Quantcast
[ 3 / biz / cgl / ck / diy / fa / g / ic / jp / lit / sci / tg / vr ] [ index / top / reports / report a bug ] [ 4plebs / archived.moe / rbt ]

Become a Patron!

/sci/ - Science & Math


View post   

[ Toggle deleted replies ]
File: 44 KB, 862x266, Point_9_Repeating.png [View same] [iqdb] [saucenao] [google] [report]
11331532 No.11331532 [Reply] [Original] [archived.moe]

Why is this true?

>> No.11331554

>>11331532
It isn't really unless you are talking about the symbols.

>> No.11331600

>>11331532
Also, there is a drawing of a cock on the one, so you might want to use a different image next time.

>> No.11331631

>>11331554
>>11331600
What do you mean?

>> No.11331700

It isn't if you understand the notation of an infinite series doesn't actually mean an infinite number of sums, but the limit to which the sequence converges.

>> No.11332016

astounding

>> No.11332054

>>11331631
What he means is that 0.9999.... < lim{x -> 1-} (x)

>> No.11332123

>>11332054
What are you saying?

>> No.11332183

>>11332054
low iq and wrong.

>>11331631
what he means is

0.9999... ~~= lim {lacid benis -> errect benis} (x) ^ bagina

>> No.11332277

>>11331532

You can use limits to prove this but I'll walk through the full argument instead of just invoking limits cold.

First choose any number 0 < x < 1, then there's some y = 1 - x, and y is some small positive number.
y has some decimal representation, choose enough zeros that something like .0000000000000000001 is smaller than y.
Then x < 1 - .0000000000000000001 = .9999999999999999999, which is still less than .9999999999999999999999999999999 going on forever.

So then any number you choose smaller than 1 can be proven to be strictly smaller than .999 repeating.
And I assume we can agree that .999 repeating isn't any larger than 1, so it must be equal to 1.

>> No.11332283
File: 10 KB, 618x175, Slope Proof .999...≠ 1.png [View same] [iqdb] [saucenao] [google] [report]
11332283

>>11331532

If .999.. = 1 then 1=0.

>> No.11332284

What is the difference between this and 0.999...?

>> No.11332286

>>11331532
dude just means if you want your dick to fit into a hole with a diameter very close to your dicks diameter it will fit even tho your ruler was not that precise. there is allways lub also.

>> No.11332288

>>11332283
The real numbers are dense, so induction does not work

>> No.11332293

>>11332283

The limit of that series of functions actually is f(x) = 0 though.

>> No.11332307

>>11332277
If 0.999999 = 1 then 1.00....1 = 1. Therefore everything is equal.

>> No.11332309 [DELETED] 

>>11332277
Why isn't 0.999... equal to something no more nonsensical than a number with infinitely-repeating digits, i.e. there are no numbers between 0.999... and 1? Who gives a fuck. It is no more nonsensical to say 0.999... is infinitely close to 1 as 0.999... is in the first place.

>> No.11332316

>>11332277
Why isn't 0.999... equal to something no more nonsensical than a number with infinitely-repeating digits, i.e. there are no numbers between 0.999... and 1? Who gives a fuck. It is no more nonsensical to say 0.999... is infinitely close to 1 than is 0.999... in the first place.

>> No.11332324

>>11332307
1.00....1 is not really a number. If you have a chain of zeros followed by a 1, then the chain of zeros is not infinite, it would have been longer if you just kept adding zeros.

>>11332316
If there are no numbers between 0.999... and 1, then what is their sum divided by 2?

>> No.11332327

>>11332307
ting is there is nothing equal in nature.

>> No.11332329

The mathematical illiteracy of this board is astounding sometimes.

>> No.11332336

>>11332324
>what is their sum divided by 2?
0.999...

>> No.11332346

>>11332329
Is the one who questions their indoctrination smart or stupid?

>> No.11332351

>>11332123
Hes saying that 0.999999.... is less than the limit of x as x approaches 1 from the left.

>> No.11332354

>>11332336

Then the following argument seems to apply:
.5*(1 + 0.999...) = 0.999...
1 + 0.999... = 2*(0.999...)
1 + 0.999... = 0.999... + 0.999...
1 = 0.999...

>> No.11332369

becuz....0.999 is not 1. It's approximately 1, but it isn't one. You'd have to use the squiggly lines for it to be true.

>> No.11332412

>>11331532
cocky numbers are an entirely different class of numbers than real numbers.

>> No.11332610
File: 9 KB, 216x144, 0≠0.jpg [View same] [iqdb] [saucenao] [google] [report]
11332610

>>11332288
>>11332293

What is the slope of line BZ? How is it different from BW? If you have two different lines with the same slope, then hasn't your number system failed?

>> No.11333219

>>11331532
intuitive and non-rigorous treatment of numbers can get you only so far. once you move past rationals, you have to say how exactly do you define "numbers" and their operations, otherwise you run into inconsistencies. in contemporary mathematics, the symbol 0.999... unarguably stands for the limit of some sequence, and this limit unarguably equals 1. feel free to invent your own number system where 0.999... is not 1, but you have to be precise. no bullshit explanations like "it only gets closer but never actually gets there".

>> No.11333285

>>11331532
because infinitesimals exist

>> No.11333310
File: 2.90 MB, 638x360, iowa.webm [View same] [iqdb] [saucenao] [google] [report]
11333310

Pajeet and highschooler central - the thread. Very embarrassing for this board, seeing the very low intelligence of the posters in this thread. I think many good people left this board because of threads like these.
Besides: have you people not been there for the last 100 times this exact thread was made in the last year? Are all of you so new here?
I am very disappointed... Perhaps I will leave.

>> No.11333327

>>11333310
Please don't leave, what kind of threads and replies do you like so we can be more satisfactory next time?

>> No.11333341

>>11333327
Threads about actual things and concepts, not arguing about semantics or things that don't have any meaning. Replies by informed and curious people, not by narcissistic schizos with not enough attention span to look up what real numbers are or what an equation even means. Also threads that have not been made literally hundreds of times before.

>> No.11333342

>>11331532
It’s just the limit of a convergent series, you cunt

>> No.11333528

Fyi the real numbers are constructed as equivalence classes of Cauchy sequences, which is why everyone always invokes the limit argument and why that argument even makes sense in the first palce.

>> No.11333555

>>11331532
real answer: it isn't true
hyperreal answer: depends on how you are defining the numbers

>> No.11333618 [DELETED] 

>>11332354
When something doesn't make sense, you need to consider the possibility that it is you who don't understand something. Have you considered that possibility?
5*(1 + 0.999...) = 9.999... obviously
>1 + 0.999... = 2*(0.999...)
>1 + 0.999... = 0.999... + 0.999...
point?
>1 = 0.999...
non sequitur, assumes 0.999... can equal 0.999... 0.999... i nonsensical in the first place. There's no reason to assume one infinity equals another, even when composed of the same number.

>> No.11333621

>>11332354
When something doesn't make sense, you need to consider the possibility that it is you who don't understand something. Have you considered that possibility?
5*(1 + 0.999...) = 9.999... obviously
>1 + 0.999... = 2*(0.999...)
>1 + 0.999... = 0.999... + 0.999...
point?
>1 = 0.999...
non sequitur, assumes 0.999... can equal 0.999... 0.999... is nonsensical in the first place. There's no reason to assume one infinity equals another, even when composed of the same number.

>> No.11333705
File: 40 KB, 657x527, help.jpg [View same] [iqdb] [saucenao] [google] [report]
11333705

>>11332324
>The real numbers are dense, so induction does not work
>0 isn't a number
lol keep the excuse coming fren

>> No.11334059

WELCOME
TO
THE MACHINE

>> No.11334069

>>11333555
Based, check'd and kek'd

>> No.11334228

>>11331532
Well if you added a dick to 0.9999... it would be true. Alternatively, remove the dick and it would also be true. Facts.

>> No.11334253

>>11331532
because 1 is not penis1

>> No.11334633
File: 655 KB, 1091x707, Camcorder.png [View same] [iqdb] [saucenao] [google] [report]
11334633

>>11332324
>If there are no numbers between 0.999... and 1, then what is their sum divided by 2?

It depends on whether or not you find it useful to keep count of infinitesimals to that level of detail or not. If you don't find that necessary then half of an infinitesimal is meaningless, like asking what 1/2 means in the set of Whole numbers.

If you want to keep track of such things then you can define an infinitesimal number line. Then:

.999... = [email protected]
(.999...+1)/2 = [email protected]

with @ being like a decimal point marking the transition between Real and Infinitesimal values. You can also include ; to mark infinite and sub-infinitesimal quantities if you want.

([email protected])/0 = 1;[email protected]

>> No.11335000

>>11332307
>1.00....1 = 1
Wrong. You not understanding the terminology and notation isn't our problem.

>> No.11335006

>>11332346
Yes, if they're questioning something obviously true just to be edgy and different.

>> No.11335014

>>11332369
Technically true! .999=/=1.

But .999...=1

The ellipses are actually important.

>> No.11336356
File: 8 KB, 272x185, download-1.jpg [View same] [iqdb] [saucenao] [google] [report]
11336356

Base infinity:

.999... = .999... = [email protected]
1+2+3+4+5+... = 1;(-1/12)@
...999 = 1;[email protected]
(.999...+1)/2 = [email protected]

> A random number generator will output a real number between 0 and 1:

Chance of .5 = @1
Chance of 2 = 0

>> No.11336550

>>11331532
https://en.wikipedia.org/wiki/0.999...

Stop being ignorant of math.

>> No.11336793

>>11336550

https://en.wikipedia.org/wiki/Talk:0.999.../Arguments/Archive_11#Time_to_face_reality

Time to face reality.

>> No.11337474

>>11336793
I accept the reality that retards are allowed to petition Wikipedia to make stupid edits based on not understanding the material nearly as well as they think they do.

>> No.11338264

if it exists...

>> No.11338270

>>11331532
Because infinity doesn't exist.

http://aynrandlexicon.com/lexicon/infinity.html

>> No.11338274

this was a big one... my proudest fap to date... felt powerful

>> No.11338284

>>11336793
how the fuck can 0.999.... = 1 these mathematic nerds blow my mind sometimes

>> No.11338295

Everyone who thinks there is a difference is too low IQ
>OMG HOW CAN 9S EQUAL 1!!!!!

>> No.11338303

Something's isn't right about this. This is the fifth time today that I've coomed to this image. Currently in the afterglow of round 5, I'm meditating on my performance overall, rounds 1-5, looking for properties, but it's weird. Round 4 was anomalous: ~3pm I was in a parking garage restroom with no internet because of all the concrete, but luckily I had the image saved on my phone. I was getting really into it when my phone died sadly. In the desperate heat of the moment I erected a pencil and scribed the formula from memory on the wall of the stall. JUST AS GOOD, and I finished in record time! Felt good at the time, but in retrospect I'm worried this might be some kind of cognitohazzard. If so, it might be malevolent. Then again, perhaps it is benevolent. My inner mathematician keeps asking, what is this shit? I just keep cooming and cooming, and the more I do, the less opaque the truth of it becomes. It keeps happening, but a new prospect vexes me, that maybe I don't really understand it at all. I can't shake that horrible feeling that I don't know it well enough, like I'm missing something somewhere. I've decided to continue researching this inequality I've taken to calling The Wang Theorem. I'll post any Wang Theoretic developments in /mg/, but it might take some time.

>> No.11338304

>>11338295
sorry bro but face reality 0.999 is not = 1

>> No.11338312
File: 112 KB, 953x613, 0.999 = 1.jpg [View same] [iqdb] [saucenao] [google] [report]
11338312

>>11338304

Oh look, it's THIS thread again...

>> No.11338318

>>11338312
i like your picture, but that's proving that 0.999... = 1. not 0.999 = 1

:)

>> No.11338320

>>11338318
learn to [math]LaTeX[/math]

>> No.11338337

>>11332346
>>11335006
>obviously true

...go on

>> No.11339452

>>11338284
How the fuck can 2/2 = 1? It's almost as though math nerds aren't stupid enough to believe that there's only one way to write down a number!

>> No.11339454

>>11338304
True, you need ellipses.

>> No.11339456

>>11338337
>>11338312
Retard who wrote comment 37, read the 12 comment written by the math CHAD.

>> No.11339466

>>11331532
because 1/9 is 0.1111111
So 0.999999 is 9/9 is 1

>> No.11339474

>>11339466
uh let me rephrase
0.111... is 1/9
and 0.999... = 9 * 0.111... = 9 * 1/9 = 9/9 = 1

>> No.11339510

>>11339474
It's sad that people are literally too stupid to understand this simple concept :(

>> No.11339609

>>11339510
Yes. It is funny that you say this, and your sadness is also a thing that is funny. I am and we are, all of us, except you, laughing at your misfortune and the other things.

>> No.11339619

>>11339609
We're both on 4chan instead of outside. To a certain extent, we are all sad.

>> No.11339660

>>11331532
The same number can be represented in different ways.

0.5 = 1/2 = 2/4.
It is not strange that the same number can be represented in different ways, you already know that a fraction can be represented in infinite different ways.

So what you have there is two different representations of the same number.


Further:
We can construct number systems in many different ways.
If we want a system where 1 =/= 0.999.... then 1 - 1 must be different from 1 - 0.999... so therefore 0 =/= 0.000....

>> No.11340754

>>11339660
>1 - 0.999... so therefore 0 =/= 0.000....
Suppose 0.999... actually does not equal 1 (which you should have been doing in the first place, you retarded NPC -- every single concept one intends to assess the truth (or falsity) value of, needs to be considered as if it were true). What, then, would the answer be? It'd probably either be something like 0.000...1, representing an infinitesimal, i.e. 0.000... ending in 1, or, since there is no standard symbol for the appropriate infinitesimal (even if this were the case, one would be defined beforehand) the answer could be "undefined." It most certainly would not be you're purposely retarded answer of 0.000....

>> No.11341519
File: 54 KB, 1024x600, Bow ties are kool. 59983.png [View same] [iqdb] [saucenao] [google] [report]
11341519

>>11339466
>because 1/9 is 0.1111111
>So 0.999999 is 9/9 is 1
>>11339510
>It's sad that people are literally too stupid to understand this simple concept :(

What is sad is that people don't recognize circular logic when they see it.

Who says that .111... is exactly 1/9? Prove it. You'll see it is the exact same question in a different form, so by bringing up 1/9, you have answered nothing.

>> No.11341844
File: 33 KB, 576x1076, consider the following.jpg [View same] [iqdb] [saucenao] [google] [report]
11341844

>> No.11343132

>>11341519
What does 1/9 actually equal, then? Any retarded two year old can say "nuh uh" over and over again. You're on the /sci/, board do some math. PROVE that 1/9=/=.1...

>> No.11343139

>>11341844
Wrong. The middle one is strictly less than .9... and 1. The 1 at the END means that the decimal expression terminates, and thus isn't an infinite series of 9's. Just because you SAY there are infinite 9's between the point and the 1, doesn't mean there are are that many.

>> No.11343802

bump

>> No.11343815

>>11333341
new sci culture these days involves replying to semantic threads and IQ shenanigans. Every time I post something interesting, it gets 0 replies.

>> No.11343827

>>11331532

If you think .999 repeating isn't equal to 1, that means you don't understand what "repeating" means here.

>> No.11343884

>>11338320
Seems like the right place to ask:
What comes into the brackets to enter TeX mode?

>> No.11343897

>>11331631
He's referring to the penis on the digit 1.

>> No.11344899

>>11343897
the fuck are you talking about

>> No.11345302

>>11344899
the penis on the digit 1.

>> No.11345305

>>11332610
They're not different lines.

>> No.11345307

>>11345302
i dont see it

>> No.11345311

>>11333310
Good, leave already.

>> No.11345316

>>11343827
Boi you really showed him

>> No.11345323

>>11341519
long division, retard.

>> No.11347218
File: 45 KB, 640x427, ' 300k.jpg [View same] [iqdb] [saucenao] [google] [report]
11347218

>300k starting

>> No.11347465

>>11332610
line BZ has slope z/.999.... and slope BW is 0, there's no problem here.

>> No.11347786

>>11345316
he's right tho

>> No.11347794

>>11331532
At 39 digits, you're already below the Planck length. Assuming the universe only exists in discrete increments, 0.99999999999999999999999999999999999999 is literally the same physical thing as 1.

>> No.11347799

>>11331532
it's not true

https://www.youtube.com/watch?v=SDtFBSjNmm0

>> No.11348015

>>11347794
You are right in that the universe probably isn't "real".
That still doesn't make 0.99999999999999999999999999999999999999 equal to 1.

>> No.11348182

>>11347799
>15 minutes of the math vlogger on the nature of .9999
I can't do that, anon. The subtle prejudices I harbor towards this mode of exposition could stunt my judgement of the theory. I will not bet against this hazard, and I dare not contemplate the consequences.

>> No.11348212

>>11333621
>infinity equals another
we are comparing numbers
>even when composed of the same number
What's that supposed to mean? Infinities are not "composed of numbers". Infinities and numbers are different concepts

>> No.11348400

>>11348015
>That still doesn't make 0.99999999999999999999999999999999999999 equal to 1.
Numerically, no, but the idea of there being a difference also doesn't matter in the slightest.

>>
Name (leave empty)
Comment (leave empty)
Name
E-mail
Subject
Comment
Password [?]Password used for file deletion.
Captcha
Action