&= \text{0x0.FF} + \frac{1}{256}\\
= \text{0x0.FF} + \left ( \frac{15}{4096} + \frac{1}{4096} \right )
&= \text{0x0.FFF} + \frac{1}{4096} \\
= \text{0x0.FFF} +\left ( \frac{15}{65536} + \frac{1}{65536} \right )
&= \text{0x0.FFFF} + \frac{1}{65536} \\
\\ \displaystyle
\Rightarrow \text{0x}0.\overline{\text{F}} = 1

>> No.9397984

Unfalsifiable as in there would be no way to show it was false if it actually was. No shit you can't show it to be false if it's true.

>> No.9397997

literal retardation. No, it doesnt equal 1, ot clearly equals solely [math]0.\bar{F}[/math]

fuck it, have fun with this instead

[math]\sum_{\stackrel{n=1}{k=10+n}}^{\infty} \big( \stackrel{+}{=} \frac{9}{10^{n}} \big)_{10} < \big( \stackrel{+}{=} \frac{k-1}{10^{n}} \big)_{k} [/math]

>> No.9398000

please type the line that doesn't equal 1

>> No.9398008

>all concepts of mathematics aren't "real", aren't present in any form in our universe if not in our imagination; there's nothing special about the axiom of infinity on this regard

>a lot of math can be used to model realit, as physicists do; but that doesn't mean that math is essencially ral or anything, what happens is that those models capture partially (often enough) of the structure of our universe so they serve as a trustworthy tool for predictons and simulations

>there's no empirical confirmation of anything in our universe that is infinite in any kind of quantity; finitists seem right when they say that infinite isn't real (i.e., in our actual physical universe)

>mathematicians don't give (or shouldn't) a shit about math not being actually something existing on our universe; modeling is enough for the applied and a bunch of physicists, and most the pure ones just enjoy playing in ZFC

>> No.9398014
File: 124 KB, 600x570, 060.png [View same] [iqdb] [saucenao] [google] [report]

The last line.

>> No.9398017

>the implication
so, every one before that equals 1 ?

>> No.9398019

>implying thats what you wrote
every line before that is some F's after 0.F

like i said, fuck it solve
[math]\sum_{\stackrel{n=1}{k=10+n}}^{\infty} \big( \stackrel{+}{=} \frac{9}{10^{n}} \big)_{10} < \big( \stackrel{+}{=} \frac{k-1}{10^{n}} \big)_{k} [/math]

>> No.9398022 [DELETED] 

[math]\bar{\infty}_{\infty} = 1[/math]

>> No.9398024

so, every one equals 1 ?
Nothing hand wavy about it, punch the line of your choice in your favorite calculator and come back when you get something that isn't 1

>> No.9398025

[math]0.\bar{\infty}_{\infty} = 1[/math]

>> No.9398026
File: 9 KB, 211x239, 1513971000563.png [View same] [iqdb] [saucenao] [google] [report]

criminally retarded

>> No.9398029

not an argument

>> No.9398030
File: 3 KB, 280x272, cGIay9e.png [View same] [iqdb] [saucenao] [google] [report]


>> No.9398031


>> No.9398032

Comprehending doesn't mean visualizing instantaneously you dumb fuck.

>> No.9398036

I didn't say it's saying that those things are the exact same thing, you fucking clown. I'm (correctly) saying the analogy is retarded.

>> No.9398042

>What is this convergance bullshit

bet you failed Calc I you filthy peasant.

>> No.9398047

So for any X, you claim that people who accept/reject X are analogous to religious people/atheists? Can you really not see why that analogy is retarded, you subhuman brainlet?

>> No.9398050

A real number is an element of a complete ordered field. It's that simple.

>> No.9398051
File: 139 KB, 971x565, 1514403883630.jpg [View same] [iqdb] [saucenao] [google] [report]

Read the whole post

>> No.9398053

Do you dispute this basic fact? Yes or no?

>> No.9398064

He won't answer.
At this point he either calls you an idiot using some lame meme image, or he moves goalposts via a whataboutism.

>> No.9398085

this is how you can tell the math you've learned is worthless because it's wrong.

>> No.9398094
File: 8 KB, 363x364, 1514061519880.png [View same] [iqdb] [saucenao] [google] [report]

kek wrong format

[math]\sum_{\stackrel{n=1}{k=10+n}}^{\stackrel{n\rightarrow\infty}{k\rightarrow\infty}} \bigg( \big( \frac{9}{10}_{10} \stackrel{+}{=} \frac{9}{10^{n}} \big)_{10} < \Big(\sum_{g=1}^{g\rightarrow\infty} \big( \frac{k-1}{10}_{k}\stackrel{+}{=} \frac{k-1}{10^{g}} \big)_{k} \Big) \bigg) [/math]

>> No.9398099
File: 42 KB, 562x437, hahaha.jpg [View same] [iqdb] [saucenao] [google] [report]

Of course it diverges, wtf is the 1/10 doing in the sum?
You get inf * 1/10 - 1 = inf -1 = inf

>> No.9398118

[math]\frac{1}{10}-\frac{9}{10^n} \neq \frac{9}{10^n}[/math] you irredeemable tool.

>> No.9398122
File: 142 KB, 617x347, 1509768568403.png [View same] [iqdb] [saucenao] [google] [report]

>wolfram can't even evaluate it
higher math is literally brainletism masquerading as intelligencw. You give these boogrbodies wolfram and haskell and suddenly they feel right at home despite those things being explicitly programmed and designed to return answers within bounds. Fuck may as well just max out all your points in mastering minesweeper.

>> No.9398123

The literal fuck

>> No.9398126
File: 30 KB, 481x425, 1514070409979.jpg [View same] [iqdb] [saucenao] [google] [report]



>> No.9398128

lmao wtf are you trying to do

>> No.9398129

What's your point, fool?

>> No.9398165

infinity exists nowhere in nature or the universe.

>> No.9398175

I bet the jews did this

>> No.9398178

Jesus looked Lebanese.

>> No.9398180
File: 2.67 MB, 400x225, 1454405823973.gif [View same] [iqdb] [saucenao] [google] [report]

>more terms
>show points
>says it reaches 1.0 @ 7
>requery n=1 to 7
>requery n=1 to 20
>requery n=1 to 56
>requery n=1 to 57
>[math]\frac{999999999999999999999999999999999999999999999999999999999}{1000000000000000000000000000000000000000000000000000000000} = 1.0[/math]
ye ok sure.

>> No.9398181

finitism = Republican/Conservative
infinitism = Democrat/Socialist

>> No.9398192

57 digits of accuracy is neatly octodecillion or 1 with 57 zeroes after it. Wolfram is cutting corners

>> No.9398193


>>9398064 still applies

>> No.9398197
File: 16 KB, 498x467, 1512340128839.png [View same] [iqdb] [saucenao] [google] [report]



>> No.9398201

ooooooooh, another lame meme
the puppy shat on the carpet again

>> No.9398204

It also initially reached it at 7 decimals since that is the accuracy of a [math]float[/math] in computers. To get 57 decimals would be a [math]long long long double[/math], so in any case even though wolfram can work with big numbers, there is still a definite upper limit, and of course the simulation of infinite limits is merely face value.

>> No.9398205

It's hilarious, can't tell which is worse, his latex or his "math"

>> No.9398207
File: 60 KB, 1024x558, 1509533757591m.jpg [View same] [iqdb] [saucenao] [google] [report]

>ywn be this psychotically booty blasted
Keep crying

>> No.9398210



>> No.9398213

Of course its face value. Doing infinite work would require infinite time even with a computer that can do trillions of calculations per second. Math majors without computer science knowledge are like an art major without limbs.

>> No.9398224

[math]\sum_{n=1}^{\infty} \frac{9}{10^n} = 0.\bar{9}[/math]
Sorry pal but thems the breaks. you can cut it off at some arbitrary point like the 57th digit and round as wolfram does, but you're not really going to infinity then are ya.

>> No.9398229


>> No.9398238

It seems to have arbitrary precision but with some extra rules. It likes turning repeating 0.9's into 1 after it's reached some kind of limit of 9's, so depending on how you're trying to get the answer it will take fewer or greater steps to reach that limit. Here for [math]\sum_{n=1}^{\infty} \frac{1}{2^n} it takes 191 steps to reach a decimal accuracy that fills its limit registers with 9's to figure it wants to show 1.0, but if you click on more digits the result will change back to a 0.9999999 number so even here this show and hide more digits button bares computational accuracy on the answer even already bouunded by the rule's its trying to abide by.

>> No.9398244

[math] \displaystyle
\sum_{n=2}^{ \infty}\left ( \frac{1}{10} - \frac{1}{9^{n}} \right ) \\
= \sum_{n=1}^{ \infty}\left ( \frac{1}{10} - \frac{1}{9^{n}} \right ) - \left (\frac{1}{10} - \frac{1}{9} \right ) \\
= \infty -1 -1/10 + 1/9 = \infty

>> No.9398246
File: 147 KB, 1920x1080, 1487295147773.jpg [View same] [iqdb] [saucenao] [google] [report]

Only maths worth doing.

>> No.9398273
File: 195 KB, 1650x1050, njw.png [View same] [iqdb] [saucenao] [google] [report]

See the thing about using real numbers is that they work. Physics works, biology works, space stations work and the computers that you use work, to allow to post dumb shit about how real numbers don't work.

If you guys want to say that real numbers don't exist and there are no numbers bigger than 100, fine. But early on people realized there is use in defining things like "reals, convergence, imaginaries" because it allows to do stuff that we couldn't without them like calculus which is used everywhere today. And this led to what are known as geometric series, as in, $\sum {\frac{9}{10^n}}$, which can be evaluated with this new, interesting, mathematical framework (outside of just naturals) to 1. As a shorthand we sometimes use 0.999... to denote this sum.

Sometimes people who don't understand the more advanced math system think that 0.999... is like a process of adding on the digit 9 to the decimal number 0.9 and can never be really completed. This leads them to the incorrect conclusion that 0.999... isn't 1.

I recommend that such people either take a basic calculus course in highschool or take a basic real analysis course in university.

>> No.9398277

Lol no
[math]\sum_{\stackrel{n=1}{k=1}}^{\infty}\frac{k}{k+1^n}[/math] has been shown to simply just equal [math]0.\bar{9}[/math].

you only get one with lazy evaluation.

>> No.9398284

>I recommend that ... take ... highschool ... university.

Good luck with that, they can't even take a shower.

>> No.9398285

go back to masturbating at bus stations

>> No.9398287
File: 114 KB, 256x256, otfr7LYS.png [View same] [iqdb] [saucenao] [google] [report]

...are you projecting or do you know people who've done this?

>> No.9398288


What is [math] 0.\overline{9}^{2} [/math]?

>> No.9398293

we've all seen your videos anon

your condom is on all wrong too so you can't handle latex there either

>> No.9398300
File: 179 KB, 645x729, 1514387854434.png [View same] [iqdb] [saucenao] [google] [report]


>> No.9398303

>"believing" religion to work, when in reality religion produces working results regardless if you "believe" while atheism aka lazy brainletism doesn't give enough shit to actually figure anything out towards the effect of either contradicting believe or supporting it.

>> No.9398304

yup, that's how you look on the videos just before the climax

no thanks for reminding me

>> No.9398309

if you meant [math](0.\bar{8}+0.\bar{1})^2[/math] the answer is 1. Its undefined for [math]0.\bar{9}[/math] but since you like to nig around you were meaning to ask [math]1^2[/math] which, [math]0.\bar{8} + 0.\bar{1}[/math] neatly sums.

>> No.9398311
File: 81 KB, 315x360, 1511761761718.jpg [View same] [iqdb] [saucenao] [google] [report]


>> No.9398320

lame meme time again

>> No.9398333

Does pointing out that you constantly et shit on make it easier to deal with? You'd think simply not responding would be the more tactical approach, no?

>> No.9398341

>simply not responding would be the more tactical approach, no?
how about taking your own advise

>> No.9398699
File: 5 KB, 250x174, q5OL30E.jpg [View same] [iqdb] [saucenao] [google] [report]

I couldn't care less if I make a fool out of you though. Your humiliation is very low on my list of priorities. You are simply getting ruined as a byproduct of your own replies. I come here to talk about math and you come here to cry about tumblr feelings so it's not like there isn't evidence only one of us needs to fuck off.

>> No.9398712
File: 19 KB, 333x500, snooty.jpg [View same] [iqdb] [saucenao] [google] [report]

>the abstract way which he writes a sum of infinite values is so much more unrefined than the abstract way I write a sum of infinite values, charles. I mean, really, who does he think he is trying to instantiate multiple variables? I'd wager he doesn't even know math at all!

>> No.9398718

>believes the existence of imaginary friends
>doesn't believe infinite sets exist

>> No.9398723

Id you're the same tard who was talkin about jerkin off in a bus station, the only imaginary friend you've got is straight up lying to you about how to respond to or interpret conversation. No joke, you are fairly mentally damaged right now.

>> No.9398729

No. Kys.

>> No.9398745

Not the same guy. He's probably right if you disagree with him, though.

>> No.9398761 [DELETED] 

[math]A < B[/math]
[math]0.\bar{9} \neq 1[/math]

Evaluate and compare a partial sum for any equal n without using wolfram alpha or a computer lacking true arbitrary precision.

>> No.9398762

Please, put some effort in your bait

>> No.9398770
File: 255 KB, 726x544, 1509576930017.jpg [View same] [iqdb] [saucenao] [google] [report]

Thats really retarded logic. Either he made no claims and therefore isnt right about anything and is only senselessly attacking, or his first position was disagree with me which then makes me right.
And i doubt anyone would defend him so you can't really imply you aren't him, you fuckin' wierdo.

>> No.9398775 [DELETED] 



[math]A < B[/math]
[math]0.\bar{9} \neq 1[/math]

Evaluate and compare the partial sums for any equal n without using wolfram alpha or a computer lacking true arbitrary precision.

>> No.9398779

Not him, but limits have nothing to do with infinity

>> No.9398782


[math]A < B[/math]
[math]0.\bar{9} \neq 1[/math]

Evaluate and compare the partial sums for any equal n without using wolfram alpha or a computer lacking true arbitrary precision.

If the latex fucks up again i dont care.

>> No.9398786

cry me a river snowflake

>> No.9398795

oh look you missed a bus again

>> No.9398798

>or his first position was disagree with me which then makes me right.
>Thats really retarded logic
Isn't it already time for your daily prayers to wild burger?

>> No.9398824

if we work within the shortcomings of wolfram and substitute [math]\infty[/math] with 64, it will give us a fraction and only try to approximate it to 1 rather than outright equate to 1, even though the fractions have entirely different strings of numbers.
Change 64 to 65 and wolfram cant solve it.

>> No.9398840

Shit stale meme only spergs are still too dumb to post

>> No.9398883

You can imagine numbers as being infinite something, and infinite nothing (zero) merging together and separating equally and infinitely.

Therefore all numbers are ultimately infinite, but to us they are finite.

>> No.9398941
File: 2 KB, 148x44, MSP3119iga7e0dbabaiba00005iihh58d88d3h71f.gif [View same] [iqdb] [saucenao] [google] [report]

realy makes u think

>> No.9398943
File: 6 KB, 244x206, j23g90924gj02k4.png [View same] [iqdb] [saucenao] [google] [report]

>tfw they don't know what a limit is

>> No.9398957
File: 34 KB, 601x508, e7db9e4e33592de521b23e955084488e.jpg [View same] [iqdb] [saucenao] [google] [report]

>if i pretend he's wrong then he will be wrong

>> No.9398981
File: 140 KB, 1278x990, 2017-12-28 11.07.29.jpg [View same] [iqdb] [saucenao] [google] [report]

rly maks u think

>> No.9399000
File: 20 KB, 306x306, 79e0f76f22f429dc6a79ebbe8f3b484d.jpg [View same] [iqdb] [saucenao] [google] [report]

>[math]\frac{7}{8} = 1[/math]
>this is what mathematicians actually believe

>> No.9399012
File: 38 KB, 413x395, 1507881703152.jpg [View same] [iqdb] [saucenao] [google] [report]

>graph literally and unironically shows divergence
>"it converges"

>> No.9399019
File: 136 KB, 412x304, Screen Shot 2017-12-28 at 11.29.34 AM.png [View same] [iqdb] [saucenao] [google] [report]


>> No.9399094

heres the arbitrary precision control command for wolfram
N[ value, digits of precision]
[math]\sum_{n=1}^{3} N\big[\big(\frac{9}{10^{n}}\big), 2\big] [/math]
proves [math]\big( \frac{9}{10} + \frac{9}{100} + \frac{9}{1000} \big) = 1[/math]

there is still a limiter working in the background but it can be used to extend the limiter beyond what it does without the command

>> No.9399148
File: 5 KB, 308x164, laugh.jpg [View same] [iqdb] [saucenao] [google] [report]

>Sets precision = 2
>Tries to use this as an argument

>> No.9399162

It was merely to demonstrate where N<n, you get 1.0 as a result. So receiving 1.0 as a result under any circumstance, the background precision will be less than the amount of digits, the equivalent of concatenating. The arguement is wolfram cannot be used to evaluate infinite sums because it's going to end up using its own precision override if set to infinite precision.

>> No.9399204

Setting the precision to infinite actually has deleterious results compared to not using N
N[sum[9/(10^n), {n, 1, 7}], infinite] = 1
sum[9/(10^n), {n, 1, 7}] = 0.9999999
unless you plug in big numbers intentionally for precision then its only useful for minimal precision, not maximal

>> No.9399223

I think you are right.

>> No.9399335


This question was directed at those folks who think [math] 0.\overline{9} [/math] is just an infinitely long string of nines after the decimal point.

In their view of that number, if they square it there is never a terminating 1 and therefor that number squared is equal to itself.

>> No.9399464

Is this how wolfram gets away with trying to equate 0.9... to 1?
this summation towards 0.888... randomly just puts a 9 as the last digit even though the last operation to get that last digit is still the same operation that got all the preceeding 8's. It's like wolfram is not-so-sneakily adding an infinitisemal of rounding up the last digit. It does this for 5,6,7,8 and 9, but not for 1,2,3 or 4, and since 5 is usually the cutoff point for rounding up then its pretty clear what is going on here.

>> No.9399473

Jesus Christ people.
[math]\sum_{k=1}^\infty \frac{9}{10^k} = \lim_{n \rightarrow \infty} \left( \sum_{k=1}^n \frac{9}{10^k} \right ) = \lim_{n \rightarrow \infty} \left(1 - \frac{1}{10^n}\right) = \lim_{n \rightarrow \infty} 1 - \lim_{n \rightarrow \infty} \frac{1}{10^n} = 1 - \lim_{n \rightarrow \infty} \frac{1}{10^n} = 1 - 0 = 1[/math]

That's all there is to it. Are you going to dispute the definition of a limit as well?

>> No.9399491

b-but 1/3 =/= 0.333...

>> No.9399554

it does though

>> No.9399561

ah, failed calculus i see.

>> No.9399570

Question m8, what do you imagine you're implying when you claim [math]\sum_{n=1}^{\infty} \frac{9}{10^{n}} = 1[\math] ?

>> No.9399592
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>> No.9399608



You know infinite sums are proved and not assumed, right?

You can prove the result of the sum through induction in terms of n { f(n) }. Once you have f(n), then in this case you can find the limit using epsilon-delta definition. This is another proof.

>> No.9399615
File: 5 KB, 224x100, 843.jpg [View same] [iqdb] [saucenao] [google] [report]

Seems pretty airtight to me.

>> No.9399672
File: 39 KB, 1080x590, Its literally proveable 0.9••• cant equal 1.0.png [View same] [iqdb] [saucenao] [google] [report]


my favorite part about [math]0.\bar{9} = 1[/math] is how you have to literally pretend there are no greater numbers than [math]0.\bar{9}[/math], if not be just satanically retarded.

>> No.9399775
File: 8 KB, 499x306, 824.png [View same] [iqdb] [saucenao] [google] [report]

You've proven wolfram alpha doesn't handle this question consistently, which is a different thing from proving 0.FFF... is greater than 0.999...
It looks to me like every additional iteration of the product of 9*10^-n and E*F^-n returns a number closer to 1.
27 / 32 = 0.84375
4347 / 5120 = 0.8490234375
695547 / 819200 = 0.84905639648
111287547 / 131072000 = 0.84905660247
17806007547 / 20971520000 = 0.84905660376
Can you tell me at what specific iteration this pattern will stop? When do the iterations of products suddenly stop getting closer to 1? After 1,000 iterations? 1,000,000 iterations?

>> No.9399792

they never get close enough to 1 to be considered 1.

I set the limit to 9999 here cause it wont evaluate with infinity. I test j=k at every iteration and it returns false for every iteration, that the value of J at n is not the value of K at n. I imagine setting it to infinity is breaking it because it's trying to say [math]\infty false + 1 true[/math], or just cause its a boolean evaluation problem rather than a numbers problem where fudging and rounding can surpass infinity so it would instead attempt to perform actual work on each n which it's totally not going to do given it would be infinite work and take infinite time.

>> No.9399808

Why is it so strange to trust that [math]0.\overline{9} \neq 1[/math]?

[math]0.\overline{1}[/math] doesn't equal anything but itself.
[math]0.\overline{2}[/math] doesn't equal anything but itself.
[math]0.\overline{3}[/math] doesn't equal anything but itself.
[math]0.\overline{4}[/math] doesn't equal anything but itself.
[math]0.\overline{5}[/math] doesn't equal anything but itself.
[math]0.\overline{6}[/math] doesn't equal anything but itself.
[math]0.\overline{7}[/math] doesn't equal anything but itself.
[math]0.\overline{8}[/math] doesn't equal anything but itself.
but [0.\overline{9}[/math] should equal itself and 1?
8 out of 9 numbers can't be wrong, there is definitely some kind of self-evident proof here.

>> No.9399821

So let's say 0.FFF... is greater than 0.999... for the sake of argument.
Then 16/17 + 16/17^2 + 16/17^-3... would be greater than 0.FFF...
And 17/18 + 17/18^2 + 17/18^-3... would be greater than 16/17 + 16/17^2 + 16/17^-3...
Then (ω-1)/ω + (ω-1)/ω^2 + (ω-1)/ω^3... would be greater than all preceding finite denominator fraction sums.
What would be the difference between 1 and (ω-1)/ω + (ω-1)/ω^2 + (ω-1)/ω^3... ?

>> No.9399823

proof by self-evidence is my favorite kind of mathematical proof

>> No.9399830

These numbers actually do equal something else naturally though, and that is as a fraction over 9.

It makes sense that [math]0.\bar{9}[/math] wouldn't exist here cause while [math]\frac{8}{9} = 0.\bar{8}, \frac{9}{9} =
\frac{3}{3} = \frac{1}{1} [/math] simply just equals 1.

>> No.9399836

yeah but 0.9... = 1

>> No.9399840

The sum of infinitesimals would be greater? how so

>> No.9399846
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>> No.9399853

I don't believe it would.
I explicitly said *for the sake of argument* it would be greater following the idea that infinite sums of increasingly larger numerators and denominators would somehow be progressively larger values distinct from 1.
e.g. anon's alleged assertion of 15/16 + 15/16^2 + 15/16^-3... being greater than 9/10 + 9/10^2 + 9/10^-3...

>> No.9399857

Also they're not infinitesimals (1/infinity would be an infinitesimal), they're the sum of infinity minus one over infinity with the denominator raised by increasingly large negative exponents i.e. the logical conclusion to anon's distinction between 15/16 + 15/16^2 + 15/16^-3... and 9/10 + 9/10^2 + 9/10^-3...

>> No.9399863
File: 2 KB, 500x343, 6FHwa.gif [View same] [iqdb] [saucenao] [google] [report]

Lmao no?
[math]\frac{1}{11} + \frac{10}{11} = \frac{11}{11} = \frac{1}{1} = 1[/math]
I'm not sure how you don't see that [math]0.\bar{9}[/math] is the objectively wrong answer.

Maybe your problem is that you're not calculating with intermantissa, or rather not calculating with the understanding that a repeating number [math]\bar{N}[/math] does not abide by arithmetic in the same way as normal number [math]N[/math]; not understanding that [math]\bar{N} \neq N[/math]

>> No.9399865

This isn't an easy, settled issue. Maybe the term infinity in math is really several terms, some of which are invalid concepts.

>> No.9399870

What is the decimal notation for 1/11?
What is the decimal notation for 10/11?

>> No.9399872

I dunno then, it would probably just sum to [math]\bar{ω}[/math] just the same as every number before it.

>> No.9399873

It's an easy, settled issue for actual mathematicians.
It's a recurring troll topic for 4chan.
There's a difference between these two contexts.

>> No.9399876

What's greater than 0.ω¯ and less than 1?

>> No.9399881

People have been wrong in the past. It is highly probable they will be wrong in the future. I always doubt everything and try to figure it out on my own. If you don't, you are basically just regurgitating knowledge you mostly don't even have. You are like that monkey in Searle's Chinese Room.

>> No.9399887

there are such things as stupid questions

>> No.9399893

Yes, but I really doubt there won't be any new fundemental work on infinity, or that all current work on infinity will stand forever.

>> No.9399909

The Chinese Room is a shit thought experiment to begin with, it just exploits the understandable sense of difference you'd have when comparing a normal brain going through 100 billion operations per second with a room that would need to be the size of a galaxy and have millions of years time available to answer 1 simple question.
When you warp a situation's physical size and duration to that extreme a degree of course it will seem intuitively unequivalent. Churchland's counterargument addresses this point:
>Consider a dark room containing a man holding a bar magnet or charged object. If the man pumps the magnet up and down, then, according to Maxwell's theory of artificial luminance (AL), it will initiate a spreading circle of electromagnetic waves and will thus be luminous. But as all of us who have toyed with magnets or charged balls well know, their forces (or any other forces for that matter), even when set in motion produce no luminance at all. It is inconceivable that you might constitute real luminance just by moving forces around!" The problem is that he would have to wave the magnet up and down something like 450 trillion times per second in order to see anything.
Making a vague distinction between "understanding" vs. "just producing outputs" is ironically itself a lazy and not very thoughtful way of conceptualizing what understanding is. If you actually try to approach in specifics how understanding works you will end up breaking it apart into smaller non-understanding components of input and output.

>> No.9399915

Maybe the light produced is of such low frequency it's undetectable to the human eye, and/or it's too low amplitude

>> No.9399921

No, it is a great metaphor for what you apparently think math is.
Instruction set:
>check wikipedia
>look for any current controversies
>look for words like "consensus"
>repeat "knowledge" just gained from wikipedia to others without citing sources

>> No.9399927

Thank for reminding me to continue developing the document for intermantissa and i explained it in another thread, 0 and 9 would retain overline representation but referred to as inter-zero and inter-nine adopting the same inter-prefix as the actual inter-numbers.

0 and 9 actually occupy the same singular spot on the intermantissa line, which i realize the first document does not show. This visual attribution would encourage students counting on the line to treat 9 in a sensible way that leads to the correct result for multiplication and non-zero addition in the least, but looking at this specific problem and using addition requires some continued developmental effort.
From right to left, evaluating inter-nine plus inter-zero would want to turn into 10 as the upper dominant of the two
0.09090[9]... = 10, carry the one

0.9090[9] evaluates 10, carry the 1

0.090[9] evaluates 10, carry the 1

counting from 0 to 9 on the IM line counts to "0" and considers that a loop, or otherwise knowing the 9th symbol on the intermantissa line is "0", where the roll over acts as the same as counting past 9 on the normal number line to get "10", except with inter-numbers there are only 8 numbers, so passing inter-8 rolls up to 0.

>> No.9399934

Did you want a source for Churchland's argument? Here:
>low frequency
>too low amplitude
That's the point. When you warp the scale of processes you get results which don't seem the same, which is why it's not a good argument to warp the scale of processes and then point to how they seem different.

>> No.9399939

Im not sure that question has relevance.
Like asking what is the next biggest number after [math]0.\bar{1}[/math] is. If you're providing it as an argument against the specific proof that a larger base will always have a larger number between the previous base's maximal repeating decimal and 1, you still haven't reached base infinity, and base [math]0.\bar{\infty}_{base\infty} = 1[/math] looks slightly too tarded for me to trust from multiple angles.

>> No.9400079
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fuck just found the fatal flaw with intermantissa

[math]0.\bar{905} + 0.\bar{286}[/math]
with the fuckin intergarbafe countable sensibility gives me 1.a0b when it should be 1.a9b, but since i dont treat [math]\bar{9}[/math] like a normal number i cant sum 9 even under arbitrary circumstances mother fuuuuuuuuuuuucker.
fuck it fails basic addition and ita like only useful for multiplication.
i still don't think [math]0.\bar{9}[/math] exists as a normal number without crafting it from an infinite sum

>> No.9400086

but all numbers are infinite sums

>> No.9400272

>8 out of 9 numbers can't be wrong

>> No.9400279

you really need the "/s" ?

>> No.9400636

If x = 0.FFF... - 0.999...
What's x?
I'm pretty sure x has to be 0. Otherwise you run into the problem of finding a nonzero number x which when added 0.999... gets you 0.FFF...
It can't be 0.666... because 0.999... + 0.666... is clearly greater than 1, and 0.FFF... is clearly not greater than 1.

>> No.9400747
File: 1.89 MB, 400x400, Even Aqua-sama thinks you're pathetic.gif [View same] [iqdb] [saucenao] [google] [report]

It's like an abstract form of autism

>> No.9400769


Yeah his argument is of a rather invalid.

A. 0.F_{16} > 0.9_{10}: True
B. 0.FF_{16} > 0.99_{10}: True
C. 0.FFF_{16} > 0.999_{10}: True
D. Let n be the total number of F's following after the hexadecimal point and m be the total number of 9's following after the decimal point, if n=m, then the hexadecimal number must be larger than the decimal number. : again true.
E. n=∞, m=∞ \implies n=m \implies 0.\overline{F} > 0.\overline{9} : false and does not follow.
For any number, infinity is of a greater magnitude than that number. n can not be defined as infinity. The same applies to m.

>> No.9400770


Yeah his argument is of a rather invalid premise.
A. 0.F_{16} > 0.9_{10}: True
B. 0.FF_{16} > 0.99_{10}: True
C. 0.FFF_{16} > 0.999_{10}: True
D. Let n be the total number of F's following after the hexadecimal point and m be the total number of 9's following after the decimal point, if n=m, then the hexadecimal number must be larger than the decimal number. : again true.
E. n=∞, m=∞ \implies n=m \implies 0.\overline{F} > 0.\overline{9} : false and does not follow.
For any number, infinity is of a greater magnitude than that number. n can not be defined as infinity. The same applies to m.

>> No.9402491

bruh I think you missed some [math] tags.

>> No.9402651
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>> No.9402655
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>constructing real numbers
that's freshman stuff assberger

>> No.9402679


>> No.9403196

field ops
what did he mean by this

>> No.9403256

What natural basis is there for assuming the existence of finite numbers though? A priori I don't see how we can count without some sizable number of abstractions. I'm sure experts in this area have done it properly, but spitting out some bs on 4chan it seems like you need some sort of category (the concept of the thing), a function mapping every subset of reality to {is the thing, isn't the thing}, and then youre just looking at properties of abstract sets anyway.

>> No.9403262

yeah, in my undergrad rudin course we did 3 different constructions in the first few weeks...
(dedekind cuts, cauchy sequences, construction based on arithmetic on infinite decimals). not sure what's going on in australia

>> No.9403267

Peoples inability to understand their mortality and uselesness makes them bully mathematical concept since the usage of while(true) is discouradged.

>> No.9403270

When using nondecimal numbers you gotta tell us base retard.

>> No.9403290

(1+1+1)/3 = 1

0.33333 per != 1/3
1/3 to dec returns 0.33333 per

what is so imposible to understand about that?

only if we tought a little bit we would realize

0.3 per * 3 = 1

numbers ccan't have infinite ciphers, just maximum of calculator can fit, in countable mathematics,

in accountable mathematics, we can use infinite numbers, which, being past the point finding symbol for it is just one cypther, which means pass the limit. retard.

>> No.9403292

There is no calculation whicch retruns 0.999 periodic, which renders your arguments pointless.

>> No.9403428


[math] \displaystyle
1 = \frac {3}{3} = 3 \cdot \frac {1}{3} = 3 \cdot 0. \bar{3} = 0. \bar{9}

>> No.9403698

1 - 0 = .999... = 1

>> No.9403722

Because the concept of infinity is doomed to failure from the get go.
Just because you cant count it doesn't mean its infinite.

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