????
The stories and information posted here are artistic works of fiction and falsehood.
Only a fool would take anything posted here as fact.
Only a fool would take anything posted here as fact.
????
depends
yes
>>769036126
it does, my math teacher proved it to me
>>769036126
Yes. Those are two different representations of the same number. Just divide them by 3. Next question?
1/3 = 0.333... so 3/3 = 0.999...
>>769036126
no because its not whole
>>769036607
Nice try OP, to keep this retarded thread alive, but sage grows in every field.
the argument goes as follows: 1/3 = 0.333...
and 2/3 = 0.666...
consequently 3/3 = 0.999... and how much is 3/3? 1
ergo 0.999... = 1
>>769036126
Yes.
The was proven long ago.
.999... = .999...
1 = 1
>technically
no
>for all intense sand porpoises
yes
>>769037101
>technically
yes
it's just 2 ways of representing the same number, like 2 and II
>>769037101
It is also technically true. "=" does not mean equality between string representations. Maths isn't a retarded scripting language.
Or do you think -0 does not equal to 0 either?
>>769036126
pi is exactly 3!!!!
>>769037437
>>769037580
>>769036772
Math major here
No, because 2/3=.666.... but there is a 7 at the end point, its just very long to get there
>>769037437
That's what they told us in Engineering. +-20% is good enough.
yes
>>769037656
FBI agent here (pic related, it's my badge), and that's classified information. Please stay where you are.
>>769036213
It does. Maths is inconsistent otherwise.
0.999 repeating is also the fraction 9/11, so it really depends.
>>769037636
thx anon
>>769036607
It is whole. It's 0.9... = 1/1 = 1
>>769037656
there really isnt a 7 at the end, because that would mean
2/3 = .666...7
/ 2 = .333...35
* 3 = 1.000...05
so by that logic
1*3=3
3/3=1.000...05
reality does not have rounding errors, if it did that would be ultimate proof we live in a simulation.
tis muh badge guys, stay calm
>>769037845
0.999 repeating is exactly 1
0.999 is not equal to 0.999 repeating.
>>769037845
>repeating
>9/11
I see what you did there.
>>769036126
x=0.999...
10x=9.999...
10x -x =9.999... - 0.999... = 9
9x = 9
x= 1
0.999...=1
>>769037776
Did you hook up with the red chick yet?
>>769037656
There is no 7 at the end. .666... means every digit after the decimal point is a six.
>>769037776
Wow agent Mulder in the flesh. Caught those pesky aliens yet?
>>769038203
He's not a math major at all, lol
x = 0.999999...
10x = 9.99999...
9x = 9
x = 1
>>769037991
*whoooosh*
>>769037656
you're not a math major, one of the first modules most math majors do is real analysis, and if you did it you'd know that what you're saying makes you sound like a mongoloid.
>>769036126
in practicality, yes. in reality, no.
>>769038298
>10x = 9.99999...
>9x = 9
Go back to math class idiot.
Let x=0.9 recurring
Therefore 10x=9.9 recurring
Therefore 9x = 10x - x = 9.999999 - 0.999999 = 9
Therefore x = 1
>>769038433
What is "subtracting equations from eachother"?
>>769037656
>math major
>end point of repeating number
pick one faggot
>>769038497
the correct way is
>10x = 9.9999..
>x = 0.999
the 10 goes under the 9.999 like 9.999/10.
You cannot just put 9x = ..
>>769036126
no
because 1-0.9999... != 0
which is the definition of equality
>>769036126
"close enough" is not good enough in math and science. Otherwise, Pi would not be an irrational number. We'd just round off to 3 and say "close enough".
0.999... = 1. equality means you can replace a value in a resolving equation with an equivalent one and the equation holds.
0.999... + 0.999... = 2, 6 / 0.999... = 3, etc
this is because u cant name any number between 0.999... and 1 - if u can, 0.999... =/= 1
>>769038467
dude, can you pls write that third line differently, it's confusing af
>>769038706
>which is the definition of equality
No it isn't you racist shitlord
>>769038706
What is 1-0.9999... if not 0, my man? As I see its
0.000... meaning every digit is 0, and that kinda makes it zero
>le patrick meme
>>769038706
what number does it equal? if its greater than 0, u didnt subtract 0.999..., u subtracted 0.99999999 or some gay shit
>>769038747
Take it one term at a time sweetie, Im sure you'll get there eventually. :)
>>769036126
here's the true answer slightly simplified.
since we can't talk absolutely about things that are continuous (quantum mechanics and all that shit) the definition of a real number is pretty much arbitrary.
because of the way we define the real numbers in rigorous mathematics they have some interesting properties, the most important one is that they are dedekind complete, essentially what we say is if you have a limit, a sequence where you can always find a point within a particular distance from some point, applying this to the 0.999 problem.
take the sequence
>0, 0.9, 0.99, 0.999, ...
if you want to find a term in the sequence within a certain distance of 1, you just need to find a term high enough up the sequence, because it gets closer and closer to 1, and it can technically get as close as you want, it's always possible to find a term.
by definition we say that the limit of this sequence is 1, we use the shorthand 0.999... to express this limit without explicitly writing 1.
TL;DR: they're different ways of writing the same thing.
>>769038417
Actually, in reality, also yes.
>>769037049
i like this proof
>>769038433
10x=9.999...
9x+x=9+0.9999...
9x=9
somebody is lazy and do not like to do the maths
>>769038797
it's easy to prove.
if you assume N number of 9's after the decimal point and call it x, then there must be a number between x and 1 from the properties of working over the rational number field, which means that x - 1 != 0.
You can do it for every N, thus 1 != 0.999999...
>>769039095
>if you assume N number of 9's after the decimal point and call it x
And then you take lim N->infinity, and whaddayaknow, you get 1.
>>769039095
Are you assuming that N is a finite number?
>>769039265
>And then you take lim N->infinity, and whaddayaknow, you get 1.
no you dont.
For everyone who said "no", learning that sin x/x is 1 when x=0 will blow your mind.
>>769039317
>DID YOU JUST ASSUME THAT N IS FINITE?
>>769039341
Very poor quality trolling
>>769038417
This. 0.9... only equals one if you disregard infinities
>>769039317
I proved that for every N this must hold.
Every N is also extremely large N, or infinitely large N.
>>769036126
Let S = 0.999...
10S = 9.999...
10S - S = 9
9S = 9
S = 1
>>769039452
>extremely large N
yes
>infinitely large N
no
>>769039522
>math fail
>>769039452
You only proved it for every finite integer N. the number of digits of 0.9999... is not a finite integer. Good try nonetheless, D-.
>>769036126
0.999 + 0.001 = 1
>>769039593
you are retarded
>>769039706
Oh shit, you're right, you win. Here, have a cookie.
>>769039706
You're not even trying anymore, if you're going to troll at least put more effort in
>>769039593
if anything, from the properties of rational fields 0.9999.... is the closes number to 1 that isn't 1.
>>769039095
This is why you should teach your kids number field theory. If you don't do it, someone else will, and this is the result.
>>769039830
what's wrong?
>>769039822
in rational fields 0.999... doesn't exist
>>769039822
First, I think you mean real numbers. Second, no such thing exists in the set of either real numbers or rational numbers. You might, however define a number field where 0.9999... is a different number from 1, but good luck with properly defining the operators to have field properties.
Like is 0.9999.../3 a different number from 1/3? Also, what is 1-0.99999..? Can I divide with that number?
>>769039830
Your right, i meant real number field, not rational.
>>769038622
0.999 != 0.999...
>>769040031
operators would be perfectly easy to define as far as i could tell, it just wouldn't be cauchy complete
>>769036126
yes, infinite sums (1/2 + 1/4 + 1/8... n) equal 1. This was proven like 700 years ago faggot.
>>769040201
That means you defined a good for nothing set and operators. Defining 0.9999... = 1 results in a nice little useful field.
>>769039522
>10S = 9.999...
>10S - S = 9
thats not true
S = 0.999
10S = 9.99 | -S
10S -S = 9.99 - 0.999
9S = 8.991 | /9
S = 8.991 / 9
S = 0.999
>>769040271
what about hyperreals?
>>769037776
Impersonating an officer is a crime.
>>769040201
What is 0/(1-0.99999...) then? What is x/(1-0.99999...) if x!=0?
>>769040397
some kind of an ordinal perhaps?
>>769039567
Anon’s proof is right. .99999... is an absolutely convergent series. Sorry lads, as a theoretical physicist I need to say this thread feels like a cringe one...
>>769040375
You mean something like 1-0.99999... = ϵ?
I dunno That gets messy pretty quick. That would mean
0.9999... = 1 - ϵ
Then 1/3 = 0.3333..., but 0.99999.../3 = 0.333... - ϵ/3
Also, x/ϵ also needs to be defined to be something sound, like x*∞. But then how much is 0/ϵ? This is where things get so complex it loses all usefulness outside some very specific analysy problems.
>>769040364
>10S -S = 9.99 - 0.999
9.9 recurring - 0.9 recurring = 9
>>769040945
stfu
it wasnt funny the first time.
>>769039567
You're actually an idiot
>>769041056
you weren't funny the first two time
>but your mom was xD
>>769041056
>being this dumb
>>769040945
Your rounding down. 0.9' = 7
>>769041144
2+2=5 for extremely large values of 2, amirite?
>>769041185
Close. That also = 7
>>769036126
>>769036213
>>769036216
>>769036269
>>769036310
>>769036313
>>769036607
>>769036710
>>769036772
>>769036780
>>769037049
>>769037101
>>769037309
>>769037320
>>769037437
>>769037580
>>769037606
>>769037636
>>769037656
>>769037673
>>769037706
>>769037776
>>769037809
>>769037845
>>769037847
>>769037917
>>769037939
>>769037991
>>769038029
>>769038128
>>769038165
>>769038165
>>769038167
>>769038203
>>769038246
>>769038272
>>769038298
>>769038367
>>769038374
>>769038417
>>769038433
>>769038467
please log off 4-chan
0.999.../9=0.111...=x
10x=1.111...
10x-x=1 qed
>>769036126
Rounded yes
otherwise no
>>769041326
wew, now we're talking real large 2s.
between two different number, there is always another number.
In this situation you can't find it, so they are the same
>>769040821
it gets messy sure, it's also pretty useless in applications to anything in the real world.
still it's possible to do so.
I'd argue that you just assume that multiplication behaves as an extension, so ϵ/2 is just ϵ*1/2
1/3 would be 0.3333.... +ϵ/3
defining 1/ϵ to be some number that's simply larger than 1 + 1 + 1 + ... but still smaller than 1/0 in the real limit sense.
0/ϵ you can still define to be 0
of course these rules could be altered in a few ways but it would lead to a completely self consistent system if done properly.
>>769036126
no.
now, if we could only use quantum computers to come up with a virus that kills only black people... hopefully soon.
Which infinity are you using?
It is a different number, but you can use them to get almost the same results for certain cases.
Essentially you can add infinite 9's, so it's not 1, it's just reaaaaaaaaally close.
>>769041634
It makes no sens to basically introduce definitions that make _using_ the representation harder. That's why 0.999.... is defined to be "infinite number of nines follows the decimal point", not "infinite number of nines and also some epsilon value". Going with the first definition, 0.9999... will be 1, and you could consider that to be an artifact of the representation. Still better than the alternative, second definition, because it has much more, much deeper problems.
>>769039813
if you think you can have an "infinite integer" you're the retarded one not me
>>769041399
>When you does 1/3 = 0.33 remain rest 0.01
>That mean 3/3 = 0.99 and the rest 0.01
>If you want 0.(3) you still need the rest 0.(0)1 (I don't think this exist mathematical)
>Quod erat demonstrandum 0.9999... != 1
>>769043448
That's the point, there's no such real number as 0.000....01.
Are you also saying that 1/3 is not 0.33333..., but 0.3333... + "the rest"? Because noone really agrees with you about that.
>>769043791
I don't say +
I say just remain the rest.
>>769043897
is 1/3 = 0.33333... though?
>>769036126
through proofs yes
>>769044199
if
1/3 = 0.3333...
Then if you multiply both sides with you get
3/3 = 0.99999...
3/3 = 1, so 1 = 0.9999...
Either this, or 1/3 != 0.333...
>>769044460
multiply both sides with 3*
>>769044460
>>769044489
BUT AT 1/3 = 0.333... REMAIN WITH A REST FFS.
IF YOU MULTIPLY, YOU NEED TO SUMM THE REST AT RIGHT SIDE AFTER MULTIPLY.
>>769044815
Then 1/3 != 0.333..., because of "REMAIN REST"
Also, please learn some English, this is fucking embarassing.
>>769044947
If you learn some math before, just like many others around here, including OP.
>>769044947
X / 3 = 0.33 rest 0.01
You know how to find X?
>>769045056
Either point out the actual flaw in the maths or gtfo.
>>769045191
No, because i have no idea wtf you are talking about when you say "rest".
>>769036607
This.
Two real numbers are unequal when there is a number between them. In this case it's not so 0.999...=1
>>769045191
Nigger what is rest
>>769045353
THIS! BRAINLESS
>>769046376
The "..." in 0.333... takes care of "the rest", by definition.
fags
>>769046656
no, it not. Because If I just say 0.333... mean it will continue with 3, for an infinite number of times
Fuck off OP.
>>769046841
the infinite number of 3s is exactly "the rest".
>>769046968
Thanks, I'll save that.
>>769047114
That mean it is an irrational number and if you mult , div and in any cases add/sub you don't know the answer.
This is even to this faggot >>769046968
functionally it does but i don't think it does in reality
>>769046376
>>769046841
You just arbitrarily stopped dividing at the .01 place.
5/4 = 1.25 because it stops dividing.
1/3 = 0.333... because it never stops dividing.
1/3 is not 0.34.
>>769046968
>bawww you 404ed my shitty porn thread
Hop into a woodchipper you triple nigger.
>>769047484
If the result is real, means that the original equation has undergone transformations to become real and logical. Without break the rules of math.
>>769046968
Yeah. Geometric series expansion proves the assertion easily.
Yes.
Hey faggs,
> ∞ = ∞
> ∞ - ∞ = x?
>>769047426
>1/3
>irrational
>>769047504
I didn't say 1/3 is 0.34 or 0.334 or 0.3333334. FFS. you all are brainless?
>>769048017
0.(3) is irrational XD
I am stop arguing with some brainless who don't know some basics.
>>769048178
0.333... = 1/3
Irrational is defined as "a number that cannot be represented as the ratio between two integers"
![b410fcc6-7a7b-45a0-81b9-354423866db9[2].gif](https://i.imgur.com/Dp4Hcbe.gif "b410fcc6-7a7b-45a0-81b9-354423866db9[2].gif")
>>769048088
This r is your "rest" right? You can't "rest" at a point after the decimal place. "rest" is for representing the uneven portion of a division as a fraction.
128/5 = 25 r 3 = 25 + 3/5
It would be nonsensical to let the "rest" go into the decimal place, since you use "rest" notation to avoid writing the remaining portion as a decimal.
a/b = c , rest x
a = c*b + x;
1/3 = 3*10^(-∞)[notation : w] , rest 1*10(-∞)[notation : z]
1 = w * 3 + z
even this does not make sense?
>>769041399
>log off
>>769050079
Why don't make sens for decimals? 128/5 = 25.6 = 25 + 3/5 = 25 + 0.6 ?
>>769036126
No.
/thread
>>769036313
1/3=0.333... is just as ambiguous as 1=0.999...
>>769050348
I mean like
5/4 = 1 r 1 = 1 + 1/4 = 1.25
But you wouldn't want to do
5/4 = 1.2 r 2 = 1.2 + (2*10^-1)/4 = 1.25
I guess you could do it like that, but the point of the r is to avoid writing 5/4 with decimals.
Although I suppose that would make your "rest" in >>769046376 equal to (1 * 10^-2) / 3. That is
1 / 3 = 0.33 rest 0.01
rest 0.01 = (1 * 10^-2) / 3
But
(1 * 10^-2) / 3 = 1/3 * 10^-2 = 0.333... * 10^-2 = 0.00333333333333...
so we run into the same problem.
The "rest" itself is an infinite number of threes. You can use rest notation, but it doesn't really help here.
