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/sci/ - Science & Math

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6526386 No.6526386[DELETED]  [Reply] [Original]

Time to bring back an old /sci/ topic:
Is 0.999999999(repeating) equal to 1?

>> No.6526387

I hate you.

>> No.6526389

I don't see why not.

>> No.6526392

>>6526387
>>6526389
samefag

>> No.6526394

>>6526386
troll thread pls

Its limit as the digits approach infinity converges to 1.

Its identity as .999... is what it is: .999...

>> No.6526396

>>6526392
Look at the times, moron.

>> No.6526397
File: 78 KB, 832x584, thrash_52.jpg [View same] [iqdb] [saucenao] [google]
6526397

Such EPIC maymay!!
Post something else too! XDXDDD

>> No.6526398

>>6526396

>21:06:50
>21:08:43
>21:09:02

all separated by more than 45 seconds

>> No.6526399

>>6526392
You fail at human psychology if you think someone would samefag a thing like that.

>> No.6526401

>>6526386
Define repeating

>> No.6526402

>>6526398
I'm pretty sure posting time is one minute.

>> No.6526403

>>6526398
lmao

>> No.6526408

>>6526398
Remarkable observation skills
Maybe you are the one true scientist, the one they call chose one

>> No.6526411

>>6526398
>This is the kind of people on /sci/

>> No.6526413

>tfw you'll never be part of the secret society that spam troll threads

>> No.6526415

fuck all the pure mathematicians here.

>> No.6526418

>>6526413
where my w-bros at

>> No.6526421

2^2+2^2=3^2
2+2=3

>> No.6526423

>>6526421
What does the ^ symbol mean?

>> No.6526425

>>6526423
Please tell me you're joking.

>> No.6526426

>>6526423
It means =^.^=

>> No.6526427

>>6526425
That's not very helpful

>> No.6526433

>>6526423
It means 'and'

>> No.6526436

>>6526433
No that's /\

>> No.6526451

>>6526421
(2+2)^2 != 2^2 + 2^2

(2+2)^2 == (2+2)(2+2) == 2*2 + 2*2 + 2*2 +2*2 == 16

>> No.6526455
File: 3 KB, 249x203, zero-point-nine-repeating.png [View same] [iqdb] [saucenao] [google]
6526455

>>6526386
Only to people who can't into long division.

>> No.6526459

>>6526436
>alphabets are objective

>> No.6526468

>>6526426
winrar

>> No.6526473

>>6526394
>there are people who believe this and think they're smart

>> No.6526479

<div class="math">\sum_{x=1}^\infty f(x)\not=\lim_{n\to\infty}\sum_{x=1}^n f(x)</div>

I don't think these two things are equal. Or atleast I was never told explicitly that they were in school. Even though this sort of thing is probably one of the fundamental concepts of calculus, I think it is only a useful assumption that can be used the mentally bypass the true impossibility of infinite sums. If you say .999...=1 I think you might be forgetting or neglecting to appreciate that calculus is based entirely on convergences of limits rather than more literal logic. I am not sure I want to say that .999...=1 but I feel that this statement leaves out some fundamental concepts of real number analysis.

>> No.6526482

>>6526479
Well this is new. See, this is why I love 0.999...=1 threads, there's always something surprising in them.

>> No.6526513
File: 113 KB, 953x613, hahanerds.jpg [View same] [iqdb] [saucenao] [google]
6526513

>> No.6526525 [DELETED] 

>>6526513
countersage

>> No.6526526

>>6526479
Are you trolling? The right-hand side is literally the definition of the left-hand side.

>> No.6526547

>>6526386
>Is 0.999999999(repeating) equal to 1?
The answer is no.

Here's why:
Can you find a real number that is greater than 0.999... and less than 1?
No? You can't? Then 0.9999... and 1 are the same number.

>> No.6526559

Every pair of distinct numbers has infinitely many real numbers between them. What is between 1 and 0.99...? There is nothing between them, so they are not distinct, so they must be equal.

>> No.6526576

>>6526547
>>the answer is no
>proves the answer is yes
fasng

>> No.6526579

>>6526525
why the fuck are you on /sci/ ,go back to india

>> No.6526580

>>6526547
>The answer is no.
Whoops, that should say "The answer is yes."

>>6526576
calm down bro, it was a typo.

>> No.6526593
File: 52 KB, 493x549, 00637.jpg [View same] [iqdb] [saucenao] [google]
6526593

>>6526421
>2^2+2^2=3^2
>4+4=9

>> No.6526597

>>6526580
calmer than you are

>> No.6526610

>>6526593
(2 AND 2) OR (2 AND 2) = 3 AND 2
2 OR (2 AND 2) = 3 AND 2
2 OR 2 = 3 AND 2
2 = 3 AND 2

2 3
t t t
t f f
f t t
f f t

2 ==> 3

>> No.6526612

I declare the difference between 1 and 0.99... to be 0.00...9

>> No.6526637

0.9999 recurring is not the same as 1.0 because no matter what, it will always be smaller by 1.00x10^x

>> No.6526639

>>6526612
>I declare the difference between 1 and 0.99... to be 0.00...9

>0.00000...9
^ this is equal to 0.

>> No.6526655
File: 94 KB, 321x285, 1399258373494.jpg [View same] [iqdb] [saucenao] [google]
6526655

>>6526386
Get out

>> No.6526661

>>6526637
Where x is the limit to - infinity?
Learn to limit, you troll.

>> No.6526669

>>6526639
>Thinking division can be zero
LOL

>> No.6526675

>>6526669
> >Thinking division can be zero
>implying that there was anything related to division, in this post: >>6526639

>> No.6526679

>>6526675
1/10 = 0.1
1/100 =0.01

>> No.6526688

>>6526669
<span class="math">\lim_{x \to \infty} \frac{1}{x} = 0[/spoiler].
pls go back to middle school.

>> No.6526690

>>6526688
(1/x)/(1/x)?

>> No.6526719

>>6526661
If not given a limit, it is implied that a variable is any real number

>> No.6526720

1 - 0.999... = 0

Proof ??

>> No.6526722

>>6526720
>1 - 0.999... = 0
>Proof ??
1. There is no real number that is greater than 0.9999... and less than 1.
2. Therefore, 0.9999... = 1.
3. So 1 - 0.9999... = 0.

there ya go.

>> No.6526738

>>6526722
>There is no real number that is greater than 0.9999...
0.999... isn't a real number

>> No.6526747

>>6526738
>0.999... isn't a real number
0.999... = 0.9 + 0.09 + 0.009 + 0.0009 + ...
and the real numbers form a complete metric space, faggot.

>> No.6526748

You are implying that 0.999... = 1, by that Math Philosofy sentence, thats faith.

Anyway I find the answer on net:


1.0 - 0.9 = 0.1

1.00 - 0.99 = 0.01

1.000 - 0.999 = 0.001

1.000... - 0.999... = 0.000...

since the two to rest are progresive, then the result 0.000... never reach the ...001,

so 0.000... = 0, 1 - 0.999 = 0

DAMMM i hate this, never seen this shit before.
I will not sleep tonight, my logic es mess now.
( u_U)

>> No.6526753

>>6526747
>...
Can you tell me the value of this symbol?

>> No.6526754

>>6526748
>You are implying that 0.999... = 1, by that Math Philosofy sentence, thats faith.
And you are retarded.

There is no real number that is greater than 0.999... and less than 1.
Therefore, 0.999... and 1 are the same number.

>> No.6526755

>>6526473
>i can use green text to refute someone's point without even mentioning it, too!

>> No.6526759

>>6526754
If we change bases there are

>> No.6526775

>>6526759
>If we change bases there are numbers that are greater than 0.999... and less than 1
Are you trolling or just retarded?

A change-of-base doesn't change the structure of the real numbers. In fact, it doesn't even change the numbers themselves, since a change-of-base just switches from one representation to another.

>> No.6526782

>>6526775
.999...=/= 1 in hexadecimal.

>> No.6526791

>>6526782
>.999...=/= 1 in hexadecimal.
Completely, absolutely wrong. Go back to middle school.

>> No.6526792

>>6526775
>from one representation to another.
This is incorrect

>> No.6526794

>>6526791
but he's right. in hex it's .FFFFFFF...

>> No.6526795

>>6526792
>This is incorrect
so hexadecimal and decimal representations are the same, retard?

>> No.6526799

2 = 1 ?

>> No.6526805

>>6526799
If ? = 2

>> No.6526806

>>6526794
>but he's right. in hex it's .FFFFFFF...
You fucking dumbass...

0.FFFF <span class="math">= 15 \sum_{n = 1}^{\infty}16^{-n}[/spoiler]
<span class="math">= 15 \cdot \frac{1}{15}[/spoiler]
<span class="math">= 1[/spoiler]

pls go back to middle school.

>> No.6526807

>>6526795
Yes

>> No.6526810

>>6526806
Are you drunk? or just an idiot?

>> No.6526816

>>6526806
That's not even wrong

>> No.6526825

>>6526810
This is literally 9th-grade math, at the most.
If you can't understand it, then I seriously suggest that you go back to middle school.

>> No.6526828

>>6526825
>in HS lol faggot

>> No.6526831

>>6526825
Except it's like you are arguing against yourself.
You called him a dumbass and then proved him exactly correct, because you're a total idiot.

>> No.6526834

>>6526831
>You called him a dumbass and then proved him exactly correct, because you're a total idiot.
I don't think you read the thread properly.

The person I replied to said that 0.FFFFF (as a hexadecimal number) is not equal to 1. I then showed that it is equal to 1.

Learn to read, asshole.

>> No.6526840

>>6526834
no he said .999..=/=1 in hexadecimal.
you said it was absolutely wrong.
someone called you out on it, not being too clear but insinuating that .999..=/=1 because .FFF...=1, but you have autism, so you didn't understand.

>> No.6526843

>>6526513
This picture gives me a lot of comfort about my future. Clearly, they are not equal, but from the eyes of someone naive like me there are attempts using the seemingly complex nature of the notations used in mathematics to explain that they are the same, when clearly they are wrong.

It feels good.

>> No.6526852

>>6526840
>no he said .999..=/=1 in hexadecimal.
>you said it was absolutely wrong.
Yes, that's what happened.

>someone called you out on it, not being too clear but insinuating that .999..=/=1 because .FFF...=1, but you have autism, so you didn't understand.
I'm pretty sure no one's stupid enough to say that 0.999... <span class="math">\neq[/spoiler] 1 because 0.FFF...(in hexadecimal representation) = 1.
He was trying to say that 0.FFF...(in hexadecimal representation) <span class="math">\neq[/spoiler] 1, and I showed that that is incorrect.

>> No.6526856

>>6526852
well you're wrong then.
look at what he replied to.
Do you think the person he was replying was correct?

Also .999...=/=1 in hexadecimal because in hexadecimal .fff=1

>> No.6526860

>>6526825
you keep mentioning that he goes back to middleschool and after reading this, I'm going to agree that your just a highschool autist in calculus as your highest math class. >>6526828
>>6526825
Your trying to hard in your ad hominems to the point of giving away your own bs situation.

>> No.6526873

>>6526856
>.999...=/=1 in hexadecimal because in hexadecimal .fff=1
For fuck's sake.

0.999... = 1, and 0.FFF... = 1.

Write each expression as a series, and evaluate it. You will get a value of 1 in both cases.

Please, just go talk to a math professor, and he/she will show you that you're wrong.

>>6526860
>Your trying to hard in your ad hominems to the point of giving away your own bs situation.
this makes no sense as a coherent argument. How does it prove that I am wrong?

>> No.6526892

MODS PLEASE, FOR THE LOVE OF GOD, MAKE <span class="math">0.999... \neq 1[/spoiler] A BANNED TOPIC

>> No.6526913

Consider this : if 1 & 3 are real numbers : 1 / 3 = 0,(3) => 0,(3) = real number as well(duh) ; since 0,(3) * 3= 0,(9) => 0,(9) = real number(x2) , but 1 / 3 = 0,(3) => 0,(9) = 1 , Genius !

>> No.6526943

>>6526892
Why? judging from the discussion lot's of posters on /sci/ do not understand that 0.999... is 1, so people reading this are obv learning stuff here.

>> No.6526962

>>6526892
>MODS PLEASE BAN ARBITRARY TOPICS BECAUSE I DON'T LIKE THEM

fuck you dude, you're killing this place.

>> No.6526967

>>6526892
Why, so you can have more cosmos threads?

Fuck off.

>> No.6526971

>>6526962
>>6526967
What, do you actually like these threads? What's wrong with you?

>>6526943
>people reading this are obv learning stuff here.
No one is learning anything. These threads are created by trolls, and fueled by dumbasses who refuse to change their views.

>> No.6526981

>>6526806
Since you made the effort of doing it with latex, might as well do the repeating thing correctly
<span class="math">
0.999... = 0.\overline{9}
[/spoiler]

>> No.6526997

>>6526852
in each base, to reach 1
the repeating 'digit'
has to be the largest one possible

>> No.6527002

>>6526971
it's <span class="math">tradition[/spoiler]. nerds on the internet need inside jokes to give themselves a fleeting sense of community.

>> No.6527093

>>6526386
The point is not that they are equal but retards thinking you can PROVE it.

/thread

>> No.6527168

>>6527002
I cringed.

>> No.6527171

is 0.9999999999...c the same as 1c?

>> No.6527172

>>6527093
Of course you can prove it.

It's like real analysis 101

>> No.6527178

>>6527171
the decimal number system doesn't allow for anything after the "..."

>> No.6527179

>>6526873
In hexadecimal
<span class="math">.999... = 9 \sum_{n = 1}^{\infty}16^{-n} [/spoiler]
<span class="math"> =\9\cdot \frac{1}{15} [/spoiler]
<span class="math"> =\frac{9}{15}=\frac{3}{5} [/spoiler]
Do you understand yet?

>> No.6527182

>>6527179
* <span class="math"> = 9\cdot \frac{1}{15}[/spoiler]

>> No.6527573

Bump :^)

>> No.6527590

>>6526386
Oh gee I dunno, is 1.11111... in binary equal to something?

>> No.6527623
File: 187 KB, 800x600, IMG_0147.jpg [View same] [iqdb] [saucenao] [google]
6527623

>>6526805
>2 = 1

>> No.6527635

>>6527179
>>6527182
0.9999... (hexadecimal) is not the same thing as 0.9999... (decimal).

But 0.9999... (decimal) equals 1.
And 0.FFFF... (hexadecimal) also equals 1.
(Obviously, 1 has the same representation in decimal and hexadecimal.)

Do you understand yet?

>> No.6527638

>>6526386
1/9=0.111111111111
1/9 * 9 = 9/9 = 1
0.11111111*9 = 0.99999999
0.9999999 = 1
Checkmate

>> No.6527641

>>6527590
Another great proof. Tyba
>>6527573
Fuck you. Fuck you into a black hole.

>> No.6527642

>>6527623
x-y = 0, you can't divide at line 4

>> No.6527694

>>6527642
you can divide by zero if you pray to the lord jesus

>> No.6527728

>>6527638
You could have done the same thing with 1/3, dumbass

>> No.6527754

>>6527728
Are you retarded?

>> No.6527767

>>6526386
0.999... = a
multiply with 10: 9.999... = 10a
subtract a: 9 = 9 a
divide by 9: 1 = a
qed

>> No.6528141

>>6527767
The funny part of it all is that you didn't even try.
At all.

>> No.6528145

>>6528141
is what he did 'wrong'?

>> No.6528147

>>6528145
It's kind of incomplete

He didn't spell out what an infinite decimal actually is, or whether it was ok to do the sort of algebraic manipulations he did with them, the kind we do with fractions and finite decimals.

>> No.6528178
File: 50 KB, 274x242, 1315960917418.jpg [View same] [iqdb] [saucenao] [google]
6528178

>>6526386
7 / 12 = 0.58333...
0.999... * 7 = 6.999...
6.999... + 2 = a
2 > 1
7 + 2 = 9
9 > a
7 / 7 =1
2 + 2 = 4
9 = b
b > a
1 > 0.999...
1 =/= 0.999...

Solved forever /sci/, you're welcome.

>> No.6528180

>>6527754
Are you?

>> No.6528183

>>6528180
I don't think that's related to that post.

I mean, I was so flabbergasted that I couldn't even put into words the amount of clueless I witnessed in that post.

>> No.6528184

>>6526754
>There is no real number that is greater than 0.999... and less than 1.
>Therefore, 0.999... and 1 are the same number.
That's not right.
There is no real number between .999...9 and 999...8, so they are equal.
Repeat ad infinium, and 0=1.
You fail logic forever.

>> No.6528189

>>6528184
You are going to have to define those numbers properly if you want to prove anything.
Saying .999...8 doesn't mean anything.

>> No.6528191

>>6528184
intelligent bait newfriend, you are welcome here

>> No.6528193

>>6528184
Oh shit never mind I realized what wrong with my logic.
I'll go be a faggot somewhere else now.

>> No.6528196

>>6528191
I didn't mean to bait, but I realized what I did wrong.
>>6528189
I meant .999...8 as .9 repeating 8 is place of the last 9.

>> No.6528197

0.xxxx....x
0.xxxxx.....y

Why is only one allowed?

>> No.6528199

>>6528196
>the last 9.
more bait

next you will be claiming their is a highest number

>> No.6528204

>>6528197
neither are allowed

>> No.6528205
File: 14 KB, 556x561, 1399837905389.jpg [View same] [iqdb] [saucenao] [google]
6528205

OP here
>mfw reading through all of the responses ITT and people telling each other to go back to middle school
my sides have reached neptune

>> No.6528213

1*10^-inf = 0.000...1

0.000...1 = 0

0.00...1*10^inf = 0.00..*10^inf

1 = 0

>> No.6528245

Take t such that zeta(1/2+it) = 0.

We see then from calculation that Zeta(0.4999...+it) = 0

as 1/2 =/= 0.4999..., we have found a non-trivial zero of the Riemann Zeta function with a real part not equal to 1/2 thus concluding the Riemann hypothesis is false

pls give me $999,999+ 0.9999... dollars

>> No.6528247

>>6528245
what the fuck did i even read

>> No.6528257

>>6528247
A wonderful disproof of a 150 year old problem my door boy

it took the great leap forward of 0.999.. != 1 to get us this far, if only David Hilbert were alive to see this

>> No.6528267

>>6527635
>0.9999... (hexadecimal) is not the same thing as 0.9999... (decimal).
That's the entire point you fucking faggot

>> No.6528886

Ok, what's 1/9? 0.11111 repeating.

What is 9 * 1/9? 9 * 0.111111111.

0.99999999999 repeating.

What else does 9/9 equal? 1.
So, 9/9 = 0.999999999
0.9999999 repeating = 1

QED

>> No.6528920

>>6526386
humans are trying to construct models of things which have no inherent seperation.

think about it this way, there's no such thing as a river and different streams/brooks/so-on. its just water moving towards lower ground and encountering random terrain and dividing and subdividing and merging.

we can't make sense of the world if we don't model it. but since we're biological creatures that are not one with the universe we won't understand that categories ultimately do not exist and when we make them we are just using what our biological limits force us to in order to comprehend things.

>> No.6528930

>>6528920
tldr; zeno's paradox and this question is because nothing has actual categories and its due to being human.

there's no such thing as red. we invent it to explain what it is in nature. read wittgenstein you faggots.

>> No.6528932

>>6527178
"..." is not a symbol in decimal.

>> No.6528947

1/3 = 3.3333...

10/3 = 1/3 + 1/3 + 1/3, or:
10/3 = 3.3333... + 3.3333... + 3.3333...

3.3333... + 3.3333... + 3.3333.. = 9.9999...

So if 9.9999... doesn't equal 10, then 10 =/= 10.

>> No.6528951

>>6528947
>1/3 = 3.3333...
Should be 10/3.