/sci/ - Science & Math

>>11557356
Actually, you can divide 1 L in three only in base 9, of you define 1L as 9 mL. I used L but you could call this base 9 unit something else.
With regular base 10 L, if you do that, you will get 0,3 + 0,3 + 0,4 L. Now if pay extra attention you might push the 4 way back, and obtain 0,33333 + 0,33333 + 0,33334 for instant, but if you measure it with somethibg precise enough, you will find a 4 somewhere.
This stems from the fact base 10 unit system is ill suited for divisions by 3.
If an alien species has 9 appendices and a base 9 unit system, they would find no problem with this, but would struggle with dividing by 5 for instance.
A true intelligent species would be able to switch between bases at will using widely available computing power at their disposal, but I do not expect such thing from modern math enthousiasts (from top to bottom).

>>11557372
>Inb4 you can divide the last infinitesimal unit in 3 forever
No, at some point you would have to separate a single H2O (or any other liquid) in order to achieve the perfect equality of 3 + 3 + 3 (+ 1 to be divided in 3 again) which makes no physical sense.
Same goes for spatial units, unless you're a continuous space faggot in which case kys you fairy.

No one has been able to argue against these two proofs:

Via Cauchy sequences:

0.999... = (0.9, 0.99, 0.999,...) = lim as n-> inf of 1-1/10^n = 1

Via Dedekind cuts:

Assume to contradiction that x is a rational number such that

0.999... < x < 1

0.999... is greater than any finite string of 9s so for any natural number n

1-1/10^n < 0.999... < x < 1

1-x < 1/10^n

10^n < 1/(1-x)

n < log(1/(1-x))

Let n = ceiling(log(1/(1-x)))+1

ceiling(log(1/(1-x)))+1 < log(1/(1-x))

This is a contradiction, so x does not exist and 0.999... = 1.

>>11557403

if 0.999... = 1

then 0.9 = 0.8999...

0.999... = 0.9 + 0.0999...

0.9 = 0.8999...

0.999... = 0.8999... + 0.0999...

0.0.8999... + 0.0999... = 0.9998...

0.999... = 0.9998...

>>11557511
>0.0.8999...
nice try retard

>>11557514

Are you saying 0.9 != 0.8999...?

>>11557535
>>11557514

Nevermind, I see the typo.

Corrected:

>>11557403

if 0.999... = 1

then 0.9 = 0.8999...

0.999... = 0.9 + 0.0999...

0.9 = 0.8999...

0.999... = 0.8999... + 0.0999...

0.8999... + 0.0999... = 0.9998...

0.999... = 0.9998...

>>11557372
Your measuring device, regardless of the basis, has only a limited precision. Always. Let's say the basis is 10 and the precision is up to two decimal places. Then if your instrument shows 0.33, it means that in the glass is

33/100 litres + R litres

where the error R is, in absolute value, surely smaller than 1/1000. You can measure 0.33+0.33+0.33 no prob, it just means that the error terms add up to 0.001L.

If you take a measuring device which uses base 3 and 2 places, then you will probably measure 0.10 but you can't conclude that there's exactly 1/3L in the glass. You can only conclude that there's

1/3 litres + R litres

where the error R is surely smaller than 1/27 (because 27 = 3^3).

>>11557559
(cont)

The exact amount 1/3 L is characterized as follows:

If you take any measuring device which uses base 3, then no matter how precise it is, it will always show 0.1000...00.

The exact amount 0.333...L is characterized as follows:

If you take any measuring device which uses base 10, then no matter how precise it is, it will always show 0.333....3.

These statements are equivalent by an easy argument using long division. This is the meaning of the equation 1/3 = 0333...

>>11557372
>only in base 9
the tree exists only if I look at it from this angle...
hurrrr durrrr

>>11557539
>0.8999... + 0.0999... = 0.9998...
Incorrect. Learn how to add.

>>11557356
Some guy posted it in an earlier thread but.

if .999... = 1
then it's safe to assume that
.899.. = .999...

But does .899... = 1?


If the first rule were right numbers wouldn't exist at all

>>11557617

0.8999... + 0.0999... = 0.999...8

>>11557599
You're dishonest.
0,1000... = 0,1 just like 3 = 3,000... in regular base 10, or any base.
>>11557602
Retard

>>11557599
Your explanation seems flawed, because you're mixing real life margin of error in measurements with the limitations of representation of an abstract concept, which is Math.

The fact that we can't come to a conclusion about this issue proves Math, a virtual concept humans created, is flawed.

>>11557646

That was me, I revised the argument a bit here
>>11557647

When you add 0.8999... to 0.0999... you repeatedly carry the 1 over to the left which gives you and infinite number of 9's following by an 8, which you can represent with bar notation or by ellipses as 0.999...8

>>11557599
If you apply math to measure units in a discrete plane, 0 is an absence of unit, so 0,1000...000... makes no sense, infinitely repeating 0s are not written down.
So yes, 1/3 in base 9 = 0,1 full stop just like 1/5 in base 10 = 0,2 full stop.
To divide 1 unit in three perfectly equal lesser units you need a base to do so in the first place, because 1 is the smallest unit unless the scale is off and a smaller unit, of which 1 is comprised, exists. So you need a base, and that base is 9. There is no reason to reason to do so in base 10 and obtain the retarded 0,333... + error besides convention and the fact de have 10 digits. That's literally it.
>>11557650
Thank you, you get it.

>>11557403
Now do it via almost homomorphisms of the integers (see Eudoxus reals).

>>11557646
Retard. 0.899...=0.9, not 1.

>>11557686

>>11557647
>>11557658

>>11557658
>>11557686
I fucked that up ignore that

>>11557677
And we use base 10 because we have 10 fingers.
Mathfaggs clinging to 1= 3 X 1/3 = 0,333...X3 = 0,999... = 1 are literally ugga bugga apes unable to fathom the fact you can construct units with a base that does not use all of and only their 10 niggerfingers to count.

>>11557677
1/3 = 0,3 in base 9 not 0,1 sorry.

>>11557677
>To divide 1 unit in three perfectly equal lesser units you need a base to do so in the first place,
In the material world, you will never know if you managed to divide a unit into three equal lesser units. Only up to arbitrary precision. It's totally independent of the base. Don't tell me you're disputing this.
In mathematics, things get abstract, and 0.333... = 1/3 becomes simply a logical formula which happens to be true. There's no discussion here. Your only chance is to reject a part of mathematics for some personal reason.

1 - .999... = 0?

>>11557714
Nothing wrong with choosing to represent a number in base 10. Just because it's arbitrary doesn't mean it's incorrect.

>you can construct units with a base that does not use all of and only their 10 niggerfingers to count.
So according to you, what is 0,9999... in some other base besides 10?

For example,
0,333.... in base 10 = 0,4 in base 12.

0,999.... in base 10 = ? in base 12.

What replaces the question mark in the previous line?

>>11557735
>In the material world...
Our inability, for now, to measure perfectly well X or Y doesn't mean our maths shouldn't function as if we did.
But again, you're wrong, an atom is an irreductible unit, for instance. We could measure it.

>>11557700
I saw that argument too, it’s still shit. There’s no contradiction, you’ve only proven that 0.999...8=1, which is correct as can be seen from your line of reasoning.

>>11557762
0,333... is the wacky result of a ratio in a base that doesn't support that ratio, as in 1/3 in base 10.
0,999... is a constructed abstract concept that does not exist and that represents nothing.
All numbers are constructed and abstract, but they all derive from the first primary assumption / convention that 1 is a unit that exists and 0 is the absence of 1. All the other numbers are derived from 1, by one way or the other. You can't obtain 0,999... by any natural operation other than adding 0,9+0,09+0,009+... to Infinity which makes it a limit, a function, represented as 0,999... by convention. You cant take 1 and use it do obtain 0,999... You can't do 1 - 0,000...1. You can't divide it by a certain number either, etc..

>>11557792
>0,999... is a constructed abstract concept that does not exist and that represents nothing.
Well then, I suppose that frees us to choose something for it to represent.
I choose for 0,999... to represent the same quantity as 1.

>>11557762
0,333... =/= 0,4 in base 12, 1/3 does.
1/3 is a ratio, 0,333... is not a ratio, it's the representation of an approximation because that ratio can't be properly defined in base 10. You could hace used another convention that ..333... if you wanted.
0,999... represents no known ratio, in any base, so there is no need to express by this convention something that can never occurr in the material world and does not exist.
It confuses you because 0,999... unlike other concepts in maths, uses really common symbols, but it is an impossibility, it can't exist.

>>11557792
Consider base n.

In base n, 1/(n-1) is represented as 0,111...

We know that (n-1) * 1/(n-1) = 1.

And we know from arithmetic that (n-1) *1/(n-1) = 0,{n-1}{n-1}{n-1}... where each {n-1} represents a digit.

So in any base n, 0,{n-1}{n-1}{n-1}... = 1.

>>11557800
Feel free to do that, you can also say ° = 1 I don't care man. It's just not practically true, and even theoretically it makes no sense and can easily be debunked by deconstructing the base 10 convention of 10 fingered apes. It's a childish "fun" thought to have that 0,999...=1, it has no real implications, no real consequences in ANY field.

>>11557816
>0,333... =/= 0,4 in base 12

Read carefully, I never implied that
0,333... = 0,4 in base 12.

I said that
0,333... in base 10 = 0,4 in base 12.

>>11557763
>>11557763
>Our inability, for now, to measure perfectly well X or Y doesn't mean our maths shouldn't function as if we did.
But our math does function this way. This actually speaks in favor of infinite decimal expansions, not against. So what exactly is your problem with 0.333... ?
>But again, you're wrong, an atom is an irreductible unit, for instance. We could measure it.
Obviously we're talking about quantities which are modelled well by the continuum.

>>11557830
You're wrong on you second line. It does not equal 0,111...
Try your assumption with a n=9 or n=5 and find out.
Also use a paper + pen, because I doubt your calculator lets you switch bases like that.

>>11557856
In base 9:
1/8
= 1,0/8,0
= 0,1 R1 (8 goes into 9 once)
= 0,11 R1 (8 goes into 9 once)
= 0,111 R1 (8 goes into 9 once)
etc.

In base 5:
1/4
= 1,0/4,0
= 0,1 R1 (4 goes into 5 once)
= 0,11 R1 (4 goes into 5 once)
= 0,111 R1 (4 goes into 5 once)
etc.

>>11557844
There is no evidence for continuum, I personally think space is discrete.
Anyway it's another debate but I find It gay that math decided in favor of continuum theory, even moreso that even if true, continuum theory wouldn't impacto anything besides fields way below what we notice and use everyday. Discrete space makes practical sense for 99% of our activities yet our primary tool, maths, uses continuum as truth.

>>11557869
Now do base 2 :^)

>>11557403
>No one has been able to argue against these two proofs

Apart from all the times it was debunked, sure.

>>11557830
That's where you got me wrong. 0,111... is never a valid representation. You shouldn't use it for operations, use the ratio instead, or the approximation sign.
Anyway 1/n-1 can be resolved and expressed in non ratio form in base 2 only.

>>11557889
>>11557856
lol
In base 2:
1/1
= 1

>>11557878
It's not about discrete = true, continuous = wrong. It's about what's useful for the problem in hand. The water consists of a finite number of particles, no doubt, but fluid mechanics is still modeled by PDE. Why do you think this is?

>>11557910
So in base 2, 0,111...=1 :^) clown world indeed.
Very sound theorem anon.
>>11557830

>>11557925
Because the number of particles in a volume where fluid mechanics occur is so great that an approximation is enough to correctly predict stuff with a very small infinitesimal error. Again, an approximation working for all useful purposes is a whole different statement than "=".

>>11557936
Unironically yes

So I'm confused on the .999....=1 situation.

They say "There's no number between .9 repeating and 1, so they are equal". But then in probability you have the concept of "almost 0". Like if you select a random number from the set of all reals, what is the chance you'll get 4? Well it's not 0, it's almost 0. Isn't that Almost 0 the number inbetween .999... and 1?

>>11557647
>0.8(9)+0.0(9) = 0.(9)8
This is incorrect, it's just 0.(9). Look up the algorithm for addition from the left.

This is also irrelevant to what you're replying to. Show that 0.8999... + 0.0999... = 0.9998...

>>11557904
>all the times
>can't even name one

>>11557953
And you do realize that both PDE and infinite decimal expansions are parts of one theory which either works as a whole (including small annoying technical details like 0.999...=1), or doesn't work at all, right ?

>>11557962
You’re trying to apply a measure theoretic concept and *almost* use Erdös’s probabilistic method, but that’s not what this means.
0.999... = 1 is a simple consequence of the construction of the reals by completing the rationals either by classes of Cauchy sequences or by dedekind cuts.
Also this concept of “almost” doesn’t apply except maybe to infinitesimal numbers..but the reals are constructed in a way such that 0 is the *only* infinitesimal number. This is exactly the Archimedean property.

>>11557953
>infinitesimal error
Dude the only infinitesimal in the real field is 0 by construction, since it’s the Archimedean property that shows this. The only unmeasurable distance in the reals is something satisfied by a number b such that for every nonzero real r, b < r, and the basic Archimedean and order properties of the reals ensure you can always find a smaller nonzero b.

>>11557984
So what, if you're a statistician you get a special set of reals that don't have the properties of the regular reals?

>>11557984
It's all conventions all around man. All purely math-related conventions have 0,000... use in other fields so nobody cares. Otherwise a physics guy would have btfo this retardation at some point.

>>11557962
>But then in probability you have the concept of "almost 0".
No, in probability you have the concept of almost impossible, which is just p=0.

>Like if you select a random number from the set of all reals, what is the chance you'll get 4?
What does that mean?

>Well it's not 0, it's almost 0.
LOL, it's undefined because you haven't explained what you mean by randomly choosing a real number. You don't even know if it's possible.

>>11557996
...no, the regular reals you speak of all have this Archimedean property. This is like the first chapter of any elementary analysis book. Youre complaining about something that’s counter intuitive yet ultimately follows almost immediately by the construction of the reals that everyone uses but people don’t study unless they take analysis...and statisticians generally hit at least one analysis course before grad school.

>>11558007
https://en.wikipedia.org/wiki/Almost_surely

>>11557962
those are two things which are completely unrelated. there's nothing else to say.

>>11557993
What if space is discrete nigger?
Your field presumes X then deduces Y then wonders why retardation like 0,999...=1 sees the light of day and instead of revising the theorem / definitions plunges its head further down its ass and never really demonstrates anything because "muh maths don't exist in the real world" when any experiment based on geometry, mass or light speed could be imagined to put it to test. That's why you're not a science but glorified philosophy.

>>11558001
Nothing here is “about conventions.” This is the simple fact that the reals field does not have unique labels for rationals given its structure, which we see both by classes of Cauchy sequences and by dedekind cuts. A physics guy cannot generally btfo people at math because they apply math on a need to know basis - so they’re the last guys, unless we’re talking about mathematical physics in the math department, who could help doing a proof problem

>>11558031
Whatever.
Maths are just a tool, I reject your faggoty bullshit out of rational integrity but don't give a fuck one way or the other. 0,999...=1 has no impact whatsoever in any field outside of maths, and I'm fine with it.

>>11557658
You can't have an infinite number of nines, show me anywhere in the world where there is an infinite number of nines

>>11558025
>what if space is discrete
Discrete in what sense? The reals do not have the properties you desire, ie, there is no neighborhood of a real number lying in the set of all reals that is empty.
>Your field
My field is what? What exactly is your field?
>presume X deduces Y
Exactly what are X and Y here, or do you have a problem with basic implication structure? I think you’re probably the guy who hates nonstrict inequalities too
>retardation like 0.999... = 1
A simple non intuitive fact about the real field is suddenly the end of the world?
>muh maths
Lol europoor
>doesn’t exist
No...it’s that these labels refer to the same object. You don’t need an ontology to confirm or refute that. The issue at hand is pure and no “real world evidence” has the power to refute or corroborate it.
>not a science
Math produces stronger results than science that are used comfortably everywhere lol. You’re probably also the crowd that hates imaginary numbers but has no issue about how they work magically in circuits problems.

>>11558045
>whatever
You made the wrong argument and want to brush it off?
>maths is just a tool
Trivializing the topic at hand is a clear way to try and downplay you’re lack of reasoning, I get it, but why are you so visibly salty?
>out of rational integrity
No; you have a feeling these things can’t be equal likely out or a lack of understanding the canonical construction of the reals or what they aim to “complete” in the first place. Any effort to say this has been met with “muh dogma.”
>has no impact
I mean I agree that this result is not the big life changing theorem. But it is the stepping stone to nontrivial topics. I bet if you took measure theory you’d shit your pants at “the bullshit” even though even in application, everything works out precisely as expected.

>>11558025
0.999... = 1, or more generally the fact that a number may have two distinct decimal representations, is a minor technical abnormality of the decimal system, which otherwise works just fine. If you have a better idea what should we use to represent real numbers, feel free to share.

>>11558045
>Maths are just a tool, I reject your faggoty bullshit out of rational integrity but don't give a fuck one way or the other. 0,999...=1 has no impact whatsoever in any field outside of maths, and I'm fine with it.
see >>11557980

>>11558058
Discrete in that you can divide it in smaller boxes up to a certain point where you can't divide anymore, therefore rendering an infinite number of X like on 0,999...999...impossible.
>Your field
Maths I presume.
>My field
Law. I have an interest in "science", or more specifically physics and biochemistry.
>Define X and Y
X = continuous space that makes Y = infinitely repeating 0,xxx... possible in a vacuum.
>Europoor
My country (Switzerland) is superior in every indicator to the USA
>No real world evidence
Just like religion and philosophy, agreed.
>Not a science
Still not a science if you aren't willing to put it to test. Some mathematical theories, most of them actually, are sound and produce results. But others are not and you lack the integrity AND vision to reconsider them or to put them to test. Philosophers were right about most things too, even some religions for some things right, still not scientists.

>>11558087
It works, It just occurs to me that the approximation sign should be used out of integrity. 0,997 € = 1 € for all useful purposes as well, same should apply here.

>>11558073
>Canonical construction
Agreed.
>Muh Dogma
Yes.

>>11558018
Almost surely = 1

So what?

>>11558136
Make up a new sign for almost surely and stop using = nigger.

>>11558113
>Discrete in that you can divide it in smaller boxes up to a certain point where you can't divide anymore
Yeah that’s the same as claiming there’s a neighborhood of a real sitting in the reals such that it’s empty - and this is NOT true by construction lmao. So no, the reals are not a discrete space as you claim
>my field is law
>interest in physics and biochem
That’s great and all but neither of those equip you with the necessary tools to even address this argument. You’re using a 3rd grader’s understanding of the reals lmao and then trying to overfit empirical misunderstandings.
>X = continuous space that makes Y = infinitely repeating 0,xxx... possible in a vacuum
LOL it’s not continuous spaces that imply this alone. It’s continuous + completion + least upper bound property + Archimedean property + completely ordered field + rational subfield + equivalence classes of Cauchy sequences of rationals / dedekind cuts = one small quirk about the unique (up to isomorphism) field called the reals about the labels of rationals.
>Swiss
And yet still wrong, so your education didn’t do much for you
>not a science
Math is math, and as such science cannot make statements about mathematics, but mathematics is needed for the advancement of science, much to the chagrin of experimentalists. That being said, scientists do this in a collaborative manner - many do not understand the mathematics past its basic description, which makes many of them them clearly ill equipped to even start doing proofs

>>11558140
But we have equality by the way measure theory works
Imagine not understanding the generalization of length via measure and trying to argue about the reals

>>11557647
Wrong, retard. The 0.999...8 is not infinite because there's an 8 AT THE END.

>>11557749
What do you expect me to say other than "duh"?

>>11558161
The construction you have is wrong in nature then. You go from 1 unit to breaking it into smaller units. Your construction is the result of humans not comprehending what the smallest unit could be at the time so every unit we made up could be broken by a base. It does not mean it's true for all units.

>>11558215
You’re crying foul because you think the reals behave in a way they don’t...so then someone tells you that by definition you’re wrong...so then you double down and say nature is quantized so math should be as well. Don’t you see the folly? I know the (You)’s are addicting, but you’re making claims way outside your expertise / experience here and it shows

>>11557800
no you cant make u maths 0.9999... = 1 because
1/9 = 0.111111...
2/9 = 0.22222...
therefore
9/9 = 0.99999...
9/9=1
therefore 0.99999... = 1

or more abstractly the more 9s you wright the smaller the difference between your number and 1 theirfore if you wrote an infinte number of 9s the diference would be 0 making 0.99999... = 1

retard

>>11558215
>>11558161
Follow me on this.
1 Atom is the unit, lets call this unit mAtm.
1 Atm = 1000 mAtm.
0,9 Atm exists, so does 0,99 Atm, so does 0,999 Atm, but everything past that, let alone 0,999..., makes no sense.
Now imagine every unit ever is comprised of the equivalent to an Atom, something so small it can not be divised any further, which is what every evidence points to, do you see why 0,999... makes no sense now?
>B-but It works for fluids
Yeah so does Newton's law of Gravity for most things, doesn't make it a sound system, just a useful faulty system.

>>11558240
your analogy breaks down because you cant get decimals of an atoms (excluding sub atomic particles). by your analogy 0.75 wouldn't exist either

ps different atoms way different amounts google relative atomic mass

>>11558224
There is an interaction of units in nature that exists without a human observer. You do not hold a monopoly on how to retranscript them and the Reals theory is not a natural law that can't be circumvented. It's just right 99,9999999% of the time so there is no need for a new system, however, you seem to not understand the implications and the ideas behind what numbers and decimals are. You just know a lot of "how" but have no clue on "what". Understanding the nature of "what" is not technical, anyone can do it by logical thinking, no technical skills involved.

>>11558256
0,75 can or can not exist depending on the unit. 0,999... we are certain can not exist was my point.
>Muh atom weight
A neutron, a quark, doesn't matter, it stops being possibly broken down at some point.

>>11558276
you can have 0.9999... of an atom its the whole thing

>>11558284
You're a faggot running in circles unable to escape his conditionning. There is no hope for you Anon...

>>11558290
what youve got to realise is that when the whole world disagrees with you your probably wrong.

>>11558239
You CANT WRITE an infinite number of nines!!!!

You can only write a FINITE NUMBERE!

>>11558295
Ok mister the Archbishop.
Take my children and spread the good word now.
>>11558317
The Infinite is not the problem dishonest fagg. The "infinitely" small is.

>>11558317
[math]0.\bar{9}[/math]

>>11557968
>>11558173

Was playing around with this some more. I thought that by 8 being after the 0.9bar would weaken the equivalence between 1 and 0.9bar but it actually makes the argument stronger because the 8 has virtually no arithmetic effect because a 9 always precedes, meaning arithmetically 0.9bar8 is equivalent to 0.9bar. in fact you could put any number after the 0.9bar and it wouldn't have an arithmetic effect because the 9's would always precede whatever you put after them rendering it ineffective when adding left to right.

So weird.

>>11557356
We have been through all of this, all the retarded mental gymnastics, all the lies and intellectual dishonesty, all the parroting and indoctrination,
It has already been proved that 0.999... DOES NOT EQUAL 1.

You SODOMITES were beaten. The HOLY CHURCH of the FINITE was victorious. FACT: The Universe is finite and it is discrete.

Its time to give up. Stop making these ridiculous troll threads.

>>11558602
Based

>>11558602
This. It's settled. The sophists have lost.

>>11558602

>>11557686
If 0.9999999...=1 and 0.899999999......=0.999999999999
Then if a=b and a=c then you’d assume a=c

>>11558794
>0.899999999......=0.999999999999
delete this nephew

>>11558794
Sorry a=b and a=c then b=c I mean

>>11558794
0.89...=.9 You fucking mongoloid.

>>11558801
Oh shit def see where i fucked that up.

>>11558317
Correct, which is why we write '1' instead.

>>11558602
Wrong, retard.

>>11558819
Stop posting gibberish

>>11558825
It's literally a mathematically rigorous proof that 0.999...=1
Just because YOU are too stupid to understand the argument doesn't mean it's true.

>>11558837
""""""""rigorous""""""""
>assuming that 0.9999...=1, then 0.9999...=1

that's how dumb you sound

>>11558837
Show me 0.999... in nature or your """proof""" is nonsense.

TIMES UP.
Sorry, 1-0.999.. = Almost 0. Deal with it homo

>>11558849
Where does it do that? Give me the line. Show me how "dumb" I am by showing me that line.
>>11558852
I'm holding up 1 middle finger at your post. Since point nine repeating equals one, I'm flipping you off with point nine repeating fingers. Give me an actual math disproof. The Reals are dense, thus if 0.999...<1 then there exists a 'c' such that 0.999...<c<1
Give me one such number or naturally fuck off.

>>11558875
Cringe. This is the state of American "debating"

>>11558878
You're right, I should've just said they're 'cringe' and left it at that. *rolls eyes*

>>11557356
Infinity is only a potential, not an actual existent.

>>11559797
Stop typing stuff as though you actually know what you're talking about.

>>11558878
You're the one saying that 0.999 =/= 1
So, this means you're assuming that there exists some number x such that [math]0.999 < x < 1[/math]
proof or gtfo

>>11558878
You're the one who's saying that [math]0.999... \ne 1[/math]
That means you're assuming there exists some number [math]x[/math] such that [math]9.999... < x < 1[/math]
So, post proof or gtfo

>>11557356
You can't pour it into 3 glasses equally you faggot.

>>11559844
>That means you're assuming there exists some number x such that 9.999...<x<1
How does that supposed to prove anything?
I mean there are infinitely numbers between 0.999... and 1. If not therefore it got to be a number next to 0.999... also, so does that mean every real number are equal?

>>11559873
>How does that supposed to prove anything?
Don't be such a brainlet. [math]0.999...[/math] is, in fact, equal to exactly [math]1[/math] and this can be proven with simple algebra.
Just because the alias doesn't look alike, doesn't mean they don't share the same *value*, in the same way that [math]0.5[/math] doesn't look like [math]\frac{3}{6}[/math].

>>11557356
Prove that 1/3=0.333...
>>11557403
Literally doesn't know the definition of limit. 1/10^n never reaches 0

>>11559902
You can't multiply and infinitely large number by 10.
Prove that 1/3=0.333... protip you can't.
Prove the formula of sum of an infinite geometric progression.

>>11558240
The math itself isn't and cannot be "faulty". The only thing that's faulty is that it doesn't model reality 100% correctly. But NO physical theory does this and no theory ever will. There's no theory of everything. So does that mean ALL of math is faulty?
You have already acknowledged that continuous math is used for fluid dynamics, simply because it's useful and easier than the alternative. So the question is: should we not use it, because the fluid is not actually continuous ?
You can say "yes", it's a perfectly valid stance. But then you're practically saying that all of math should be finite, discrete, there is some largest integer past which we shouldn't count, there is some smallest fraction past which we souldn't divide. Again, ultrafinitism is a perfectly valid stance, it's just that your issue with math is much much bigger than just "0.999... doesn't exist". Or you can agree that even though spacetime is probably discrete, continuous math is still plenty useful, but then 0.999... = 1 is an irrefutable consequence of the theory.

>>11560390
First high IQ post itt.
Yes, this is my stance.
0,999... = 1 is no more valid than pic related, but the non-valid system producing it is useful indeed.
I still think we will switch to a more complete, "true-in-nature" (in the sense physics are, I know we will never get ris of the subjectivity attached to the observer) model as our computing power will increase and the simplification needed and brought by continuum in maths will no longer be necessary. Then 0,999...=1 will no longer make sense. Or maybe space is Indeed a continuum or maybe there is a God that created maths, but I don't see either of those being proven correct, it's counter-intuitive and it would make for an irrational world in the physics sense.

>>11560421
>>11560390
Forgot pic related.
This is an equivalent to the continuum maths theory, a valid system if you don't look too close.

>>11560390
I think there is no upper bound but there is a bottom bound past which we can't divide.
It's part of the same reason why Time travel in the future is theoretically possible but time travel in the past is not. Time freeze is also impossible, that's why the current model of black holes is incomplete, we don't know the smallest time unit / lapse possible yet, and will probably never will.

>>11560442
>>>/x/

>>11560444
https://en.m.wikipedia.org/wiki/Chronon
We're still far from being able to form a 100% correct theory, the continuum model is the best we have so far, knowing fully well it most probably isn't the correct model, and by extent that 0,xxx... makes no sense.

>>11559982
>Literally doesn't know the definition of limit. 1/10^n never reaches 0
Wrong and irrelevant. Try again.

I see the SODOMITES still have not given up, despite being proven wrong time and time again. GOD will punish them in due course.

Lets make this abundantly clear. 0.999 does not equal 1. There is no further argument. We are moving on now.
The Universe is discrete and finite.
So are numbers.
The biggest number is MOAN ( Motherfucker Of All Numbers). Nothing can be added to MOAN. There is nothing left in the Universe to add to it. It lies at the end of the number line. Attempting to go past MOAN results in you sailing off the edge into non-existence.

Our mission now is to rewrite all the textbooks, cleanse the Earth of Heresy and shout DEUS VULT very loudly, seeing as those faggots at Paradox have lost their balls.

>>11557650
>The fact that we can't come to a conclusion about this issue proves Math, a virtual concept humans created, is flawed.

I disagree.. It actually proves humans are flawed.

guys guys what if 1 isn't even the smallest representation of a unit and all numbers are actually fields, in the same way that quarks make up atoms

And and then even though using the numbers the way we always have is fine, breaking down a number into its constituent patterns, then running those bits through sub-calculations, then putting them back together (or N O T ) gets rid of all the inconsistencies in coǹventional math?

And also the light-bearing aether field they thought was required for light to travel through is actually just the pattern of very small things to suddenly round themselves up?

>>11560455
>0,xxx... makes no sense
https://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel

>>11560691
Interesting idea. I still stand by my statement that space is quantised and so should be numbers, but you gave the first real argument for the opposite and for 0,999...=1. The other faggs just parroted b-but it is the way it is even though it isn't but it was made up to be with no valid theory or reason grounded on any real science.

>>11560696
I know about that. It's a mathematician jerking himself of and aiming for his mouth. A common thing among mathematicians.

>>11560696
Here's another equally valid thought experiment.
Imagine an infinite hotel where only the last three rooms are occupied, because lol why not fuck logic.

>>11557936
yes
1/2 + 1/4 +1/8 + 1/16 +... = 1

>>11560709
go tell hilbert and wikipedia immediately !
your fields medal is in the mail

>>11557372
>Actually, you can divide 1 L in three only in base 9

Lmao

>>11560706
>t. 4chan schizo shitposter jerking himself off and aiming for his mouth.

>>11560710
Hello based department?
>>11560712
Mother Theresa has a Nobel prize. Those things are no better than Oscars.

>>11557648
>>Retard
>i have no argument

>>11560713
Remove "only" and I stand corrected. Stop being a pedantic fagg.
1L can't be divided in a unit made up of 10 smaller units. It can be if you use a unit made up of 3, 9 etc smaller units.

>>11560716
>Nobel prize
lrn2read

>>11560725
There is no Nobel prize in mathematics so you have a cope second rate prize.
Even economics have their Nobel lmao

>>11560724
or infinite units
1/3 = 0.3...

>>11560729
nah, a fields medal is solid

watch less tv
read a book

>>11560731
>Infinite units
My point and argument was you can't do that. Feel free to correct me by providing a unit that can be divided infinitely.

>>11560734
Well it's made of metal but otherwise it's bullshit back tapping.
Anyway Abel Prisen is much more comparable to a Nobel prize.
>Before 40 yo
Gay award tbqhf

>>11560754
>ignorant rambling
the dumb, they're never wrong

>>11560739
>providing a unit that can be divided infinitely
any real number

>>11560805
K whatever fagg

>>11560808
A number is not a unit. It represents a unit.

>>11557356
if .999... = 1
Using the
x = .999
10x = 9.99..
9x = 9
x = 1
analogy

How would you prove .00...1 = 0?

>>11560822
It does not stand in any base other than 10.
It's just because the 9 is the last digit you add before you obtain 10. 0,111... does not equal any number because you can always add a 2 anywhere and prove there is a C in between A (0,111...) and B (hypothetical).
If a unit = 7 smaller units for instance, 0,666... would be equal to 1 because 7 would not exist.
It's a stupid concept that only works because chimps have 10 fingers. An alien intelligence would laugh at us.

>>11560001
infinitely large != infinitely long

>>11560810
welcome to math

>>11561055
Well it's very gay, bye.

>>11560390
>>11560421
>>11560424
Mathematical theories and physical theories are not the same thing.

Math theory is about abstract objects, which are defined solely by their properties and relations to other objects. Using formal logic you deduce more relations from these definitions. A math theory is "valid" if it's consistent, i.e. if the axioms don't lead to contradictions.

Physical theory only uses math theory as an instrument. To material objects you assign the abstract math objects, the theorems give you relations which should hold, you check them with an experiment. If the theory doesn't work, it doesn't mean that the math is faulty in any way. It literally means that this sort of math used in this sort of way isn't suited for this problem.

It's always the case that not everything in the math has a direct physical counterpart. A physical theory uses only a small part of the mathematical theory, the physical part. This doesn't render the unphysical part obsolete or invalid. It's what makes the useful part possible in the first place. If you took it away, all the inner logical structure would disappear and you would be left only with statements which you take for granted.

>>11561204
Well put.
I can agree to that.

>>11560822
>.00...1 = 0

I've thought about this. So basically the issue here is whether any numbers come before, but not after the ellipses, or bar if you're using bar notation. Earlier I thought that by showing that

0.999... = 0.9 + 0.0999...
0.9 = 0.8999...
0.999... = 0.8999... + 0.0999..
0.999...8

That this would show the equivalence to be wrong. But when you actually try adding this number 0.999...8 to anything, the 8 has no effect, because there is always a 9 preceding it. Likewise, in the case of 0.000...1, there is always a 0 preceding, thus 0.999...8 is effectively the same as 0.999... and 0.000...1 is effectively the same as 0.

Any arithmetic operation on 0.999... produces the same effects as if it were 1, but with a different decimal representation.

for example:

2 * 1 = 2
2 * 0.999... = 1.999...8

You might again say that, well 1.999...8 is not the same as 2, but, once again, if you realize that anything after the ellipses has no effect, then you are left with 1.999... which means that

0.999... + 0.999... = 1.999...

Which could only be true if 0.999... were equal to 1.

So, since 0.999... has the same arithmetic effect as one, it must be equal to 1.

It's interesting this debate is actually is a good segue into abstract algebra because it forces you to determine whether two numbers are equal based on their effects on other numbers rather than just what they "look like," i.e. this is a unit because it behaves as a unit, rather than, this is a unit because it looks like one.

Those who think 0.99... = 1 are like lawnmower mechanics. They can follow instructions very well and are capable of diagnosing and fixing small mechanical problems. In many respects they are useful people, although not absolutely essential. Left to themselves they are very capable of surviving but would never invent anything.

>>11561295
well, that's my argument against:
>math is faulty
>math is invalid
>"you just define it to be true, that doesn't make it true"
>0.99.. = 1 has no real world implications
>0.99.. doesn't exist
>infinity doesn't exist
and more

by the way the math behind quantum mechanics is actually continuous

>>11563435
Well yes because we're still operating at a relatively speaking "huge" scale in physics.
And as I already admitted, 0,999... is so close to 1 it practically equals it so everything works, this being of course the case for other repeating to Infinity digits in continuous maths.
Continuous maths might default when applied to further practical applications of quantum mechanics in a distant future.

>>11557356
This entire stupid debate is contingent on the notion that there must be one correct answer. Truth is that it entirely depends on the context of which we are thinking. If you're only concerned about real numbers then sure, you can define 0.999... to be 1. But if you're also concerned about surreal numbers (look it up), then you begin to see that they might not always be the same.

It's the same thing with the sum of all positive integers, whether it diverges to infinity or becomes -1/12 is entirely based on the context of which you are speaking. Both sides are right in some way, and both sides are wrong about the other side being wrong. Unlike science, in maths the rules are made up, they're built up of axioms which defines the fundamental rules, rules we take for granted without needing to be proved. Because if we had no axioms, no things we could fundamentally accept as true, there would be no way to prove anything,you cannot prove anything without using logic to derive implications from things you already take to be true. What I'm trying to say is that maths is about as arbitrary as anything we humans have ever made, it's just a language we've made to describe abstract logic, and just like any language the definitions can vary depending on context.

For some 0.999... = 1, and that's fine, you can logically justify it with the axioms of which you operate with. For others, 0.999 =/= 1, and that's also fine, because they can also logically justify it within the context of their own axioms.

I hope this settles it.

>>11559902
>You might thing infinitely small numbers (0.000...01) exist. The don't

They do, surreal numbers. They exist just as much as complex numbers and negative numbers; while they might not have any real-world equivilent, they do exist in theory. You can divide 1 by 0.000...01 and get infinity, whereas if you were to divide 1 by 0 you would get undefined.

>>11557356
Here's your proof

.9...=x
9.9...=10x

subtract
9=9x
1=x

tada

>>11564315

-1/12 is what happens when you apply a type of smoothing function to the infinite sum of consecutive natural numbers. it is a technique for assigning unique values to divergent series.

If you read my post here >>11561310

You'll see that I can demonstrate that due to the infinite expansion of 9's, despite obviously being less than 1, it has the equivalent arithmetic effect as 1, because any of what you would "lose" from adding or multiplying it to another number is rendered ineffective by the infinite expansion.

This makes it a very strange number and makes me tempted to classify it as something that is not 1 even though it is effectively the same as 1.

To show that it was not equivalent to one you would need to show that there is some operation on it that would yield an amount that is "less than" it but no such operation could exist because of the infinite 9s and the effect they have on any operation you throw at them. Each operation you can attempt on 0.999... must first be applied indefinitely to the 9s which ultimately will just lead to the same 9s again, even if trailed by something less than 9.

Imagine you had a set with two infinite sequences, {1, 2, 3, ... 0, 1, 2, ...}

If you fed this into a product function, where each consecutive element of the set was multiplied by the previous in the usual ordering, it would always be non-zero because it would never reach the 0 after the ellipses.

The same situation with 0.999... You can multiply it, exponentiate it, add it, doesn't make a difference because anything that comes after the 9s from the first step will never be used in later operations. You'll always be starting off with 9's after each operation.

>>11564342
Irrelevant because we're not talking about the surreals, retard.

>>11564315
>For some 0.999... = 1, and that's fine, you can logically justify it with the axioms of which you operate with. For others, 0.999 =/= 1, and that's also fine, because they can also logically justify it within the context of their own axioms.
Let's pick a random 0.999... = 1 poster and a random 0.999... != poster. Ask them to describe the axiomatic system they're working in and to logically deduce their preferred answer. What do you think will happen ?

How do you define .9999...? If you define it as pic related, then you can't deny that it equals 1, since you can use the definition of a limit to prove it

>>11564417
>clunky
[math] \displaystyle
1 = \frac {3}{3} = 3 \cdot \frac {1}{3} = 3 \cdot 0. \bar{3} = 0. \bar{9}
[/math]

>>11564466
Again, look up surreal numbers. It's essentially the point you're trying to illustrate here.

Math is made up and not real.

>>11564619
that's kind of the point

>>11564599

Will do anon, thanks.

>>11558825
>grug no understand math symbols

>>11564315
>>11564599
See >>11563008

>>11557356
x = 0.999...
10x = 9.999...
9 + 0.999... = 9.999...
9 + x = 10x
10x - x = 9
9x = 9
x = 1

>>11559873
>I mean there are infinitely numbers between 0.999... and 1.
Name one.

>>11564979
>9 + x = 9x
Anon...

>>11557356
What people miss about this vital equation is that it is a simple proof of the principle of non-duality. All you need is finity and infinity and all numbers become non-dual. 1 and 2 are both 0% of infinity. Infinitesimal numbers just show that the non-dual union of numbers works via continuum.

Its actually highly redpilled.

1/0 = x
10/0 = 10x
(10 / 0) / 10 = (10x) / 10
10 / (0 / 10) = (10x) / 10
10 = 10x / 0
0 = 10x
x = 0

>>11557356
Ok so what about this?

>>11565186
he's right tho

>>11565577
This kind of proof is what Pauli meant by "not even wrong"

>>11566740
this guy knows the problem. equating this that are BY DEFINITION different entities, is an "phase fallacy". the point where you do the subtraction, you are manipulation variables that are in different "phase" or "information set" of examination

>>11565577
(10/0)/10 = 10/(0*10)

>>11566740
not really

>>11566759
>equating this that are BY DEFINITION different entities
you seem to know a lot about this topic, can you please tell me the definition of "1" and "0.999..." ?

>>11557356
I think writing fractional numbers as decimal doesn't make sense. All these problems go away if you stop trying to handle infinite decimals.
Just like having sex.

>>11566854
what problems ?

Those who think 0.99... = 1 are like lawnmower mechanics. They can follow instructions very well and are capable of diagnosing and fixing small mechanical problems. In many respects they are useful people, although not absolutely essential. Left to themselves they would never invent anything. Its generally best to let them keep believing in simple things, they can get very upset if their ideas are challenged in any way. As they are usually incapable of changing their world view educating them for the better is usually not worth the effort.

>>11557646

Numbers DONT exist at all. Congrats on taking the red pill. Our universe is all ratio based, not quantity based.

>>11566957
Those who think 0.99... != 1 are like lawnmower mechanics. They can follow instructions very well and are capable of diagnosing and fixing small mechanical problems. In many respects they are useful people, although not absolutely essential. Left to themselves they would never invent anything. Its generally best to let them keep believing in simple things, they can get very upset if their ideas are challenged in any way. As they are usually incapable of changing their world view educating them for the better is usually not worth the effort.

>>11566957
>Those who think 0.99... = 1 are like
people who know that the LHS is the representation of 1 in decimal expansion.

This board sure has a lot of replies for something that gets covered in the first week or two of a real analysis class.

Can you define a real number between .999... and 1? .999... and 1 are not distinct. They are equal.

>>11566974
Subtle.

>>11557356
I think the problem most people have with this is actually very simple but often not addressed: There's this assumption that every number that starts with "0." has to be less than one; that whatever comes after the comma can never make up for the fact that we start with "0.". And that just means they don't understand the notation of infinite decimals and actually work from different assumptions. So there's no use trying to convince people that 0.999...=1 based on all kinds of arguments. The actual issue is just in how you actually define the notation of infinite decimals.

Once everyone agrees that 0.999... has to be the limit of 0, 0.9, 0.99, 0.999, ..., the conclusion is inescapable.

CAN WE PLEASE JUST USE FRACTIONS INSTEAD OF DECIMALS TO RETIRE THIS DUMB QUESTION

you guys will love this one:

So take this purely true fact about arithmetic:

take any number and divide it by the 9's as long as the number has digits and you will create an infinite repeating decimal of that number.

for instance 123/999 = 0.123123123...

or 1/9 = 0.111111111...

or 100/999 = 0.100100100100100

you get the point, it creates the infinite decimal of the number.

now lets see the infinite decimal of 9's by the same method:

9/9 = 1

>>11566957
dude im literally creating proofs from pure intuition and random bits of math i know and youre calling me the uncreative one. youre just parrroting some supposed common sense about non terminating digits not having a terminable value. wow well done, we invented something called convergence to satisfy this problem. you should probably look it up.

>>11568565
Sure thing Slim. lets hide the truth by just using fractions, which are unsolved equations. You do know that, dont ya?
3/2 is 3 divided by 2. What is 3 divided by 2? Nah, lets not solve that, lets just leave it as 3/2

>>11564466
Any good decent God fearing person can look at something like 1 + 1 = 2 and know that it is both true and ordained by God.
But when we are expected to believe that in obviously BATSHIT insane bullshit like -1/12 crap, that's where we get pissed. For obviously that can not be true. Any convoluted proof that supports such nonsense is obviously the work of the DEVIL and SODOMITES! Smug faced greasy little SODOMITES sitting in fluro-lit little offices, fiddling with their tiny little penises and thinking up more mathematical OBSCENITIES with which to plague the sanctuary of a FINITE AND DISCRETE Universe. Laughing as they release their EVIL creations upon an innocent and unsuspecting world,.

Well, we have had enough. Now we are fighting back. We are reclaiming the mathematical world for the GLORY of GOD and RIGHTEOUSNESS. We shall prevail. DEUS VULT! DEUS VULT!

>>11565186
>can't read

>>11566740
epic xD

>>11568901
0.9999.. being one im ok with, but the -1/12 people are witches plain and simple.

>>11557356
Your conclusion is correct, but your reasoning is wrong. How do you know 3 * 0.3333... = 0.999...?

>>11569217
by induction and by the fact that R is a field