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/sci/ - Science & Math

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10437694 No.10437694 [Reply] [Original] [archived.moe]

There will always be an infinitesimally small distance between them. Why is this even still up for debate?

>> No.10437705

>infinitesimally small

so, 0.

>> No.10437708
File: 319 KB, 795x567, IMG_1089.png [View same] [iqdb] [saucenao] [google] [report]

t. Retarded fucking idiot

>> No.10437729

My thoughts regarding the picture:
Therefore 9x=/=9

>> No.10437751

What do you mean by “infinitesimal”?
What do you mean by “distance”?
Why do you say “always” when numbers are eternal and not time-dependent?

You should try working on your formal jargon because I have no idea what you are trying to convey

>> No.10437754

What about the right side?
9 x 1/9

>> No.10437755

Wow it's almost like there's a distinction you're purposefully choosing to ignore, a number greater than zero cannot also be zero

>> No.10437761

infinite isn't a number
infinitely small also isn't a number

>> No.10437764

So what number is in between .999... and 1?

>> No.10437767

Again, a value greater than zero cannot equal zero

>> No.10437777

Again, infinitesimal is not a quantity

>> No.10437784

I never said it was. That was OP, I'm telling you 0 =/= >0

>> No.10437785

(0.999.... + 1) / 2

>> No.10437797

That’s 1, anon

>> No.10437802

What does the decimal expansion look like?
What does the decimal expansion of 1-0.999... look like?

>> No.10437807

1 - ((1 - 0.999...) / 2)

>> No.10437808

>What does the decimal expansion look like?
I typed it out but too long to post here

>> No.10437809

What does 0 have to do with this now?

>> No.10437814

At least your response was remotely clever

>> No.10437815


>> No.10437817

A number greater than zero

>> No.10437818


>> No.10437823


>> No.10437831

What number?

>> No.10437832

But that's a false statement anon

>> No.10437834

that is only true if you can show that there is a number between 0.999... and 1.

>> No.10437835

>1/3 = 0.3333...
>being this stupid

>> No.10437842

prove it wrong
even better, give the "correct" answer

>> No.10437850

the correct answer is: 1=1

>> No.10437854

Hey OP, can you help me solve this?

>> No.10437864
File: 90 KB, 474x711, brainlet4.png [View same] [iqdb] [saucenao] [google] [report]

Infinitesimals don't exist in the field of real numbers since the real numbers are defined by the completeness axiom. Everything bounded above has a least upper bound. What could the least upper bound be other than 1. Every real number is defined in terms of cauchy sequences, where for all epsilon we can find an element of the sequence such that all successive elements will be within epsilon of its limit. If you were correct the irrationals would also never equal what they are. Stop posting this garbage.

>> No.10437869

how is that /pol/?

>> No.10437877

anti-/pol/tards are in a constant state of seething about /pol/

>> No.10437929

and your penis is infinitesimally small. why is this still up for debate?!?

>> No.10437983
File: 2.61 MB, 360x360, x.gif [View same] [iqdb] [saucenao] [google] [report]

A distance is something finite and measurable so if you say that there is a distance between 0.9... and 1 you are saying that there is a numer x that satisfies 0.9...+x=1
So please find x :)
And don't tell me x=0.0...01 because as soon as you put a digit 1 after zeroes your are telling that x has finite digits, but x must have infinite digits since 0.9... has infinite digits, and so the only possible answer is x=0.0...=0.
And pls don't even tell me that x=1-0.9... come on don't be a brainlet ;)

>> No.10437987

yeah, 0.000... is patrician-tier

>> No.10437994

its funny because literally no one likes /pol/, i guess we're all seething together, its not so bad desu

>> No.10438014
File: 157 KB, 1035x1083, 1543864027575.jpg [View same] [iqdb] [saucenao] [google] [report]

fucking this

>> No.10438040


>> No.10438043


>> No.10438044
File: 119 KB, 583x482, 1551545614196.png [View same] [iqdb] [saucenao] [google] [report]

>another 1=0.999 thread

>> No.10438048 [DELETED] 

You seem smart, can you help me with a really simple problem? Current through a 300mH coil increases at a rate of 50uA per 10us, how much is the induced voltage?

It should just be V=L (di/dt), which I computed as 1.5V but the correct answer is 1.5kV

>> No.10438056

post in >>10412555 or >>>/wsr/

>> No.10438057


>> No.10438078
File: 43 KB, 530x378, brainletsbtfo.png [View same] [iqdb] [saucenao] [google] [report]

>> No.10438088

yeah but its 0.999.....
not 0.999...999
Then nines do not end.

>> No.10438194

That implies that .999... terminates

>> No.10438199

No it doesn't. Go back to >>>/x/ fucking retard

>> No.10438268

Yes it does. Go back to >>>/lgbt/ fucking retard

>> No.10438270

Based tired old frog poster

>> No.10438350

9/9 equals 1
9/9 does not equal a "0.999..." that is different to 1

>> No.10438358

0.999... x 10
= 9.999...
9.999... - 0.999... = 9

>> No.10438394

0.999... is and infinity sum that converges toward 1. how stupid can you be

>> No.10438396

(Using a geometric sum)

Never post here again

>> No.10438427

That .1 you think exists is actually accounted for. There is no end to the number but if you pretended there were and you wanted to add that ...1 and equal 1 you wouldn't be able to without going over one because in reality there is no goddamn ...1 because again there is no end to the number.

The number .999 aint shit it's just a way of saying 3/3 which equals one

>> No.10438448

/pol/ is an example of an idiot

>> No.10438487

cry some more

>> No.10438780

Yes it does you fucking brainlet

>> No.10438804 [DELETED] 
File: 321 KB, 546x697, 10333444-1479822591311.png [View same] [iqdb] [saucenao] [google] [report]

Why are you even talking still when you already lost? Rope yourself you fucking baffoon.

>> No.10438810

This is my first reply in this thread you braindead subhuman
.999... /= .000001
.999... Doesn't end

>> No.10438861

1/9 = 0.111...
8/9 = 0.888...
9/9 = 0.999...

>> No.10438869

Thank you for confirming what I just said
Learn to read next time

>> No.10438882
File: 154 KB, 640x398, Alberta-Industrial-Heartland.jpg [View same] [iqdb] [saucenao] [google] [report]

If 0.999...=1
then 0.999...8=0.999...
and 0.999....7=0.999...8
and so on
therefore 0.000...=1

>> No.10438893


>> No.10438900
File: 98 KB, 1200x900, nysw7k-b88582437z.120151203130923000g5mdhska.10.jpg [View same] [iqdb] [saucenao] [google] [report]

Who cares about that ...8? its never coming anyways. Might aswell throw a ....73 in there

>> No.10438910

>and so on
flesh this out a bit

>> No.10438916

>then 0.999...8=0.999...
Isn't correct

>> No.10438927

You can't terminate a recurring decimal at an arbitrary point and say it's equal to another recurring decimal.

>> No.10438931

is too

>> No.10438937
File: 71 KB, 800x536, s3.reutersmedia.net.jpg [View same] [iqdb] [saucenao] [google] [report]

I didnt make it through the whole video, got stuck on 9:59:59...

>> No.10438940

How about 0.999...=1.000...?

>> No.10438947

As long as you don't terminate either decimal that equation is correct

>> No.10438952

and 0.999...888...=1.000...?

>> No.10438955

oh bullshit, terminate on the right just as you please

>> No.10438960

Life gets so much easier when you figure out how to differentiate semantic arguments from ones of substance. "numbers" are symbols for abstract concepts that can describe lengths and amounts

Does the symbol 0.999... represent the infinite series 1/(10^k), or does it represent it's sum? If it's the sum, it's 1, but if you wanted to say 1 why not just 1? If it's not the series, then it can't be compared to any real number, but then why is it written sort of like a number? Either way, who cares? Not me.

Most philosophy is rubbish, but study pragmatism.

>> No.10438962

0.999...888... = 0.9... = 1

>> No.10438964

>who cares? Not me
>writes a wall of text

>> No.10438967


>> No.10438968

Both 'proofs' use infinite series in their premises. That's literally the problem.

>> No.10438970 [DELETED] 
File: 69 KB, 200x200, julie_steinbacher.png [View same] [iqdb] [saucenao] [google] [report]

0.999.... == 0. ... 01. Nice try you worthless sack of shit.

>> No.10438971

You're wrong anon
Implies the number is decreasing, which doesn't make it .999...

>> No.10438975

As mathematics student i can tell you 0.9999is a defined number and there is a space between 0.9999 and 1 for example 0.99995 but if there is no space between 2 numbers p.e. 0.9'(' stands for ongoing ) there is no countable number between 0.9' and 1....further the left side of the picture is the right method to get the value for x ...the ' is resembled by the .... (Sry for bad english im german)

>> No.10438978

0.9...8...7...32...1...76352...42... = 0.9... = 1

>> No.10438981

anything after '...' is zero

>> No.10438984

>0.999.... == 0. ... 01
No it doesn't
.999... Goes on for eternity, if you know the end of the sequence then it is just an infinitesimal number, therefore it isn't .999...
You are either baiting or genuinely retarded

>> No.10438988

It's boutta get even more ironic

I'm gonna go ahead and prove the second option I said was true and 0.999... is not a number to save time because that's where this debate always leads eventually

I hope we can agree that
if 0.999... is a number, 0.999... is irrational

From the definition of equality of real numbers (no number in between)
if 0.999... is a number, 1=0.999...

So if 0.999... is a number, 1 is irrational
1 is not irrational

Therefore 0.999... is not a number

>> No.10438992

You're looking at it the wrong way
Imagine you've got 2 cars driving next to eachother on a long road, printing 9's onto the path behind them
These cars are printing the same number
At some point, the 2nd car decides to stop printing 9's and start printing 8's
The two cars are now printing different numbers, and the gap between those numbers will continue to grow forever.
0.999... = 1 = 1.000... (closest number to the right of one)
Though that might be going a bit to far for the people in this thread

>> No.10438993
File: 52 KB, 1024x576, 715928128-norilsk-industrial-area-chimney-architecture-factory.jpg [View same] [iqdb] [saucenao] [google] [report]

0.9...a cat...mitch hedberg...3...(you)...=1?

>> No.10438994

No, it represents the number repeating itself

>> No.10438997

>0.999... is irrational
retards say the darndest things

>> No.10438999

>.999... is irrational
But can't you represent it as a fraction, 3/3?

>> No.10439001

0.1 = 10^-1
0.01 = 10^-2
0.001 = 10^-3
0.000...1 = 10^-inf = 0

>> No.10439002

https://de.m.wikipedia.org/wiki/0,999… answer of your question I guess

>> No.10439009
File: 26 KB, 645x773, 1511812775109.png [View same] [iqdb] [saucenao] [google] [report]

>0.000...1 = 10^-inf = 0

>> No.10439023

Ok that's wrong but the original point still stands.

Decimals are an engineering format, fractions are the true representations of numbers. There's no such issue in fraction form and no need for this ... bullshit.

>> No.10439043
File: 498 KB, 680x649, brainletSlur.png [View same] [iqdb] [saucenao] [google] [report]


>> No.10439046


[math] \displaystyle
\boxed{0 < p < 1} \\
p^n-1 = (p-1)(p^{n-1}+p^{n-2}+ \dots +p+1) \\
\dfrac{p^n-1}{p-1} = \sum \limits_{j=0}^{n-1}p^j \\
\lim_{n \to \infty} \dfrac{p^n-1}{p-1} = \lim_{n \to \infty} \sum \limits_{j=0}^{n-1}p^j \\
\dfrac{0-1}{p-1} = \sum \limits_{j=0}^{\infty}p^j \implies \dfrac{1}{1-p} = \sum \limits_{j=0}^{\infty}p^j

>> No.10439104

the fuck is this supposed to prove??

>> No.10439111


>> No.10439122

I know what a geometric series tell me what it is you're trying to prove buddy.

>> No.10439128


>> No.10439164

How so? Your final equation holds

>> No.10439186

1 - 0.999 = 0.001
The one who agree with this, please suck my cock

>> No.10439206

>my cock
sounds about right

>> No.10439222

How much greater than 0 is it?

>> No.10439265

p=0.1 \\
\dfrac{1}{1-0.1}=\frac{10}{9} = 1 + \frac{1}{9} \\
\sum_{j=0}^\infty 0.1^j= 1 + \sum_{j=1}^\infty 0.1^j \\
9+1=9+9\sum_{j=1}^\infty 0.1^j \\
1=9\sum_{j=1}^\infty 0.1^j \\

>> No.10439291

Oh so it's literally just the 0.000...1=0 circular reasoning argument but with Latex?

>> No.10439296

point at the failing line
instead of making hand wavy overemotional gasps

>> No.10439314

line 4 of your first post.
p^n goes to 0 with infinity.

I know what you're going to say, and the problem is actually on the right hand side of the equation. You can't keep it in series form once you take the limit. You have to take its sum using the identity you used in the line above.

>> No.10439326

>line 4 of your first post.
>p^n goes to 0 with n->infinity.

so I'm good
if that's your objection, I simply don't care

>> No.10439336

>I don't care that I'm wrong
good for you
bye bye

>> No.10439353

that's just a variation of 1/inf

>> No.10439364

Other guy is a retard who didn't read the second part of my post. Don't be like other guy. Read the second part of my post.

>> No.10439370

>can't keep it in series form once you take the limit.
[citation needed]

>> No.10439388

you cant compare rational and irrational numbers

>> No.10439400

well fuck, there goes my theory that 3 < pi

>> No.10439404

OP is stooped.
0.9> = 1.0>
Because the point is infinitly small the point doesnt exist.
like relativity no one fucking notices that small of a disturbance.
BTFO half cup fool nigger.

>> No.10439407

the pills won't help if you don't take them

>> No.10439408

Ok forget the second part of what I said actually. it is p^n that's wrong.

c=p^n as n->inf
b=p^-n as n->inf
cb=(p^n)(p^-n) as n-> inf
cb=p^0 as n-> inf
if c=0, cb=/=1
therefore c=/=0

inb4 you just post wolfram instead of actually using reason like a human being

>> No.10439410

tell me how large the distance between 0.9> to 1.0>
write it.
write it.....

>> No.10439419

>just post wolfram
it's done already
>reason like a human being
I'm sure WA doesn't calculate it, it reads it from a database that a human mathematician created.

>> No.10439428
File: 9 KB, 218x231, duuude.png [View same] [iqdb] [saucenao] [google] [report]

that scribble, my eyes
use latex you beast
or at least write it on paper using normal math notation and send the picture

>> No.10439430

appealing to authority in an argument of logic is nothing short of conceding defeat

>> No.10439431


>> No.10439435

>I know more math than WA but can't figure out how latex works

>> No.10439439

I've written countless homeworks and lab reports in latex
But why the fuck would I take the time just so a couple NEETs on 4chan can read my post in 5 less seconds?

>> No.10439443

>why write math when talking math

>> No.10439444

who gives a fuck as long as the information is there

are you gonna make a reply or not?

>> No.10439445

>as long as the information is there
it isn't, it's just madman scribble

>> No.10439446
File: 112 KB, 953x613, C7473FA965194B0B8FE526924E00C01D.jpg [View same] [iqdb] [saucenao] [google] [report]

>> No.10439449

what's an infinitesimally small distance

>> No.10439450

so if you cancel the nines, x=
nothing? is x an empty number?

>> No.10439451

this just means that infinitesimals don't exist because space is continuous, it's the same thing as with Zeno's paradoxes

>> No.10439452

are you retarded? What don't you understand, besides the fact that you're wrong?

>> No.10439453


>> No.10439458

Just admit you're wrong, freak.

>> No.10439466

there are no infinitesimals in R
in the filed of the reals the convergent series 0.99999... is equal to 1.
your argument would be valid in the hyperreals (*R)

>> No.10439479

sure, me, WA, wikipedia, every math course in every university everywhere

We're all wrong, thank god we are now saved by the 4chan mathjesus, who writes to us in zodiac killer scribble

>> No.10439482

I'm glad you've finally admitted defeat, oh good champion of math

>> No.10439492

I see your deduction capabilities are intact.

>> No.10439580



No, because 0.00..1 is the next number after 0. By your logic 1 = 2 because there is no number between them (in the domain of natural numbers).

>> No.10439587

>every real number is DEFINED
It's really fucking dumb when people use model processes to try and explain reality.

We didn't DISCOVER the Bayer Process. We INVENTED it. We MADE A PROCESS. It produces a result. This result is a direct consequence of a process, not a fact of the nature of aluminum. For fuck's sake. We didn't "bring out the natural aluminum." We fundamentally modified a reality.

>> No.10439592
File: 54 KB, 625x325, retard.jpg [View same] [iqdb] [saucenao] [google] [report]

By your logic Z is R

>> No.10439601
File: 60 KB, 442x509, nytRiitti.jpg [View same] [iqdb] [saucenao] [google] [report]


>> No.10439622

How so?

>> No.10439625

>living rent free in your head

>> No.10439627

Will people ever stop falling for this bait?

>> No.10439632

Not him but you're assuming that
[math]|(0,1)|=\aleph_0[/math] (this is wrong btw)
Which is probably what he's getting at

>> No.10439909
File: 2.06 MB, 2976x3968, IMG_20190305_153826.jpg [View same] [iqdb] [saucenao] [google] [report]

>> No.10439944

>let's pretend finite is infinite

>> No.10440025 [DELETED] 
File: 53 KB, 685x567, 10349128-1547749908968.jpg [View same] [iqdb] [saucenao] [google] [report]

Stop trying, just admit you've lost.

>> No.10440063

>that autistic looking handwriting
You should have been drowned at birth

>> No.10440067

where did i pretend that finite was infinite?

>> No.10440071

autistic looking handdrawing for an autist (you)

>> No.10440080

prove him wrong instead of spouting ad hominems

>> No.10440083

8.99... = 9 though

>> No.10440091

Nayeth! Thyne logic hath no bearing on the purity of my argumentation!
0.000... - 0 > 0 since therewith following mine ellipsis there beeth an 0.000...1!

>> No.10440105

Then lick my boiclit

>> No.10440106

0.00...1 isn't a number though
If it were then >>10439632 would be true because you could create a bijection
By having f(1)=0.00...1, f(2)=0.00...2, etc.
This is wrong though, see https://en.wikipedia.org/wiki/Cardinality_of_the_continuum

>> No.10440110

by showing finite examples
and alluding that the infinite case is similar

>> No.10440130

not alluding but reasoning that the infinite case is similar...

or do you see any fallacies?

>> No.10440134

how does the 3rd row equal the 4th row?

>> No.10440165


for All natural numbers n serie [math]\sigma_{i=1}^n 9/10^n [/math]
is less than one. But the limit is one.

>> No.10440169

It's a geometric sum

>> No.10440171

infinity changes everything

>> No.10440178

Congratulations on proving every mathematician ever wrong internet warrior.

>> No.10440179

>.33333... = 1/3
>3×(1/3) = 1
>3×(.33333...) = .99999... = 3×(1/3) = 1

>> No.10440249

This is what I was thinking, is the whole .999... = 1 issue just a result of using a base 10 system? I've never thought of how the choice of base affects the "decimal" representation of fractions.

>> No.10440255

>just a result of using a base 10 system
nah, in base 2

in base 16

>> No.10440346

so what part about infinity didn't you understand?

>> No.10440355


>> No.10440365

>next number after 0
wanna know i know you never studied math seriously?

>> No.10440409

What would be a good explanation of why this is false? Would it be sound to say it is because there exist a number between any two other real numbers?

>> No.10440422

I already did. Why are redditors always this incompetent?

>> No.10440435

basically yes. also that decimal expansion doesn't work in a way that you can write 0.000...1, there is no such thing as putting a 1 after "infinite" zeroes.

>> No.10440444

why the quotes?

>> No.10440454

because infinity is not a number or a quantity per se

>> No.10440489

not a number, but the definition does use the word quantity

An unbounded quantity that is greater than every real number.

>> No.10440505

the wikipedia definition uses neither.

>> No.10440520

No you didn't
refer to >>10439445

>> No.10440580

>Why is this even still up for debate?
It's not. 0.999...=1

What horrible thing happened in your childhood that you think everyone who doesn't like you is just offended? You're not even offensive, just annoying. That's it. There's no deeper layer to it.

>> No.10440655
File: 120 KB, 634x815, IMG_1109.jpg [View same] [iqdb] [saucenao] [google] [report]

Nigger, you're retarded. I'm telling you, 0.999 isn't equal to 1

>> No.10440716

You didn't say .999 in any of your posts

>> No.10440846 [DELETED] 

So are you pointing out that arithmetics are basically flawed?

Yes we can agree with this.

So this agreement would end these stupid threads forever?

>> No.10441017

>please don't give me correct answers
Ok. (the leading zeros are for formatting)
01x = 0.999
02x = 1.998
03x = 2.997
08x = 7.992
09x = 8.991
10x = 9.99
There's one less trailing decimal so if x=0.999... then 10x has one less after infinity then 9x does. While related this isn't a answer to the question you asked so you can still pretend you're correct without issue.

>> No.10441025

this is why i hate decimals

>> No.10441103
File: 55 KB, 1080x1920, Screenshot_20190305-232247.png [View same] [iqdb] [saucenao] [google] [report]


>> No.10441236
File: 70 KB, 640x1136, IMG_1161.jpg [View same] [iqdb] [saucenao] [google] [report]

0.11111111... * 9

>> No.10441245


>> No.10441298

I fucking love the demonstration that 0.999 is equal to 1 without buying into it. It's like ye old troll physics comics but if someone shitposted in academy. And people are SPASTIC about it.

>> No.10441380

0.999... is not a number. It is a nonsense phrase created with symbols.
If it is a number, then show it to me. Show me an infinite string of 9s after a decimal point. "..." is not an infinite string of 9s and it is not a sufficient substitute.

>> No.10441389

Based retard. The reals have certain mathematical properties. It is a complete metric space which means it's defined in terms of the completeness axiom, which means that every bounded sequence has a least upper bound. The hyper reals (the field extension where infinitesimals are defined). This means every cauchy sequence is convergent which means that the argument is true.

Any 2 different reals have an uncountably infinite number of numbers between them (nonzero measure). Are there an infinite amount of numbers between the limit of the sequence and 1? No, there are zero

>> No.10441406
File: 18 KB, 637x631, dumb_wojak_5.png [View same] [iqdb] [saucenao] [google] [report]

Pi is not a number. A whole lot of numbers after a decimal and then a "..." because of weak excuses like "we can't calculate that" is not a number. I like my numbers with a beginning and an end.

>> No.10441416

>If it is a number, then show it to me

>> No.10441422

[eqn] 0.9999.... = 0.9 + 0.09 + 0.009 + ... [/eqn]
[eqn] = 9(0.1 + 0.01 + 0.001 + ...) [/eqn]
[eqn] = 9 \sum_{n = 1}^\infty (\frac{1}{10})^n = 9( \sum_{n = 0}^\infty (\frac{1}{10})^n - 1) [/eqn]
[eqn] = 9(\frac{1}{1 - \frac{1}{10}} - 1) [/eqn]
[eqn] = 9(\frac{10}{10 - 1} - 1) = 9(\frac{10}{9} - 1) [/eqn]
[eqn] = 9(\frac{1}{9}) = 1 \qquad \square [/eqn]

There are no assumptions in this proof other than that you need to accept that 0.999... can be expressed as a series which turns out to be a geometric series whose limit is easy to calculate.
Anyone who thinks they can dispute this has no hope achieving anything with mathematics.

>> No.10441436

nigger why do you write your 9 like a g

>> No.10441527

>Arguing based on a fundamental misunderstanding of definitions
LMAO at you brainlets

>> No.10441539

That's literally all this board is along with a handful of self-hating actually knowledgable people

>> No.10441548


1 is a number, 0.999... is not

>> No.10441647

>1 is a number, 0.999... is not
Impossible, they're the same thing. They're either both a number or neither of them are. So you're saying 1 is not a number?

>> No.10441650

it's not a number? well 1/9 is not out of |N nor Z but it is in Q and |R

>> No.10441870

Man, I know you're right but fuck you. Your way of writing [math] \mathbb{R} [/math] and [math] \mathbb{N} [/math] triggers me more than faggots saying 1≠0.99...

>> No.10442070

What if we constructed a countable set of numbers that includes all reals?

And we all know Wikipedia is correct about everything.

>> No.10442081
File: 5 KB, 221x250, 1505942714133s.jpg [View same] [iqdb] [saucenao] [google] [report]


How about you spergs learn what a real number is?

>> No.10442599

>And we all know Wikipedia is correct about everything.
about math it typically is, yes
wikipedia math articles are often edited by career mathematicians and professors

>> No.10442604

hello, undergrad
did you feel smart last week when the prof introduced dedekind cuts?

real men use cauchy sequences

>> No.10442608

>What if we constructed a countable set of numbers that includes all reals?
why don't you ask Cantor and see what he says

>> No.10442675

You probably added lots of 1 to represent 0.111... but you have to divide 1/9 to get infinite ones
I as well get 0.999... if I just write myself lots of ones

>> No.10443386

I would have just said that the constant coefficient is [math]0.9[/math], not [math]9[/math], but overall well done. I love seeing the truth [math]\LaTeX[/math]ed out.

>> No.10443404

>he thinks the multiplication rule of limits holds for infinite limits
Based retard

>> No.10443493
File: 38 KB, 713x673, proof.png [View same] [iqdb] [saucenao] [google] [report]

>> No.10443601

ok so what's 1-0.999...?
you keep doing this but you never stop, it's 0.0000... by induction all the next ones are 0 too so it's just 0

>> No.10443628

c=p^m as m->inf
b=p^-n as n->inf
cb=(p^m)(p^-n) as m,n-> inf
cb=p^(m-n) as m,n-> inf

>> No.10443787 [DELETED] 

>[math]0\times\infty[/math] cannot equal [math]1[/math]
[math]0\times\infty = \lim_{x\to 0} x\times\frac{1}{x} = 1 \\
0\times\infty = \lim_{x\to 0} x^2 \times\frac{1}{x} = 0 \\
0\times\infty = \lim_{x\to 0^+} x\times\frac{1}{x^2} = \infty \\
0\times\infty = \lim_{x\to 0^-} x\times\frac{1}{x^2} = -\infty
They're called indeterminate forms, retard. I bet you think [math]1^\infty = 1[/math] as well.
Leave immediately and do not come back until you have taken a high school calculus course.

>> No.10443809

>[math]0\times\infty[/math] cannot be [math]1[/math]
They're called indeterminate forms, retard. I bet you also think [math]1^\infty[/math] cannot be anything but [math]1[/math].
Leave immediately and do not come back until you have taken a high school calculus course.

>> No.10444035

dy/dx is undefined, dx is 0

>> No.10444082

10s = 9.999....
s = 0.999......

10s = 9.999....
-s = 0.999...
9s = 9.000...
s = 1.000....

This is how numberphile explained it, but a better way to explain is

10s = 9.999....
s = 0.999.....

10s = 9.999...
- 0.999...s = 0.999...
9.00000000000000000......1s = 9
(9.00000000000......1s)/(9.000000......1s) this is sort of like the same question as ∞/∞ but we could argue 9/9.0000000000....1 = 0.999999..... but 0.000000000....1 = 0 because 0.99999 = 1, an infinitesimal gives you the illusion that 9 = 9.0000001 but really 0.999999 strings on for infinity so this one googleplexth is undefined.

>> No.10444206
File: 121 KB, 220x286, infinitely based.png [View same] [iqdb] [saucenao] [google] [report]

>"To those who ask what the infinitely small quantity in mathematics is, we answer that it is actually zero. Hence there are not so many mysteries hidden in this concept as they are usually believed to be." -Leonhard Euler

>> No.10444219
File: 242 KB, 1200x1211, 1551873509686.jpg [View same] [iqdb] [saucenao] [google] [report]

I will say this one last time, you FUCKING, fucking retards.

0.333333..... is an incomplete expression. It represents 1 as being constantly divided by 3, therefore 1/3.

Multiply 0.33333... and you get 0.9999....
They are both incomplete expressions. It's just a inherent problem of the numbering system humans invented.

>> No.10444225

Worst post ITT

>> No.10444256

>It represents 1 as being constantly divided by 3
No, [math]\cfrac{1}{3\cdot\cfrac{1}{3\cdot\cfrac{1}{\cdots}}}\ne0.\bar9[/math]
If you take the partial fractions you'd see it doesn't converge

>> No.10444262

sorry, meant that it approaches zero

>> No.10444265

also meant [math]0.\bar3[/math] lol

>> No.10444267

Just use convergence test and geometric series formula

>> No.10445983

Missing a for all n bigger than N there buddy.

>> No.10445990

Do you think it's necessary to learn aboit dedekind cuts because some nice idea is used in the proof or something like that? I was only taught the method with the equivalence classes of Cauchy series recently.

>> No.10445991

>1/3 = 0.333333...
>2/3 = 0.666666...
>3/3 = 0.999999... = 1

>> No.10446224
File: 12 KB, 279x288, 1503296250350.jpg [View same] [iqdb] [saucenao] [google] [report]

>1/3 = 0.333333...

>> No.10446264

/pol/ lives rent-free in everyone's minds. they don't even think about you

>> No.10446361

Get on the next level.


You don't trust me? Do ...9999*....999 and admire the result.
Or just do 0-1 in a naive way.

>> No.10446728

wew you're retarded

>> No.10447278
File: 396 KB, 562x518, 1551249868908.png [View same] [iqdb] [saucenao] [google] [report]


>> No.10447305

that statement isn't even true now fuck off
the x in 10x=9.999 is different than x in 9x=9 why the fuck you tryin to say 1=.999

>> No.10447371

What are you talking about?
I think you've misunderstood
x = .999
10x = 9.999
10x - x = 9
9x = 9
/9 /9
x = 1
Therefore .999 = 1

>> No.10447373

thats literally valid in the p adics you fucking undergrad

>> No.10447374

>valid in the p adics
So it's nothing

>> No.10447387

its not even prime you moron
nicely done showing off that you dont know what youre fucking talking about though

>> No.10447390

You are the biggest brainlet ITT
Not even worth my time to explain how wrong you are
Never post on /sci/ again for the sake of the rest of us

>> No.10447462

because you are trying to say x=.999=1 by using two different equations, the fuck you smoking bro?

>> No.10447576

And you failed.

>> No.10448018

Please explain your reasoning to me

>> No.10448509

Although, zero is an absence of quantity

>> No.10448888

It's the same equation
You're allowed to add, subtract, divide, multiply, and take the root of one side assuming you do the same to the other side and maintain the equality
You should know this from elementary school

>> No.10448923

Quads of truth and this anon is still wrong hahahaha

>> No.10449785

1/3 = 3/10 + 1/30
= 0.3 + 1/30
= 0.33 + 1/300
= 0.333 + 1/3000
= 0.3... + 1/inf
= 0.3... + 0
= 0.3...

>> No.10450713

Based Euler

>> No.10451532

exactly 1=/=.999 you just fucked up OP

>> No.10451622


>> No.10451904

There's a lemma stating that two real numbers are unequal to each other if you can find at least one number between both of them.

You wont find one between 0,9999... and 1

>> No.10451937

>Why is this even still up for debate?
Because /sci/ still takes the bait after 9 years of existence.

>> No.10453044

how is that induction?

>> No.10453082

>de bait

>> No.10453413

it's shit

anon's lemma: two numbers are equal if they're equal

>> No.10454237

top b8

>> No.10454272

>Unironically using limits which are just as unconstructive as infinitesimals, R and all the other 0.999... garbage

>> No.10454288

fuck off back to >>>/x/

>> No.10454293
File: 58 KB, 1280x720, maxresdefault.jpg [View same] [iqdb] [saucenao] [google] [report]

Not so fast... This guy want to have a talk with you.

>> No.10454294


>> No.10454296

pedos don't count

>> No.10454304

A: "your proposed mathematical therorem doesn't sufficently hold"

B: "Wow you're a pedophile"

>> No.10454309

>[math]\pi[/math] doesn't real!!! REEEEE

>> No.10454315

>bus stop masturbator screams at people walking by

sorry, no Fields medal for you

>> No.10454319

please, for holy fuck's sake, don't do this. reads like the function 9 applied to the parameter 0.1. what does it cost to add the multiplication operator?

>> No.10454329

Every response before this verified your claim.

>> No.10454405

I'm sure you agree so far. However, here's the thing about infinite sums, they
are — by definition — equal the limit of their partial sums.
That means:
So that [math]0.999999...[/math] is in fact equal to the limit of the following sum:

Which is obviously equal to 1. So begone, brainlet.

>> No.10454412


>> No.10454415

WTF my latex got messed up but it worked in the box where you try it. I hate this.

>> No.10454444

thats a weird name for a variable

>> No.10454483

If I had a cake and a paper thin slice of cake was taken from me, I might as well have a full cake.

>> No.10454496

Is this a hot new meme or are you really that autistic

>> No.10454498

Use \text{*put text here*} if you want to write in math mode

>> No.10454504

Anti-polsmokers are just autists that fear political discussion. They use pol an excuse to invalidate whatever that person just said if it isnt not political. Ironically anti-polsmokers make things political.

>> No.10455887

Literally all the things you listed are rigorously defined you retard lmao

>> No.10455910
File: 18 KB, 326x294, bike.jpg [View same] [iqdb] [saucenao] [google] [report]


>we invent, not discover, emergent processes in already existing systems

People invent the signifiers to describe the process. The process itself already exists in potential.

>> No.10455965

>already existing systems
That we invented.

>> No.10456621
File: 175 KB, 971x580, BergWilder.jpg [View same] [iqdb] [saucenao] [google] [report]

>Literally all the things you listed are rigorously defined

>> No.10456625
File: 264 KB, 1149x700, BergWilder2.jpg [View same] [iqdb] [saucenao] [google] [report]

>all the things you listed are rigorously defined

>> No.10456627
File: 265 KB, 1149x700, BergWilder3.jpg [View same] [iqdb] [saucenao] [google] [report]

>rigorously defined

>> No.10456652

Just go full Pythagoras, it solves the problem

>> No.10456681

Is there number between it and 1? No? It's one. Welcome to real numbers.

>> No.10456712

Always post a jpg image of a charlatan and crook if you want to get believed on /sci..

>> No.10456714



>> No.10456731

Fuck you and your bullshit opinion

>> No.10456733

>i have no argument

>> No.10456745

By infinitesimal they mean infinitely small.
By distance they mean difference (think [math]\|x-y\|[/math])
By always they mean that no matter how many more digits you consider, you always get some difference; that is, you never get to exactly 1.

Where they are wrong, however, is in how infinite sums work. You can get arbitrarily close to 1 by factoring a sufficient amount of digits, so it equals 1.

>> No.10457110

>after infinity

>> No.10457175

Neither of those two statements are contradictory.

x = 0.999... = 1

>> No.10457215

Why does this literal zero effort shitpost continually get responses and why am I responding to it too?

>> No.10457257
File: 78 KB, 562x467, 1523535101781.jpg [View same] [iqdb] [saucenao] [google] [report]

>He has to use first principles

>> No.10457401

wow Euler was based

>> No.10457461

it's pronounced inductriontation

>> No.10457568

then 1 = 3/3 = 3/3
1/3 = 0.333...
1/3 * 3 = 0.999...
0.999... = 3/3 = 1

>> No.10457610

>even this schizo retard can't deny the undeniable prowess and rigor of based Rudin

>> No.10457832

ok let's say we have this:
[math]\lim_{x\rightarrow\infty}-\lim_{y\rightarrow\infty} , (x,y) \in \mathbb{N}[/math]
The problem with this is that it doesn't has any meaning but it would if we wouldn't write it up like an actual retard.

This functions can be executed by something in reality, f.e. you could try to count from x to inf without ever raising y or you could go like x+1 and y+1 or the other way -> y+1 and x+1. The way how the function is executed is hidden because inf says just "heh I'm totally random until I'm too big for you little boy".

And you actually didn't mean inf when writing this, you're meaning "arbitrary close to inf", not inf itself. If so then just write it down:

[math]\lim_{x\rightarrow k}-\lim_{y\rightarrow a} , (x,y) \in \mathbb{N} , (k,a) \in \textup{arbitrary high}\in
\mathbb{N} \textup{ simultaneously counted per cycle}[/math]

>> No.10457864

The decimal system was a mistake

>> No.10457873
File: 57 KB, 550x467, 41948209381.jpg [View same] [iqdb] [saucenao] [google] [report]

Funniest thing I've ever seen on this board

>> No.10457903

Literally illegible. Take your pills, Wildasberger.

>> No.10458161

it's not 1, but for all intensive purposes its 1.

>> No.10458649

For all intents and purposes*, it is 1, because it is 1.
Also, if you study it intensively, you will see that it is 1.

>> No.10458664

>you actually didn't mean inf

>> No.10458668

>it's not 1,
it's exactly 1

>> No.10458680

Constructivists literally don't believe in excluded middle lmao gtfo with your nonsense axioms

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