[ 3 / biz / cgl / ck / diy / fa / ic / jp / lit / sci / vr / vt ] [ index / top / reports ] [ become a patron ] [ status ]
2023-11: Warosu is now out of extended maintenance.

/sci/ - Science & Math

View post   
File: 247 KB, 1700x2200, ONETARDS BTFO.png [View same] [iqdb] [saucenao] [google]
11594817 No.11594817 [Reply] [Original]

Now can we stop having these threads and talk about real math and science?

>> No.11594828

>>11594817
I agree that these threads must stop but I disagree about your conclusion

About argument 1: The burden of proof now lies upon you to show that there exists such a number.

About argument 3: Why would 0.999... not be allowed to be manipulated in such a way? It's very clearly a real number and as such these manipulations are legitimate.

>> No.11594829

>>11594817
>Doesn't refute any of the actual proofs, only those which are written specifically for his retard brain to understand.

>> No.11594837

> (0.999... + 1) / 2
circular reasoning, as it must be implicitly assumed for 0.999... < 1 for this to be true.

>> No.11594845

How can it equal one? If 0.999... equals one that means that 0.000...1 is of no value because one minus 0.999... has no effect. 0.999... is less than one because 0.9 is less than one, so what's 0.999...? Should be less than one, but we're told it's one, and that cannot be.

>> No.11594848

>>11594837
burden of proof on you.

>>11594829
not an argument

>>11594828
1. burden of proof is on you to show that it does not exist
2. because infinity. see the proof that 1+2+3+...=-1/12. same shit

>> No.11594853

>>11594848
>durrhurr you cant use circular reasoning in your argument but i can to refute it
you realize these threads are only fun when the person arguing this isnt braindead right?

>> No.11594856

>>11594848
yeah that number exists beside the teapot orbiting the moon

>> No.11594871

>>11594853
If I say that 1 = 2 who has the burden of proof? The psychology of onefags...

>> No.11594877

>>11594817
Congrats, you defeated 3 non-rigorous arguments intended to introduce children to a difficult idea.
now find the flaw in the actual proof >>11591966

>> No.11594927

>>11594877
I just didn't have enough space. I needed to fit all the text on one page for easy circulation.

>> No.11594972

>>11594927
Disprove the actual proof then. It's been provided, so the burden now lies on you.

>> No.11594973

>>11594817
As a onetard myself (I firmly hold that 0.99...=1) I agree with OP that the "proofs" many people provide in these threads are not proofs at all and circular. I commend OP for recognizing faulty logic. There are mathematically illiterate people on both sides.
The truth, OP, is in how you define 0.9999...
If you want all infinite decimal expansions to represent actual numbers the rationals don't suffice and you have to deal with equivalence classes of Cauchy sequences or Dedekind cuts.
Although if you're willing to accept that not all decimal expansions have meaning (so you can stay in the rationals), then using the definition that:
for a sequence of digits a_1, a_2, a_3.... (formally defined as a function f: N -> N from the naturals to the naturals where f(n)=a_n) the number 0.a_1a_2a_3..... is such a number x (if it exists!) that for all rational numbers (i.e. fractions) e>0, there exists a natural number N such that for all n>N,
|0.a_1a_2....a_n - x| < e.

With this definition, we can take each a_i to be 9. Then all that 0.999...=1 is claiming is that for all rational numbers e>0, once you add enough digits, the finite decimal expansion is as close to 1 as e is to zero.
It's rather simple and clearly true. And remember, all it boils down to is how you define 0.999...

How do YOU define 0.999..., OP?

>> No.11595036

>>11594817
this is retarded
saying "clearly seen" is no way to rigorously prove the first point
also 1/3 = 0.33... is not a "decimal approximation- the numbers repeat forever. 0.333 is a decimal approximation, not 0.33... .
I invite 0.999... =\= 1 ists to tell me the supposed "true" decimal representation of 1/3.

>> No.11595069

>>11595036
decimal representation can only express numbers of the form n/10^k, where n,k are integers.

>> No.11595075

>>11595069
Then the whole argument is moot, since 0.999... is not a number.

>> No.11595098
File: 247 KB, 1700x2200, onetard.png [View same] [iqdb] [saucenao] [google]
11595098

Updated version. Fixed some mistakes.

>> No.11595103

>>11595075
its just not rational.

decimal representation can only express *rationals* of the form n/10^k, where n,k are integers.

>> No.11595114

>>11595103
It's already known that you cannot represent irrationals exactly with a decimal expansion, so no, 0.999... is not irrational.

>> No.11595128

>>11595114
*repeating decimal expansion

>> No.11595137

>>11595114
0.999... is irrational. You think it is rational because you think it is 1. Circular reasoning.

>> No.11595144

>>11595137
No, I think it's rational because it is. No irrational number can be written as a repeating decimal. Does 0.999... repeat? Then it isn't irrational.

>> No.11595158

>>11595144
>No irrational number can be written as a repeating decimal.

But that's wrong. Counterexample: 0.999...

>> No.11595163

>>11595098
Honestly, if you don't agree that
9.999... = 9 + 0.999...
then there is no use in even talking another word with you.
The analogy, you are trying to use there, does not work, since that's an entirely different mess about converging sequences vs. non-converging sequences.
If you claim that 0.999... does not converge, or similarly retarded nonsense, then you may just as well start your own mathematics from zero. Leave us alone, unless you find something interesting doing that.

>> No.11595180

>>11595158
https://en.wikipedia.org/wiki/Irrational_number
>In the case of irrational numbers, the decimal expansion does not terminate, nor end with a repeating sequence.

>> No.11595184

>>11594877
>doesn't know what a limit is

>> No.11595187

>>11595098
> 1/3 is not equal to 0.3333...
lmao get a load of this retard

>> No.11595193

>>11595163
>>11595180
>>11595184
>>11595187
the onetards run out any actual arguments.

>> No.11595197

>>11594848
>1. burden of proof is on you to show that it
we have:
0.99... > 0.99..9 for any finite number of 9's
0.99...9 with exactly n nines = 1 - 1/10^n
therefore 1 - 0.99... < 1/10^n for all n

suppose now 0.99... < x < 1. then

0 < 1 - x < 1 - 0.99...

and using the above we have

0 < 1 - x < 1/10^n for all n.

since zero is the only number which is lesser than 1/10^n for all n, we have 1 - x = 0. contradiction.

>> No.11595222

[eqn]Let \; x=0.999...[/eqn]
[eqn]∴10x=9.999...=(9+0.999...)=(9+x)[/eqn]
[eqn]∴9x=9[/eqn]
Which line do you disagree with?

>> No.11595230

>>11595197
0.000...01 is also less than 1/10^n

>> No.11595236

>>11595222
Read the OP pic idiot

>> No.11595240

>>11595230
if by 0.00...01 you mean zero, than you're right

>> No.11595241

>>11594871
ask terrence

>> No.11595266
File: 73 KB, 973x553, Screenshot_20200423-124952_Samsung Notes.jpg [View same] [iqdb] [saucenao] [google]
11595266

Why can't we just say that this series converges to 1?

Can someone please explain why this is insufficient?

t. don't know how to type math symbols

>> No.11595271

>>11595230
0.000... per the idea of "..." has a never-ending stream of 0s, there can be no 1 after them, since there is no after. It is never-ending

>> No.11595277

>>11595266
the sum of the series is equal to 1
the limit of the sequence of partial sums is equal to 1
the sequence of partial sums converges to 1
[math]\sum_{n=1}^{\infty}\frac{9}{10^n} = 1[/math]

all of these are completely equivalent

>> No.11595278

>>11595266
They believe that that is simply not equivalent to 0.999...

>> No.11595288
File: 243 KB, 3600x1300, latex sci.png [View same] [iqdb] [saucenao] [google]
11595288

>>11595266
yeah that's what non-idiots do

>> No.11595290

>>11594848

1: How is the burden of proof on us? You claim that there exists such a number so you must provide it. Also most of the mathematical community agrees with us, so since you disagree with the generally accepted statement, you must disprove it

3: "because infinity" sounds a lot like you're a brainlet and have no idea what you're talking about. For example manipulating the infinite sum 1 + 1/2 + 1/4 + 1/8... is perfectly legitimate, "because infinity, same shit" is not a valid argument.

>> No.11595291

>>11595271
According to your logic there are infinite numbers in [0,1) so nothing can come after, because its infinite, so 1 doesn't exist

>> No.11595296

>>11595288
Uh sorry for being stupid but in which program do you guys write your LaTeX equations? I'd like some kind of preview but I don't have such an extension

>> No.11595300

>>11595290
If I say 1=2 and you say 1 is not 2 who has the burden of proof?

>> No.11595301

>>11595291
Simply wrong. Never did I say that all Infinities are never-ending, simply that 0.999... is defined by its never-ending stream of 9's.

>> No.11595305

>>11595193
>Can't respond to facts.
>Say it's not an argument.

>> No.11595309

>>11595291
>According to your logic
no

>> No.11595310

>>11595300
The generally accepted answer in the mathematical community is that 1 does not equal 2. The burden of proof is on you in both cases.

Also, it really has a bad image if all you do is try to pass the burden of proof onto us and avoid giving such a number as hard as possible.

>> No.11595315

>>11595230
I don't think so, pal. if 0.00...1 > 0, then it surely is larger than some 1/10^N

>> No.11595318

>>11595296
If you are at uni, you should be able to use overleaf. Otherwise, just google it and you'll find something.

>> No.11595324

>>11595098
"By this logic 1 is equal to 2 since there is no integer between 1 and 2"
You're just trying to seem retarded, aren't you? You fully know that this is not the same as 0.999... and 1, yet you chose this argument.

>> No.11595325

>>11595291
Cardinals are not the same as ordinals. Learn the difference, fucktard.

>> No.11595328

>>11594817
>burden of proof in math
retard

>> No.11595333

>>11595325
You're not too intelligent either, just throwing buzzwords around. In this case we're talking about neither ordinals (order) or cardinals (amount), it's about what happens at the infinite point ("limit infinity")

>> No.11595336
File: 69 KB, 500x333, fairviewgoattower.jpg [View same] [iqdb] [saucenao] [google]
11595336

>>11594845
Golden.

>> No.11595338

>>11595318
Thanks a lot, it seems to be free for one person, is that correct?

>> No.11595341

>>11594817
IF YOU WANT THE 0.999... THREADS TO STOP THEN DONT MAKE THEM YOU FUCKING RETARD
>BUT THE 1TARDS
YOU ARE ONLY MAKING IT WORSE BY DISCUSSING THIS MATTER AGAIN YOU ARE FUCKING RETARDED REEEEEE

>> No.11595343

>>11595325
it's not really about cardinals or ordinals. more like it's completely unrelated.

>> No.11595350

>>11594845
You sound like the 1x1 = 2 dude (Terrence Howard)

>> No.11595357

>>11595343
As I said, it's an endless stream. Assigning it an amount is pointless since you could always surpass that amount (since there is no greatest cardinal/ordinal)

>> No.11595365

let me clear this entire retarded argument.
1. repeat after me - INFINITY IS NOT A NUMBER, IT'S A SERIES. IT'S AN OPERATION
2. as far as we're concerned, nothing so far in this universe is infinitely divisible, therefore 0.999...has an endpoint.
3. from point 2 we deduce that 0.999.. < 1 BECAUSE 0.999.. has an endpoint somewhere along the line.
so, after all of this, we can safely say that the continuous series of >>11595266 converges to 1. And 0.999.. =/= 1 since it's not a series but a finite number (because a number cannot be infinite - it makes no sense)

NOW FUCK OFF

>> No.11595368

>>11595338
I don't know. I just use my uni email, but maybe it is free for individuals.

>> No.11595377

>>11595365
>. as far as we're concerned
speak for yourself kid. math doesn't give a shit about the universe
>0.999.. has an endpoint somewhere along the line.
it doesn't. see above.
>we can safely say that the continuous series of >>11595266 converges to 1
and 0.999.. denotes the number which this series converges to. therefore 0.999... = 1.

>> No.11595380

>>11595365
>Infinity is a series and an operation.
Literally what?
>The series that literally defines 0.9999... converges to 1 but is not equal to 1.
If an infinite series converges to some number, then it is said to be equal to that number. Learn your definitions.

>> No.11595383

>>11595377
math exists inside this universe dumbass

>> No.11595385

>>11595365
>arguing about how we can't talk about something in maths because it doesn't exist in the real world

Dude, please. Are you an engineer or a brainlet physicist?
In both cases, get out of pure math threads

>> No.11595387

>>11595383
plenty of people live inside this universe and they don't give a shit about it. your point ?

>> No.11595388

>>11595368
Yeah it works, thanks for the recommendation Anon. Do you always create a project everytime?

>> No.11595389

>>11595387
you're comparing apples to oranges

>> No.11595392

>>11595315
1/10^n has finite zeros in its decimal representation. 0.00....1 does not. Therefore 0.00...1 is smaller

>> No.11595393

>>11595392
and is 0.00...1 > 0 ?

>> No.11595394

>>11595324
Both arguments are equally retarded. It's a non sequitur

>> No.11595395

>>11595392
Thing is, 0.000...1 doesn't exist, since 0.000... is per its idea a number with a never-ending stream of 0's. You can't have a 1 after that since there is no "after".

>> No.11595402

>>11595393
Yes

>> No.11595403

Lmao! One-tards actually belive that the rational number 1 has two infinite decimal representations 0.999... and 1.000...

How can one be so retarded? OP you tried to show them the truth but they are stuck to their religious and irefutable belief that 0.999...=1

>> No.11595406

>>11595388
Yeah. For any paper you want to write, just choose create project, and generally choose a blank project.
For a some things, you're going to need to add a package, so you just add that package like is done at the top of the document.
For anything you don't know, just google search it. For tables, matrices, etc. you can find generators online as well.
$ math $ will put things in math mode.
$$ math $$ will also, but will put it on its own line and center it.
You can also use e.g. align environments, etc. for other math modes and to make it pretty.

>> No.11595407

>>11595402
You cannot compare an undefined number and a real number.

>> No.11595411

>>11595395
1 comes after 0 even though there are infinite numbers in between. In 0.000...1 the 1 comes after infinitely many 0s.

>> No.11595413

>>11595403
Not an argument. If you wanna make a circlejerk thread, go for it, but this thread is for discussion.

>> No.11595414

>>11595403
What theorem or axiom contradicts that a real number can have two different infinite decimal representations? Without showing that this gives some contradiction, your statement is equivalent to saying that 1/2 and 2/4 are different numbers because they have different fraction representations.

>> No.11595417

>>11595402
then

1/0.00..1 > 0

and so

log_10(1/0.00...1) exists. this is a real number and thus there is some integer N such that

N > log_10(1/0.00...1)

for example just apply the ceiling function. then

0.00...1 > 1/10^N

>> No.11595420

>>11595392
If 0.00...1 has infinite zeros then 0.00...1 = 0.

>> No.11595423

>>11595417
Buddy, this retard isn't going to see anything wrong with that. Also, he probably didn't even follow past line 1.

>> No.11595428

>>11595423
I know

>> No.11595430

>>11595414
>no rational number can have two infinite decimal represantations implies that no rational number can have two rational representations
Yikes

>> No.11595431
File: 75 KB, 618x741, 1572294171181.jpg [View same] [iqdb] [saucenao] [google]
11595431

>>11595406
Thanks

>> No.11595433

>>11595420
Also why Cantor's argument isn't an argument.

>> No.11595435

>>11595417
Log(1/0.00...1) just counts the number of zeros. This is high school math. So log(1/0.00...1) is infinity. There is no integer larger than imfinity

>> No.11595438

>>11595420
Nope
0 = 0.000... != 0.000...1

>> No.11595443

>>11595266
>t. don't know how to type math symbols
Read this: https://en.wikibooks.org/wiki/LaTeX/Mathematics
The $-equivalent on /sci/ is [math][/math]. (Do not copy those, type it yourself.)

>> No.11595445

>>11595413
The argument is that a number can't have two infinite decimal representations

>> No.11595446

>>11595430
Nice try. No, I said that the statements are equivalent (logically). Using the language of OP, the burden is on you to prove your claim that no number can have two infinite decimal representations. Stop trying to avoid this.

>> No.11595447

>>11595443
Ah, so the TeX-button ignores zero-width widespaces, but the board software does not, okay:
[ m a t h ] and [ / m a t h ].

>> No.11595448

>>11595435
if log(1/0.00...1) = inf, then 1/0.00...1 = inf. is this what you're trying to say anon ?

>> No.11595453

>>11595435
But you're claiming that infinity is a number then, which is a contradiction. What was the assumption we made here? it was that 0.0000...01 was not equal to 0. Under that assumption we arrive at a contradiction. Hence, the assumption must be incorrect (modus tollens).

>> No.11595454

>>11595411
That contradicts the idea behind 0.000... the idea is that you have a never-ending stream of 0's. If it was about amount of 0's, then you should use a different notation like 0.000...000 and the same in the original question of 0.999...999.

0.999... is definitely equal to 1 and 0.000... is definitely equal to 0.
I'm willing to argue about 0.999...999 and 0.000...001, but you should definitely use a different notation for that since "..." generally implies a stream of numbers. You should write it like 0.9[times aleph_null] and 0.0[times aleph_null] 1.

Thing is, you're wrong even in the latter case, since adding finite values to infinite cardinals does not change their value.

Or are you not actually talking about an infinite amount of 0's (cardinals), but rather about an infinite ordered sequence of 0's (ordinals)? That would be the only case in which your statement would make sense.

>> No.11595456

>>11595448
Probably, but I might have to think about it too be sure

>> No.11595457

Basically the argument here is that infinity doesn't exist since it's only a "concept" and not a tangible "thing", right?

>> No.11595460

>>11595447
Can also use [ e q n ] and [ / e q n ] for the $$ equivalent.

>> No.11595463

>>11595460
Test.
[eqn]\sum_{x=1}^{\infty} x[/eqn]
Neat. Thanks.

>> No.11595464

>>11595430
Dude, you gave absolutely no reason for your statement and when people point out the absurdity in your idea you try to actually use logic? Maybe should've done that a bit earlier.

>> No.11595465

>>11595454
In case it is not clear, 0.000...1 means 1 occupies the omegath decimal place

>> No.11595467

>>11595433
Are you a high schooler who is too afraid to ask his teacher? The argument holds and is an important mathematical result.

>> No.11595471

>>11595456
you have found yourself a real number x such that 1/x is not a real number. moreover

x*inf = 1

I don't know, seems weird to me, anon...

>> No.11595473

>>11595435
What type of infinity are you talking about here? You need to be specific about the central point of the discussion.

>> No.11595474

>>11595453
I'm not the one who tried to use infinity as a number. Its just the output of log(1/0.00...1), not a number but a point in the one point compactification of R

>> No.11595475

>>11595465
So just write eps.
So you are saying 0.999...=1-eps.
But 0.999... is an infinite (larger than omega) stream of 9's following the decimal point, so it is not equal to 1-eps.
Alternatively, if you are only talking about the real numbers, eps is not a real number. We would just have 0.00...01=0.

>> No.11595476

>>11595438
The latter is not well-defined. Please give a rigorous definition.

>> No.11595478

>>11595474
>Its just the output of log(1/0.00...1), not a number but a point in the one point compactification of R
then 0.00...1 = 0 since log extended to the one point compactifications of (0,inf) and R is a bijection.

>> No.11595479

>>11595445
And what's the reason for that? Why would that be?

>> No.11595480

>>11595471
1/0.00...1 is 1000000000000000...

>> No.11595481 [DELETED] 

Silly question: Why are all of you bothering to respond to an obvious troll? He's going to keep refuting you with bullshit arguments and won't be able to ever be reasoned with, just give up now.

>> No.11595484

>>11595480
>1000000000000000...
and this is inf or not ?

>> No.11595486

>>11595448
Equals what infinity? Please specify and reveal your definition.

>> No.11595489

>>11595486
the one >>11595435 is using

>> No.11595492

>>11595474
So we're dealing with S^1 then, not R? Well the function 1/x from nonnegative numbers to S^1\R^- is one to one, so 1/0=1/0.00...01, implying that 0=0.00...01.

>> No.11595496

>>11595484
No it is less than infinity. In fact, it is less than 2000000000...

>> No.11595497

>>11595465
Then your notation is completely fucking retarded - as I said, "..." indicates a never-ending stream. However if we're actually talking about ordinal infinities then I must agree with you - such a number, which is a member of the surreals is bigger than 0. The same goes for a the 0.999 and so forth case - this would not equal 1. However your notation is very, very, very bad.

>> No.11595500

>>11595492
1/0 is undefined.

>> No.11595501

>>11595457
There are three concepts of infinity: cardinals (amount), ordinals (order) and "limit infinity" (which is what the "..." notation would imply)

>> No.11595505

>>11595478
And?

>> No.11595506

>>11595500
Not if the codomain is the one-point compactification of R.

>> No.11595510

>>11595471
I doubt this is a real number in any standard definition (Cauchy sequences, dedekind cuts, etc.)

>> No.11595513
File: 196 KB, 1598x393, TIMESAND___0zpf85nem0yf002utuddu6bfnu18c1xoumdvbnnbr9yo56d.png [View same] [iqdb] [saucenao] [google]
11595513

For pic to be easily seen, you have to first assume that 0.999... is not equal to 1. You're implicitly assuming that 0.999... is not equal to 1 to prove that 0.999... is not equal to 1. Circular reasoning.
>Circular reasoning

>> No.11595516

>>11595496
if 100000.... is a real number less than infinity, then log(10000...) is a real number less than infinity

>> No.11595518

>>11595475
First of all, it would be 1 - 0.1^omega which is different from epsilon.

Also he clarified with 0.000...001 he was talking about not the infinite stream which the notation would imply but rather an infinite ordered sequence with 1 at the omegath position

>> No.11595525

>>11595480
And that's a real number? Under which definition of them?

>> No.11595527

>>11595506
The codomain of log is the compactification, not 1/x. That would just be silly

>> No.11595530

>>11595489
He also didn't give a definition or clarification.

>> No.11595532

>>11595518
0.000...01 is not 1-0.1^omega, you trog.
Also, he never said that 0.00...01 was a sequence. And that wouldn't even make sense. He's using it as a number, not a sequence.

>> No.11595533

>>11595510
It is ontological real

>> No.11595534

>>11595527
>The codomain of log is the compactification
range of log_10 is R

>> No.11595535

>>11595496
Define those, please. I'm pretty certain that number is not an element of the surreal numbers and therefore not an actual number, since the surreal numbers are the largest ordered field. I might be wrong though, so give a nice definition please.

>> No.11595539

>>11595527
So your saying that the codomain of 1/x is the real numbers? But claiming that 1/0.000...01 is infinity (omega)? That doesn't work. If the codomain of 1/x is real numbers, then 1/0/00...01 is undefined as well. In which case, log(1/0.00...01) is also undefined, since it is the logarithm of something undefined.

>> No.11595541

>>11595533
Not a thing in math. Define it.

>> No.11595542

>>11595534
Log_10(10000...) = infinity because the input has infinity zeros

>> No.11595545

>>11595539
1/0.0000...1 is the ontological real number 10000...

>> No.11595547

>>11595438
Cauchy sequence: (0, 0.0, 0.00, ...) = 0

>> No.11595548

>>11595542
then 100000... = infinity because log is bijection between (0,inf) and R

>> No.11595552

>>11595545
So not a real number? Define the ontological reals, and prove that it's different from S^1. Also, tell me what the codomain of 1/x is.

>> No.11595558

>>11595552
numbers that actually exist irl

>> No.11595565

>>11595558
Not a definition. Also, show me where in real life 100000000... is in real life.

>> No.11595569

>>11595565
>inb4 "in this thread"

>> No.11595599

>>11595532
For any real number we can define a sequence of it's decimal places.

>> No.11595612

>>11595533
This is about mathematics, not philosophy. I want you to answer my question.

>> No.11595615

>>11595542
What infinity?

>> No.11595628

>>11595599
The number is not the same as the sequence, which is what you claimed.

>> No.11595629

>>11595558
numbers don't exist. If you're talking about our universe, you will have to admit that Infinities actually don't exist.
We're talking about pure math here and that requires proofs from axioms and definitions.

>> No.11595637

>>11595569
I kek'd

>> No.11595643

>>11595628
Never did I claim such a thing. You can transform one into the other, and in the sequence, 1 sits at the omega'th place according to his definition.

>> No.11595671

>>11595643
No real number can be represented by a transfinite sequence of numbers.
Also, looking back, your original post is irrelevant to my post. I never said that 0.00...01 is an infinite stream.

>> No.11595686

>>11595671
Indeed, we would need the surreal numbers. But inside that field, a 0 with an [math] \omega [/math] amount of 9's after the comma is not equal to one. View my current OP please (the one with the table)

>> No.11595696

>>11595686
>a 0 with an ω amount of 9's after the comma
That is not the same as 0.999...
Since the reals are a subclass of the surreals, For this reason, 0.999... in the reals is the same as 0.999... in the surreals.

>> No.11595728

>>11595696
I agree with this post.
0.999... is a symbol which already has a meaning. In surreal numbers there might be some other object which is intuitively "0 followed by omega 9's", but it's misleading to say that it's 0.999..
Also if you redefine 0.999... in surreals to get 0.999... < 1, this implies that actually every decimal representation of a number is lesser than the number it's supposed to represent. So there's the question if this is really what we want.

>> No.11595761

>>11595728
I absolutely agree and already argued for this point earlier on in the thread - the "..." implies limit infinity. However the other guy claimed he was talking about that weird surreal number so yeah I guess that's what he meant.

About any number's decimal representation being smaller than its value, that's wrong. 0.999... (actually never-ending, not the weird one with omega length) is still equal to 1. I don't see where you get your conclusion from.

>> No.11595802

>>11595761
>About any number's decimal representation being smaller than its value, that's wrong. 0.999... (actually never-ending, not the weird one with omega length) is still equal to 1. I don't see where you get your conclusion from.
I've said that 0.999... should stand for the same thing in the surreals as in the reals. However if you take 0.999... to be something different in the surreals (for whatever reason) and you get 0.999... < 1, then also 3.14.. < pi, 0.333... < 1/3 and so on. probably 5.00.. would still be 5 though.

>> No.11595931

>>11595802
Yeah I definitely agree, the standard notion of 0.999... is also 1 in the surreals. The thing is that that guy wanted the notation to stand for something different.

>> No.11596172

>>11594817
1:
Now, you have made the claim that (0.999... + 1) / 2 != 1, so the burden of proof is on you.

2:
>0.333... != 1/3. Why? Because calculators disagree
fucking lol

3: The sequence (0.9, 0.99, 0.999, 0.9999, ...) converges, so that can be done. (1, 0, 1, 0, ...) doesn't converge, and that's why you can't use algebric manipulation.

>> No.11596271

>>11594817
Assume 0.999... ≠ 1

Then (0.999... + 1)/2 ∈ (0.999..., 1)

In particular, (0.999... + 1)/2 ≠ 0.999...

⟹ 0.999.../2 + 1/2 ≠ 0.999...

⟹ 0.4999... + 0.5 ≠ 0.999...

⟹ 0.9999... ≠ 0.999...

⊥

∴ 0.999... = 1