/sci/ - Science & Math

Nah, that one makes sense if you understand how 0.333... = 1/3.

It's this "equation" that tells you somebody fucked up mathematics. Probably Godel or Liebniz or something.

>>11944809
"No!"

>two extra 9s
I agree

this machine kills the robinson-lightstoner

>>11944868
>its wrong cuz waahhhh

>>11944914
Tell you what, right now I'll pay you 1/12 of a dollar, rounded up. Hell I'll be generous and make it 10 cents. A whole shiny dime.

In exchange I want you to pay me a dollar tomorrow, then two dollars the next day, then three dollars the day after.

What do you say?

>>11944962
Oh I forgot the most important part, you have to keep doing that and pay me more and more. Forever.

Don't worry, eventually you'll come out ahead!

>>11944965
>extrapolating math into the real world
>thinking anything could happen forever here
>with our finite fucking lifespans
>without the ability to give that much money every day
>eventually youll come out ahead
way to show off how fucking little you understand about infinite processes

>>11944990
>extrapolating math into the real world
Wow, so you guys really are useless then?

>>11944868
>Nah, that one makes sense if you understand how 0.333... = 1/3.
bait

>>11944995
Say that to the "useless" math thats explained quantum mechanics which has made it possible to manufacture incredibly tiny chips and fucking 7nm flash memory

>>11944995
>cant into Analytic and Synthetic distinction
ok brainlet

>>11945124
Look, guys, it's OK to admit you fucked up - every field does from time to time. Engineering's had its Challenger disaster, the soft sciences have their reproducibility crisis, and you have some glitches like -1/12 and Banach-Tarski.

You just own up to the problem and work on fixing it. That's all.

>>11945158
>thinking banach is a problem
not getting -1/12 is one thing

>>11945181
Look, I didn't spend years getting a math PhD but I think we all know a collapsed bridge when we see one, ya know?

>>11944809
Couldn't rounding be a natural law of order?

>>11944962
>o pay me a dollar tomorrow, then two dollars the next day, then three dollars the day after.

>numbers are a choo-choo train that keeps chugging along over time

>>11944868
analytic continuation my friend

>>11944809
>sigh
SAGE
A
G
E

>>11945317
OK, good, we're making progress. You need to fix your analytic continuation because it's throwing out garbage answers.

>>11944995
thats the dream

t.hardy

>>11945158
the imcompIeteness theorem is the reaI fuck up that every mathematician just pretends to ignore.

>>11945196
You would think that but it's clear that you don't.

>>11944809
0.3333....*3= (1/3)*3
0.9999.... = 1

>>11945605
Okay now do that in base 9 retard

>>11945614
0.3 * 3 = 1
where's the problem ?

>>11945385
No need to fix anything there, since [math]\zeta(-1)=-\frac{1}{12}[/math] makes absolute sense in that very context. It's no "garbage answer".
The important thing to remember is that doesn't make [math]\sum_{x \in \mathbb{N}}x[/math] equal to [math]\frac{1}{12}[/math], although it would seem like that, when you look at the definition of [math]\zeta(x)[/math], since it's only the analytic continuation.

>>11944809
Attention

.It is important to realize that mathematics exists only to make life easier for us Humans . and is not absolute truth

It's close enough OK?

>>11945614
What's 3*3 retard

>>11947565
the integer three multiplied by the integer three is equal to the integer nine.

>>11945617
>0.3 * 3 = 1
0.3 * 3 = .9

>>11944809
It follows by the basic construction of the reals via Dedekind cuts or equivalence classes of rational valued Cauchy sequences. All this really says is that rational representation in the reals is not necessarily unique - particularly, any integer [math] n [/math] can be written as [math] (n - 1) + 0.9... [math].
In fact, 0.9... = 1 is essentially equivalent to the Archimedean property of the reals.

>>11947613
fuck, meant it as [math] (n - 1) + 0.9... [/math]

>>11947613
>In fact, 0.9... = 1 is essentially equivalent to the Archimedean property of the reals.

In other words, the set of Real numbers was explicitly designed to ignore infinitesimals. It's the same as using the properties of Whole numbers to prove that 1/2 does not exist.

>>11947634
BUt you fail to realize that there are people called 0.999...=1 Deniers. they are
immune to reality.

>>11947634
introducing infinitesimals doesn't change the meaning of a symbol already defined.
>>In fact, 0.9... = 1 is essentially equivalent to the Archimedean property of the reals.
is not true.

>>11947593
>.9 in base 9

>>11947741
>.9 in base 9
Is meaningless. Like .A in base Ten.

>>11947647
>they are immune to reality.
Proof by insults.

>>11947732
>the meaning of a symbol already defined.
Proof by I say so.

Maybe YOU are the reason people disbelieve the equality?

>>11948018
>Proof by I say so.
what proof are you talking about?

>>11948046
>what proof are you talking about?
The thread is about what .999... means and why. You(?) just declared that .999... was "a symbol already defined."

I've found that every justification for .999... = 1 is based on circular logic of some kind. They all assume their conclusion in one way or another.

>>11944809
1/9 = 0.111...

.999/9=0.111...

0.000...1=0

In real life there's no such thing as "infinite xyz". This is all just a tool of mathematics. The same tools that say a coffee mug is the same as a doughnut.

>>11948131
>I've found that every justification for .999... = 1 is based on circular logic of some kind.
then youre really shit at reading, as if your other posts arent proof enough of that
the justification of .999... = 1 is done through the definition of the fucking real numbers, theyre the completion of the rationals, its that fucking easy

>>11944809
ITT /sci/ doesn't understand zenos paradox

>>11948176
>0.000...1=0
no

>>11948180
>the justification of .999... = 1 is done through the definition of the fucking real numbers,

And the justification of 1/2 = 0 is done through the definition of the Whole numbers. Maybe it would help if you spent less time swearing and more time thinking?

>>11948372
there is no justification of 1/2 = 0 in the whole numbers, maybe in computing, but nowhere else
you cant define 1/2 in the whole numbers, thats why we made the rationals

0.999...
x= 0.999...
1000x = 999.9...
999x=9
x=9/99
x=3/333
x=1/111

Did I do it right? I started studying math a week ago.

>>11948392
>you cant define 1/2 in the whole numbers, thats why we made the rationals
You can't define infinitesimals in the rationals, that's why we made the hyperreals.

My point is that insisting on using the Real set to talk about an infinitesimal is like refusing to acknowledge anything but the Wholes when someone is asking you about 1/2.

>>11948427
what’s an infinitesimal?

>>11948427
i would agree with you, except there is nothing infinitesimal about 1 - .999...

>>11948471
>what’s an infinitesimal?
https://en.wikipedia.org/wiki/Infinitesimal

>>11948498
>i would agree with you, except there is nothing infinitesimal about 1 - .999...
Prove it. And not using a number system designed not to see infinitesimals.

>>11948647
>>11948647
[math] x = 1 - .999... \\
10x = 10 - 9.999... = 10 - 9 - .999... = 1 - .999... = x\\
x = 0
[/math]
so why is this proof InVaLiD
>Prove it. And not using a number system designed not to see infinitesimals.
>the reals are designed not to see infinitesimals
youre a retard btw

>>11948647
i mean what’s an infinitesimal in the context of your whole number analogy

>fuck an 18 year old
>ACTUALLY SHES 17.999... YOU SICK FUCK
the state of 1cucks

>>11948679
>10x=10−9.999...

You added a significant digit by multiplying by 10. This would never happen in any finite multiplication, and you have no reason to think it would here. The problem with this is "Infinity only works when we want it to." There is no consistent logic to what can emerge from the endless string of nines and what can't.

>>11948711
>i mean what’s an infinitesimal in the context of your whole number analogy
It is simply "something that is not a real number" just like 1/2 is not a whole number. You know what else is not a real number? Infinity. And yet you need to invoke it for .999... to have any meaning at all.

Praise God! At last there is a growing number of enlightened people who will not accept the BLASPHEMY of 0.999...= 1.

Brothers and Sisters of the ONE TRUE FINITE AND DISCRETE Universe, soon we shall reclaim Constantinople and Mathematics for GOD! We march! Verily, those GOD CURSED SODOMITES who claim such absurdities to be true shall perish before our swords and be sent into finite DAMNATION where they shall writhe within the discrete flames of HELL! PRAISE GOD!

Amen.

>>11948796
>You added a significant digit by multiplying by 10.
I did no such thing

>Infinity. And yet you need to invoke it for .999... to have any meaning at all.
So you just admitted to not knowing how series are defined, why should i take anything you say seriously?

>>11948796
>would never happen in any finite
let's pretend finite is infinite

>>11948815
found the pedo

If 0.999... is not equal to 1, then there is a smallest positive real number epsilon such that
[math] 1-\varepsilon=0.999... [/math]
This is an interesting issue because I have seen a lot of evidence that there is no least positive real number.

>>11944809
The most intuitive explaination is that 0.333... is one-third. Add that three times and it's exactly equal to one. Not close, exact.

1/3rd +1/3rd +1/3rd = 3/3rds = 1

0.333... + 0.333... + 0.333... = 0.999... = 1

>>11948131
>You(?) just declared that .999... was "a symbol already defined."
are you saying 0.999... is not a well defined object?

>>11948796
>There is no consistent logic to what can emerge from the endless string of nines and what can't.
there is, you're just too retarded to grasp it

>And yet you need to invoke it for .999... to have any meaning at all.
lol brainlet. you don't need ∞ at all to talk about limits or suprema.

>>11944809
>.6=1
Checks out if you're not a mong who takes it seriously

>>11948471
>what’s an infinitesimal?
1/infinity, which is 0.

>>11948849
>I did no such thing
You have the original exactly plus a nine on the other side of the decimal point. Yet somehow you didn't add a nine. Also, it is exactly nine more than the number before multiplying. But you didn't add nine.

>>11948849
>So you just admitted to not knowing how series are defined, why should i take anything you say seriously?
This is how religion is defined. You don't accept the secret doctrine therefore you don't understand it. And no one can quite explain the secret doctrine, but they sure know to reject anyone who questions it.

>>11948940
>This is an interesting issue because I have seen a lot of evidence that there is no least positive real number.
There is a lot of evidence. Says none of it. Religion again. There is a lot of evidence that the square root of negative one does not exist.

>>11949002
>The most intuitive explaination is that 0.333... is one-third. Add that three times and it's exactly equal to one. Not close, exact.
Yet again, WHY? This is like attending a prayer meeting.

>>11949120
>are you saying 0.999... is not a well defined object?
Well, at some point you carry the one, and all the nines become zeros. But there is no "last digit" so where does the one come from? And if you treat the infinity as a completed step, then why can't you append anything to it?

>>11949131
>there is, you're just too retarded to grasp it
Proof by name-calling. This is the closest 4chan gets to an admission of defeat.

>>11949298
>>what’s an infinitesimal?
>1/infinity, which is 0.
Countable or uncountable infinity? What happens if you use one of the other infinities?

>>11949536
[math]0.999 \dots = \lim_{n \to \infty} \sum_{k=1}^n \frac{9}{10^k} = 1[/math]

>>11949536
what exactly do you find controversial about the generally accepted definition of real numbers and the decimal expansion?

To all the retards using their simple minded, low effort algebraic "proof":
If you believe that
0.999...=x
9.999...=10x
9+x=10x
9=9x
1=x
Then by that same logic,
...999=y
...9990=10y
y-9=10y
-9=9y
-1=y
And
...999.999...=z
...999.999...=10z
z=10z
z=0
It works out when you see that ...999+0.999...=...999.999... and (-1)+1=0
Sounds fucking ridiculous right? Yet i dare you to disprove that ...999=-1 and ...999.999...=0.
>inb4 some lousy cauchy/dedekind cut explanation
Its foolish to apply algebra when dealing with infinity, and just goes to show how little you understand about the concept of infinity. If you want to have your way and still think the other 2 equations are incorrect but 0.999...=0 is somehow exempt, as i said before you are free to try to disprove them.

>>11949678
>...999
not a real number

>>11945145
The dumbfuck faggots on this board are not nearly intelligent enough to understand Kant, anon. Don't be mean

>>11949691
Wrong, it has a place on the number line therefore it is real

>>11949709
give a natural number larger than or equal to ...999

>>11949696
>T
>>11949696
It's irrational but it is real

>>11949721
...999.9

>>11949765
Retard.

>>11949770
lrn2math

>>11949770
>R-retard!

>>11949765
very nice. now define ...999.9 using only the successor function, addition, multiplication, and the numbers 0-9.

>>11949678
>Then by that same logic,
>...999=y
we have no justification for claiming that ...999 is a number, so no, youve made a huge jump in logic actually, its not the same
but yeah, if you plug in 10 into the geometric series you get -1/9, this isnt news
>>11949709
no it doesnt

>>11949833
>no it doesnt

Yes it does. It is -1. The other anon just proved it. If you can't accept that, then why accept .999...?

>>11949721
>give a natural number larger than or equal to ...999
Zero. It is +1 larger.

>>11949602
>what exactly do you find controversial about the generally accepted definition of real numbers and the decimal expansion?

If you accept a definition you must also accept WHY the idea was defined that way. Real numbers exist precisely to ignore the infinitesimals that kept cropping up from Newton and Leibniz's calculus. You aren't proving anything when you use Real numbers to claim that .999... = 1. You are just blinding yourselves to alternatives.

>>11949866
>If you accept a definition you must also accept WHY the idea was defined that way.
Not true. For example, no Scrabble players know what all the valid letter strings mean. They accept that those strings are defined as words in a common dictionary without accepting why they are so defined.

>>11949866
>You aren't proving anything when you use Real numbers to claim that .999... = 1.
?

>>11949866
The sequence 9, 99, 999, ... does not have a cluster point on the real line
the analytic continuation of the geometric series in the unit ball to the rest of the line does map 10 to -1/9, but that is algebraic
it does not have a point on the number line, even though it can be consistently algebraically mapped onto -1

so the sequence 9, 99, 999, ... does not correspond to a number on the real line to begin with, unlike .999...

>Real numbers exist precisely to ignore the infinitesimals that kept cropping up from Newton and Leibniz's calculus.
this is totally untrue
the real numbers were invented to complete the rational numbers, infinitesimals are not a topological concept, they are algebraic
unlike the construction of the reals from the rationals

>>11949900
>cluster point
>analytic continuation
>topological concept
>implying he knows what that means

>>11950006
i dont know how to explain it any better to him
ill never be a good professor at this rate

>>11949887
>>You aren't proving anything when you use Real numbers to claim that .999... = 1.

I've answered this twice already, we are going around in circles. Read the "1/2 in Whole numbers" stuff above.

>>11949900
https://www.youtube.com/watch?v=WYijIV5JrKg

>>11949536
Look children, a murrikan educated person.

>>11950019
theres a world of difference between 1/2 and .99...
1/2 is not in the whole numbers, but .999... is in the real numbers
you cant just keep saying 1/2 over and over, it doesnt relate

>numberphile describes infinitesimals geometrically
>therefore ?
and? we teach kids numbers by counting shapes, that doesnt mean theyre fundamentally geometric
you cant properly define infinitesimals geometrically, but its insanely easy to do algebraically

>>11948176
>1/9 = 0.111...
True.
>.999/9=0.111...
False. That would be 0.111.
>0.000...1
That's literally not even a real number.
>In real life there's no such thing as "infinite xyz".
You are probably right about this, though.
Any kind of infinity or infinitesimal has ultimately turned out to be the result of a lack of understanding so far.
Space may very well be "infinite", but effectively it's finite due to the finite speed of causality.

>>11950036
>world of difference
nah, just 0.4999...

>>11949721
-1 is equal to ...999 as proven earlier

>>11950036
>1/2 is not in the whole numbers,
It is if you insist that 1/2 = 0. That is what happens in the Whole set, therefore it must be true in all other sets. Two goes into one zero times.

>>11950057
see >>11949900

real numbers are cauchy sequences of rational numbers
since 9, 99, 999, ... does not have a cluster, it is not a cauchy sequence
the fact we can assign a value to the series as -1 does not mean that the representation is valid

>>11950114
>That is what happens in the Whole set, therefore it must be true in all other sets.
thats not how it works at all you idiot

>>11944809
NGMI as a machinist there OP, sorry to break it to ya.

>>11950168
Oh you said "obvious bullshit". I misread your post, sorry there OP. Your not a faggot today.

>>11950118
>>That is what happens in the Whole set, therefore it must be true in all other sets.
>thats not how it works at all you idiot

It is EXACTLY the same circular logic that you guys are using to assume that .999... = 1. You recognize that it is wrong in this context, but then suddenly accept it when it says what you want it to say. That is why so many people reject your arguments.

>>11950208
>It is EXACTLY the same circular logic that you guys are using to assume that .999... = 1.
explain yourself retard, stop just dropping single sentence shit without justifying it

>>11950168
>NGMI as a machinist there OP,

Why would a machinist ever use real numbers? Whole numbers correctly describes what happens if you try to cut a proton in half.

>>11950212
>explain yourself retard, stop just dropping single sentence shit without justifying it

>>11944868
>>11944872
>>11944880
>>11944900
>>11944990
>>11944995
>>11945145
>>11945196
>>11945181
>>11945317
>>11945385
>>11945412
>>11945426
>>11945605
>>11947575
>>11947647
>>11947732
>>11948046
>>11948176
>>11948180
>>11948229
>>11948392
>>11948498
>>11948711
>>11948849
>>11948899
>>11948906
>>11948940
>>11949120
>>11949131
>>11949298
>>11949592
>>11949602
>>11949691
>>11949696
>>11949709
>>11949721
>>11949730
>>11949770
>>11949773
>>11949778
>>11949833
>>11949885
>>11950028
>>11950212
explain yourself retard, stop just dropping single sentence shit without justifying it

>>11949536 (Me)
>And no one can quite explain the secret doctrine, but they sure know to reject anyone who questions it.
>There is a lot of evidence. Says none of it. Religion again.
>Yet again, WHY? This is like attending a prayer meeting.

>>11950244
>the retard still hasnt justified himself
>and used examples of proper single sentence explanations in his rant
>and mutliple sentence posts in his rant
youre literally just stupid

It's impossible to calculate any difference between 0.999... and 1

>>11950657
The difference is 0®1

>>11951003
how did you calculate that?

>>11951040

1
-.999...
_____
= 0®1

>>11951132
what’s the difference?

>>11950208
1/2 is not zero in whole numbers you sad retard, it doesn't have any meaning in whole numbers

>>11949002
Most fucking pants on head wearing explanation ever.
0.333... = 1/3 is all its claiming.
which is just as retarded as saying 0.999... = 1
Honestly if is this is the best you can do then no wonder people think you are full of shit.

>>11951477
Honestly, if this is as smart as you are then no wonder you think actual smart people are full of shit

this fucking thread again?

2/3 = .666...7

>>11944809
That little bar = 0.001

>>11951576
>...7
>...anything
ree

0.999... + 0.111... = 1.111...

therefore

0.999... = 1.111... - 0.111... = 1

In real numbers you still need infinititesimals, because otherwise you have two different zeros:

Imagine you have a random number generator. It makes random real numbers between zero and one. Any result as likely as any other result.

>Easy: What is the probability of getting a 2?
Obviously that can't happen because it contradicts the definition of the device. So it is probability zero.

>Problem: What is the probability of .5?
You have a finite number divided by infinity, so also zero?

You have two different zeros. One possible, the other impossible. It just makes more sense if the probability is .000...1

Gets brought up here:
https://youtu.be/6_yU9eJ0NxA?t=430

>>11953701

Later on in the video they ask about the dart hitting the edge of a circle, compared to the bulls eye. Standard math can't calculate that landing on a long line would be more probable than landing on a point.

They just say "Don't worry about it." and move on!

>>11953701
Those are both the same 0, it's their interpretation that is different.

>>11953713
>Standard math can't calculate that landing on a long line would be more probable than landing on a point.
>this fucking retard has never heard of measure theory

>You have two different zeros. One possible, the other impossible. It just makes more sense if the probability is .000...1
no, theyre both just 0 probability of occuring
the proper way to deal with that is to say that the probability density function at .5 is nonzero, its 1
but the density function at 2 is 0, then you could look at neighborhoods of .5 and 2
adding infinitesimals is the worst way to deal with that

>>11953713
>landing on a long line would be more probable than landing on a point.
no, those are equally unlikely. the conceptual problem comes from the analogy itself: imagining the tip of a dart hitting a line or a point on a dartboard. those are all thick, not thin.

>>11950244

I have a dysfunctional relationship with e.
:(

>>11944962
You realise 2 = 1 + 1 has no temporality or 'afterness'. It's not that addition is a three stage process of having a object, introducing a second object, and then those combining to produce a third object. 1+1 is just a way of representing 2, as 2 is a way to represent 1+1.

>>11944809
>5/5=1 is obvious bullshit because I don't understand fractions.
That's how stupid you sound to someone who understands infinite series or analysis.
See >>11953778

>>11953778

All this stuff is circular logic. Limits are a method of ignoring infinitesimals. That is why they were invented. So naturally when you use them to examine .999... the limit will do what it is intended to do. Every proof of that equality assumes its conclusion somewhere.

>>11953701
P(X = x) = 0 doesn't mean it's impossible.
f(x) = 0, where f is the probabilty density function, means it's impossible.
apply yourself.

>>11953718
>Those are both the same 0, it's their interpretation that is different.

Which is a fancy way of saying that the two zeros mean different things. If I tell you that an even has "zero probability" you can't tell me if it is possible or not.

>>11953988
this guy thinks that the definition of 0.999... magically changes based on what number system you use

>>11953718
>Those are both the same 0, it's their interpretation that is different.

Which is a fancy way of saying that the two zeros mean different things. If I tell you that an event has "zero probability" you can't tell me if it is possible or not.

>>11953996
>If I tell you that an even has "zero probability" you can't tell me if it is possible or not.
now you get it

>>11953988
>Limits are a method of ignoring infinitesimals.
no they fucking arent
infinitesimals are not a geometric concept, they do not arise from the real numbers, since the real numbers are a geometric extension of the rationals

>Every proof of that equality assumes its conclusion somewhere.
call x = .999...
then 10x = 9.999... = 9 + .999...
so 10x = 9 + x
and x = 1

>>11953988
what is 0.999... + 0.111... ?

0.999...9 + 0.000...1 = 1.000.0 = 1

0.999... + 0.000...1 = 1.000...999... ≠ 1

>>11944809
If .999... = 1, would this imply the theoretical next number after 1 also be equal to 1? As in 1.000........1 = 1? Would the number after that one be equal to the number before 1.000......1 = 1.000......2?

>>11954099
There is no next number after 1, there are always more numbers in between.

>>11954099
1.000...1 is just a retard way of writing 1.000...

>>11944990
>he fell for the -1/12 meme in college
Nigga... You were supposed to learn the tricks for the test and then memory dump the obvious bullshit you just learned. If it's always either 0 or 1, it's never 0.5. You found the "limit" (for lack of better word) to which the two sides never converge on. You wouldn't say cosine(infinite)=0, you'd say it has no value.

>>11945158
based

>>11944868
0.333 =/= 1/3 tho. It's just an approximation

>>11954099
next as an idea only exists for a set that is countably infinite
the reals are UNcountably infinite
theres too many of them to put them in a linear order like that

>>11954157
>If it's always either 0 or 1, it's never 0.5.
yeah, none of the finite terms are ever .5, theyre only 0 or 1 by definition
thank you einstein, what a fucking wonderful insight
the point of extending 1-1+1-1... to 1/2 is not by saying the limit approaches 1/2, the limit doesnt exist everyone knows this
but we can still find a sensible definition that agrees with the limiting one (when the limit exists) and that sensible definition gives 1/2
in fact, every single sensible definition gives 1/2 to 1-1+1-1...
if you think its obvious bullshit, then you didnt learn it properly, did you only ever see the NumberPhile vid on it or some shit?
Is that why you're calling it a "limit" in quotes, cuz James Grime called it a pseudo limit?
Its got jack shit to do with limits, we arent saying 1 0 1 0 1 ... has a limit at 1/2

>>11954164
>based
based on nothing

>>11954186
.333... = 1/3
its exact

>>11954229
1-1+1-1... = 0

>>11953701
Wtf, 1/infinity is undefined, not 0.
In fact you just implied 0.000...1 is indeed greater than 0 considering there a chance greater than 0 exists

Did you guys not understand limits or something?
>>11953718 (you too)

>>11954265
>0.000...1 is indeed greater than 0
of course it is, all decimals fitting that pattern have a 1 in the nth decimal place such that n is an arbitrarily large finite integer.

>>11954265
>1/infinity is undefined
nope
r/inf=0

>>11944809
I think that we need to create a unique variable to represent the 0.(insert infinitely repeating zeroes here)1

>>11954301
nah it's 0

>>11954301
like 0

>>11954254
G = 1 - 1 + 1 - 1 + ... = 1 - ( 1 - 1 + 1 - ...) = 1 - G
so if G = 0, then G = 1

>>11954265
>In fact you just implied 0.000...1 is indeed greater than 0 considering there a chance greater than 0 exists
no, it does not have a chance greater than 0, it has 0 chance of happening

>>11954309
1-9.999999... = 0.00000000...1 the 1 is still there. 1 does not equal 0.

>>11954301
the zeros are place holders, you can't compress an infinite repetition of them into a closed interval.

>>11954320
no, 1 - 0.999... = 0.000...

>>11954320
the 1 is not there, youve just magically added it
every single digit gets subtracted away, since theres infinitely many 9s

>>11954314
the capricious bracketing of alternating divergent series is devil's play, anon.

>>11954341
its fine, i havent rearranged a single thing
and im not going to be able to introduce Cesaro or Abel summation to the brainlets here

>>11954345
i prefer the oresme bracketing
1 + 1/2 + (1/4+1/4) + (1/8+1/8+1/8+1/8) ...
1 + 1/2 + 1/2 + 1/2 ...

and so
1 - 1 + (1-1) + (1-1+1-1) ...
1 - 1 + 0 + 0 ...

>>11954320
1/inf=0

>>11954370
>1 - 1 + (1-1) + (1-1+1-1) ...
>1 - 1 + 0 + 0 ..
any proof dependent on the order of adding is bs

>>11954379
yes, exactly. that's why this>>11954314
>G = 1 - 1 + 1 - 1 + ... = 1 - ( 1 - 1 + 1 - ...) = 1 - G
>so if G = 0, then G = 1
is devil's play, not a proof.

>>11954388
>>11954379 is isnt me, hes a new anon
i know bracketing is sensitive, but its simpler than actually using Cesaro or Abel, like i said

>>11954229
>i-i-f w-we just define it as such, i-it all works out!
>Traps aren't gay i-if we just redefine gay!
I believe this is our disconnect. You believe numbers are whatever we say they are, whereas I believe numbers are supposed to be representatives of the universe we experience, and at the very least if we're gonna play with made up concepts like infinity than they should adhere to the same principles.
And again, cosine infinity has no value, it alternates between peaking at 1 and -1. I hope you can picture the parallelism. You can say at some point it does equal zero, but also at any point A either equals 0 or 1, so let's ignore between 0 and infinity. You stretch either out to infinity and neither converges. Defining an answer so our non-infinity brains can make sense of it doesn't make it so., no matter how logical.

Also why choose the word "limit"? Cause like your favorite YouTuber, I too could not think of a better word.
Also I learned the 1/12 tricks well enough to pass the final exam. You can learn so many things and not agree with any them. I'm sorry if that last sentence is new to you this late in life.


>based on nothing
We can go can back on forth on this forever, but why don't we just settle on the middle where we're both half right. Oh wait, that's a not a realistic option is it. But wait, we can just define both of us as neither being wrong nor right! Dude I think we just solved world hunger

>It's an exact value
0.333... is an approximation. It's literally infinitely converging toward a limit that it never reaches, you monobase simp. There's a (mis)understood 1/3 of a digit you're rounding off to make that work in your head.

>>11954314
Idk, you said they all have the same chance of appearing. Sounds like there's a chance, however small

>>11954470
>You believe numbers are whatever we say they are, whereas I believe numbers are supposed to be representatives of the universe we experience
theyre both
>and at the very least if we're gonna play with made up concepts like infinity than they should adhere to the same principles.
why the fuck should something unlike all other numbers behave by the same principles?
>And again, cosine infinity has no value, it alternates between peaking at 1 and -1. I hope you can picture the parallelism.
there actually is not a parallel from taking the limit of cos and defining a more general notion of summation, past taking limits
>I'm sorry if that last sentence is new to you this late in life.
wow, arent you so fucking enlightened to realize that teachers can talk shit
what an immense intellect

>0.333... is an approximation. It's literally infinitely converging toward a limit that it never reaches, you monobase simp.
the finite terms in the limit are an approximation
the final limit itself is not an approximation you fucking dropout

>>11944809
What is 1/3 in the form of decimal fraction?

>>11954470
>converging
no, writing out decimal places is converging. the value itself isn't converging, it's converged.

>>11944809
You talk of math as though it is science, when in fact math is quite arbitrary. It is merely a language we've constructed to describe logic. The rules of the language, the axoims, are entirely abitrary and changes from field to field. Whether 0.999... = 1 or not entirely depends on when you define these constructs as and the rules you apply to them.

>>11954665
you can't calculate a difference between 1 and 0.999... it's 0 forever

1 - 0.999... = 0.000...

Who the fuck is this guy who keeps making these brainlet 0.999... =/= 1 threads

>>11953701
>he doesn't understand sigma algebras
oh no no no no
https://www.youtube.com/watch?v=ZA4JkHKZM50

>>11945332
>>11954675
Wow, this makes sense!
Wtf?

>>11944809

yeah but 1/3 plus 1/3 plus 1/3 = 1
1/3 equals 0.33333333333333333
as such?

trust me I share your perhaps inauthentic issues to me dividing by zero just gives you the numerator. divide NO times.

so does 0=1 ?

not as a function of a denominator.. think of how it would be used in any serious application of calculation.. the pie is not divided.. one pie.. two pies are not divided.. two pies.

probably how it is used and operates for every engineering application. if the denominator is zero then you dont divide

go figure! one of my problems with arithmetic!

>>11954292
He is right in that you cannot say [math]\frac{n}{\infty}=0[/math].
You can't use [math]\infty[/math] in conventional arithmetic, since it's quite literally NaN.
You need to write [math]lim_{x \rightarrow \infty} \frac{n}{x}=0[/math]. Which is "the different zero" >>11953701 is talking about.
It's the very same zero, though.

>>11956214
https://www.wolframalpha.com/input/?i=1%2Finfinity

>>11944868
You can't give a divergent series a value. tThe sum of all natural numbers doesn't have a value; it diverges. BUT if you were to give it a value *wink* then it would be -1/12. -1/12 gives you information about the nature of the series but it is not actually the sum (more or less the way my professor explained this it to me).

>>11956264
WA is probably interpreting it as to what you could have reasonably meant by that nonsense, and displays the result.
Otherwise WA is quite literally wrong there. [math]\frac{1}{\infty}[/math] is undefined in the Reals, since [math]\infty \notin \mathbb{R}[/math].

>>11956363
extended number line is a thing you know

>>11956384
That's not "conventional arithmetic", though.

>>11956398
where does wolfram state that it uses only "conventional arithmetic"? what's "conventional arithmetic" anyway?

>>11956363
random 4chan guy is probably full of shit

>>11956404
>what's "conventional arithmetic" anyway?
How about [math](\mathbb{R},+,\cdot)[/math]?

>>11944868
>>11944900
>>11945605
using math to prove math is just as invalid as using the bible to prove that the bible is right

>>11956444
>using math to prove math
lol, what then, dance therapy?

>>11956414
okay, so who decided that wolfram and this thread must limit itself to conventional arithmetic?

>>11956413
>t. random 4chan guy

>>11956456
quoting WA > pulling random crap out of ass

>>11944809
no its not

makes complete sense

what's 1/3?

it's either 0.333... or something else. if you agree its 0.333... then 0.333... X 3 = 0.999... which is 1/3*3 which is one.

so what's the decimal expansion of 1/3 ?

>>11944809
A thread with a topic such as that is never going to go anywhere useful.

0,9999... has been proven to equal 1mayn times now.

fine you reject the proofs, prove that 0,999... isnt equal to 1 then, like give me a rational number between 0,999... and 1

>>11956444
u cant prove math. its why we have axioms