Discuss.

Well they look different Innit so how could they be the same

>>739477553
Well, 0,5 and ½ look different as well

>>739477553
You and op look different yet you are both faggots

0.333333333333333333 = 1/3 |*3
3*0.3333333333333333 = 3* 1/3
0.9999999999999999 = 1

>>739477498
Let x = 0.999999...
Therefore 10x = 9.9999...
10x-x = 9.9999... - 0.9999...
9x = 9
x = 1

File: IMG_7604.jpg (77KB, 750x739px) Image search: [Google]

77KB, 750x739px

>>739477498
0.99999999....9...
Constantly approaches 1.0 but will never be 1.0

However, for just about every single application, 0.999999...9... = 1

>>739477929
Damn this guy gets it

>>739477929
No, you're retarded.

>>739478030
Exactly.

>>739478102
Don't argue with the proofee, argue with the proof. I don't think it's 1 either, but you can still do a proof.

Of course the problem is it's a proof that, like many others, implicitly relies on infinity being a number when it's not.

File: 1499808078825.jpg (44KB, 541x540px) Image search: [Google]

44KB, 541x540px

Not this again.

>>739477498
>You have 1L of water in a bottle
>You put all the water in 3 cups
>Each cup have 1/3L of water, or 0.333... L
>Now you put back the water in the bottle and it is filled again with 1L of water
>But a cup have 0.333...L of water
>3 cups have 0.999...L of water
>3 cups filled 1L bottle
>1L of water=0.999...L of water
>0.999...=1

>>739477927
This only shows how decimal representations are retarded
In theory they should be adding up to 1, but the structure of a base 10 decimal system cant handle it well.
All this shows is that .3333333333333 while fine in most cases is not a true replacement for 1/3

What is a limit for 200 Alex

>>739478550
Take into fact moisture content in cup after measurements

>>739478550
What happened to the 0.0000000000.....1 drop of water? Evaporated?

>>739478569
Actually, this. Just this.

Decimal system is good enough, but inherently flawed

>>739478714
People like him don't understand the concept of approximation.

0.999... ~= 1 is true.
0.999... = 1 is false.

>>739477498
If there are an infinite quantity of numbers between 0 and 1 then all you are doing is having a schemantic argument about what number you are representing by writing .999999...

There must be a number that is 1-(an infinitely small number less than one) which presumably equals .9999999...

If there does not equal an infinitely small number to create the number that you're representing then you're just representing it badly or lazily.

0.99999999... isn't in fact 1, rounding system fixes it.

File: images (13).jpg (45KB, 478x307px) Image search: [Google]

45KB, 478x307px

>>739477498

>>739478069
yeah this guy named wikipedia and google they realllyyy get it

>>739477929
>10x-x = 9.9999... - 0.9999...
But 9.99999999999999 theoretically has infinity-1 9s after it so when you minus .999999999 which has an infinite number of 9s you are actually getting a number that is just smaller than 1 by an infinite amount
.999999999999

>>739479524
Er... sorry, messed that up
9.99999999999999 (10×.99999999)
minus
.999999999999999
Would theoretically equal 8.99999999...1
Same logic though
9.99999(infinity - 1 9s) - .999999(infinity 9s)

>>739479915
Continuing the logic
9x=8.99999999(infinity-1 9s)...1
8.9999999999...1 ÷ 9 =.999999999999
x=0.9999999999

Wow we got the same number we started out with, funny how math makes sense when you do it right

>>739479915
infinity-1 = infinity.

>>739480631
no such thing as infinity

>>739480631
Indistinguishable? Yes
Equal? No

Infinity - 1 is smaller than infinity by an infinitely small amount
Same goes for .99999999... and 1

⅓ = 0.333...
0.333... x 3 = 0.999...
⅓ x 3 = 1
∴ 0.999... = 1

>>739477927
0.333... =! 1/3

Its only a base10 approximation that is out by the same distance that 0.999... is away from 1

0.999... does not equal 1

That is an approximation moffered to high school students to keep things simple

>>739479524
>>739479524
>you are actually getting a number that is just smaller than 1 by an infinite amount
If that were true, you're assuming what you're setting out to prove.

>>739481140
>⅓ = 0.333...

You failed at the first line

>>739481140
>1/3 + 1/3 + 1/3 = 2.9999999999/3
.3333333333 ≠ ⅓
It is the closest decimals can get, but not exact

File: Math Damon.jpg (28KB, 293x300px) Image search: [Google]

28KB, 293x300px

>>739477498

File: Untitled.png (20KB, 413x408px) Image search: [Google]

20KB, 413x408px

>>739481379
>>739481430
>>739481497

Wrong.

Simple. Try to think a number between 0.999... and 1.

You can't.
So 9.999... = 1

>>739481637
.3333333 is the best base 10 decimals can do, if you dont like it dont convert to it

>>739480219
This guy gets it

>>739481685
Simple. Try to think of a whole number between three and four.

You can't.
So 3 = 4

File: accept it.png (66KB, 800x640px) Image search: [Google]

66KB, 800x640px

>inb4 (a/b)^∞ for a<b doesn't converge to 0

>>739477498
there is nothing to discuss

>>739481865
number =/= whole number

Your post is invalid.

>>739481685
I can answer this precisely and accurately with one line. Question is if you are willing to accept the answer?

>>739477498
How about this other one I found:

1/3 = 0.333...
+ 2/3 = 0.666...
---------------------
3/3 = 0.999...

>>739477498
correct. end of discussion.

Just make x = 0.99
10x = 9.9
10x - x = 8.91
9x = 8.91
x = 0.99

>>739482022
1/3 does not EQUAL 0.333...

It.is a base 10 approximation

>>739481999
I won't accept it if it's incorrect.

File: eqn.gif (1KB, 340x51px) Image search: [Google]

1KB, 340x51px

It is by definition of the decimal expansion. It's just a geometric series.

>>739482084
Prove it.

File: 5274365.jpg (48KB, 572x431px) Image search: [Google]

48KB, 572x431px

>>739481685
And this is why you're not a mathematician.

>>739482281
so, tell me the number between 0,999... and 1

x=0.(9)
10x=9.(9)
10x-x=9.(9)-0.(9)=9
9x=9
x=1

>>739482342
1-(1/inf)

>>739482342
0,9999
Tadaaa~

>>739482366
no

>>739482240

At least one other guy with a higher education.

File: images(5).jpg (8KB, 259x194px) Image search: [Google]

8KB, 259x194px

>>739482281
Tell me a number between i and e.

>>739482410
If you accep infinity in.mathematics, which you must... then you must also accept the reciprocal of infinity.

Which is the gap between 0.999 and 1

>>739482084
∞
∑ (3 / ( 10^i))
i = 1
The upper bounds of the limit, by definition, is 1/3

>>739482240
Thank you!

>>739482410
That's still 1

>>739482411
are you retarded?

>>739482557
Limits never actually reach the upper bound. You know this

1/3 =! 0.333...

File: 1500478022237.jpg (24KB, 450x504px) Image search: [Google]

24KB, 450x504px

>>739482410
>what is convergence

>>739482084
>>739482411
>what are repeating decimals

You can't just go and use the concept of infinity and be consistent its implications.

>>739482625
No its not. Its jnfinitely small, as infinity is.... well infinitely large.

1/inf is the precise definition of the gap between 0.999... where people claim no number can possibly exist therefore they are the same.

>>739482801
No its not. Its jnfinitely small, as infinity is.... well infinitely large.

You are thinking as infiinity as something that ends. but think it this way.

1 - 0.999... = 0.000...

You could "think" there is going to be a 1 at the end of the 000's but there is no end.

>>739482939
Nah. Infinity is just infinity. Not a real number, but required to be real by entire fields of mathematics.

Its valid.

As is its reciprocal.

Which destroys the assertion the 0.999...=1

>>739482666
Haha true, it is just an approximation.

>>739483041
how does that destroy it?

Just tell me a number between 9.999... and 1. It wouldn't be that hard if it was possible...

>>739483181
Again?

1-(1/inf)

Think about it for a second

>>739483312
The operation you are trying to express is known as undefined. You can't say it's between 0,999... and 1, nor you could say it even has a result.

>>739483312

Not the guy, but I can tell you in under a second that 1-(1/∞) is just another way to write 1, which definitely doesn't fit inbetween 0.999... and 1.
You're thinking of (1/∞), which is a valid but useless way to write 0.

>>739483513
>>739483597
I will come at this another way.

How many times are we expected to repeat the 9 after the decimal point?

I say: i will repeat one more time and that is your gap between 0.999... and 1.

Unless you are suggesting we repeat the 9's infinitely?

Which means the gap is the reciprocal of infinity.

Either way, it never makes it.

>>739483855
>How many times are we expected to repeat the 9 after the decimal point?

Are you kidding me? do you even know what do the "..." represent? OF COURSE the 9's are repeated infinitely. "The gap" just doesn't exist.

>>739483855
did you pass 3rd grade?

File: 1343857448003.gif (249KB, 500x364px) Image search: [Google]

249KB, 500x364px

>>739483855

You can't accept infinity and reject convergence.
That is really all this discussion is about.

>>739484066
If you agknowledge infinity then you must agknowledge the reciprocal of inifity which is BY DEFINITION, the gap.

1-(1/inf)

>>739484128
Stop rubbing it in Dave!!! You fucking dick!

>>739484284
stop with that 1-(1/inf) bullshit. 1-(1/inf) is an undefined operation. Can be considered as 1, but it's still undefined.

>>739484420
So is assuming that we can stack an infinite amount of 9s after a decimal

>>739484497
>So is assuming that we can stack an infinite amount of 9s after a decimal

I don't even...

>>739477498
Yeah, it kinda is

>>739484330
uh, give me your lunch money? something like that?

>>739477498
1/3 = .33333333333...
.3333333... * 3 = .99999999999...
3/3 = 1
.99999999999999... = 1

>>739484546
>i dont even have an argument

I don't understand how this is even a legit question and why people think 0.9999...=1
They are very close but 1-0.999999....=/=0 so they are not equal.

>>739478550
1of the cups will have slightly more than the other 2 cups to make up the missing fraction of a ml

>>739484284

If you write it in caps, please provide citation. I mean, you claimed it is useful in "entire fields of mathematics", surely it has been used somewhere.

>>739484800
1-0.999... = 0.000...

Please, it's not that hard people... think of a number between 0.999... and 1, and the whole discussion is over.

>>739478850
You don't understand the concept of infinity.

0.9999.... With infinite number of 9 IS equal to 1, real equality.

It just that people can't understand mathematical infinity

>>739484920
Every time someone writes 0.999... they are assuming an infinite number of 9s.

>use:confirmed

>>739484659

You, idiot, are a sir.

>>739485083
it's not "assuming". "..." is the literal expression of repeating decimals.

>>739485058
You say that 1/inf is undefined yet seem fine with an infinite number of 9s

>logical dissonance

>>739477498
#no

>>739485221
Seriously. Are you fucking retarded?

>>739485192
So it assumes that infinity is a real?

Ie, the number of 9s is actually infinity?

Then what if the reciprocal?

1/3 ~= 0.3333333333... but ≠ 0.3333333333...
One third cannot be expressed in Base 10. Doesn't matter if there are an infinite amount of 3's behind that decimal point, it will never be one third. Infinite 9's will still end up being 0.999... not 1. 0.999... can be ROUNDED to 1, but it is not 1. You fucking clowns.

>>739485275
yup, you're retarded, please leave this thread

>>739485250
No

Lack of argument followed by ad hominem noted

>>739485321
Fucking this!

>>739485330
I can't sit here and explain basic math rules, man. You shouldn't be posting if you don't even know what a periodic number is.

>>739485459
>basic maths rules

Like assuming an infinite number of 9s can exist?

>>739485083

One last, patient try. You claimed (1/∞) is "by definition" the gap between 0.999... and 1. I want an example of that definition used somewhere.

(1/∞) converges to 0. That's why convergent series have a sum. A real equality.

>>739479088
I was looking for this image. Thanks

>>739485321
I should state that I meant one third of a number that is not a multiple of 3, cannot be expressed in Base 10. Of course 30/3 = 10, 10*3 = 30.

>>739485546
They never reach that sum!

They tend towards it. The value can be determined conceptually but never achieved

>>739478714
No such thing as a recurrence then an arbitrarily defined number. It's either a number or not.

0.000...1 ≠ 0.000... (0)

>>739485706
Is infinity a number?

>>739481872
>>739482240
Congratulations you are the only persons that are not retarded in this thread

Also, for the brainlets here, a decimal representation cannot end with only nines, because then there would be two ways to write some numbers

>>739485748
No

>>739485633
>infinity
>they never reach it
>determined conceptually but never achieved

Infinity is a concept, bravo for noticing. Now be consistent with its implications and leave the "achieving" behind.

>>739485802
Then why is assuming an infinite number of 9s after a decimal considered valid?

>>739485848
1

>>739485848
1-(1/inf)

1 / 3 = 0.333333333
1 / 3 * 3 = 1
0.333... * 3 = 0.999999999

1 = 0.999999999

Also, there is no "0.000...1". It's infinite. You can't add a 1 to the end, because there is no end.

>>739485885
oook

>>739485933
this shit again?

>>739486005
stop living

>>739485869
It's not. It's a dumb way to represent 1.
Because infinite by definition is innumerable, yet generally regarded as being as much as possible. It keeps going forever to the point it'll always reach 1

Look at it this way. You have a length of 1 meter, and you make a mark at 9/10s into that length, and then again at 9/10s of the remaining length, and again, and again.... That gives you .9999999 of a meter. Doesn't matter how many times you do that, you will never reach the 1 meter mark, there will always be that minute distance left. And that is the thruth. End of story.

>>739486021
>this shit again

Yes. No one has debunked it yet without a logic breakdown. Or ad hominems

>>739486100
No it keeps going forever to a point where it just misses 1

>>739485933
1-(1/inf)=0.9999999999
How could it be something else?

File: tomoko_nagao_leonardo_da_vinci-the_last_supper_with_mc_easyjet_coca-cola_nutella_esselunga_ikea_google_and_ladygaga_2013_digital_art_50_x_70_cm-_70_x_100_cm_1.gif.jpg (154KB, 1024x510px) Image search: [Google]

154KB, 1024x510px

>>739486120

yanks dont recognize meters

>>739486100
They arent representing 1. They are trying to represent 0.999...

If they were trying to represent 1... they would just write 1

>>739486130
The proof is on the one who claims it, not the one who claims it's not valid.

Try to prove me that 1-(1/inf) is a number between 0,999... and 1 first if you don't want to be taken as a retard

>>739486130
I can right now.
It's infinite. Not a number, a concept. It's like 10 / Nerd. Impossible.

>>739486256
>meters

Yanks cant even spell metre correctly

>>739478550
yeah but you cant divide it perfectly into 3 3.33333... bottles

>>739486361
It's both correct.

Talking about real numbers, 0.999... = 1 and there is no other possible value for 0.999...

An infinite decimal expansion of the form:

0.abcd.... is defined as the Numerical Series:
0.abcd... = a/10 + b/100 +c/1000 + ... up till infinity.

If you sum the series 0.999... = 9/10 + 9/100 +... Guess what you get? ONE the number ONE.

So 0.999... = 1 in the same sense that 2+2 = 4 and 1/2 + 1/2 = 1.

Real numbers don't have a unique form of being expressed in decimal representation, so it is accepatle for 1 and 0.999... be the same thing, such as 1 is 20-19...

>>739486335
If its only a concept then assuming an infinite number of 9s after the decimal fails.

>>739486307
1-(1/inf) is as much as a number as pi is. It just can't be easily broken down into a set of integers.

File: dd2sq.jpg (159KB, 1116x672px) Image search: [Google]

159KB, 1116x672px

>>739486335

Okay so since some people in this thread don't seem to understand basic maths, here: https://youtu.be/ffUnNaQTfZE?t=56s

>>739486130
infinity is NOT a real number
the division you're trying to use is only defined for two real numbers, the second not being 0
you're wrong because what you said does not even make sense in a mathematical way

>>739486401
Nah. Its english. The english decide the spelling.

Its metre

>>739486405
Real numbers exlude 0.999... which assumes an infinity. The ... bit

>>739485321
An infinite number of 3's is literally 1/3.
Just like an infinite number of 9's is literally 1.
No rounding required.

.3 = 3/10
.33 = 3/10 + 3/100
.333 = 3/10 + 3/100 + 3/1000
etc.

So .333... = 3/10 + 3/100 + 3/1000 + ...
= 3/10 lim (1+1/10+1/100+...)
= (3/10) (1) / (1- 1/10)
= .3 * (1/.9)
= .3/.9 = 1/3

While it is correct that for any *finite* number of 3's it will never be 1/3, we aren't talking about a finite number of 3's. Likewise we aren't talking about a finite number of 9's. Given ANY number with a finite number of 3's .333...3, .333... has more 3's, and is thus closer to 1/3.

To put it that way again, .333... is *by definition* closer to 1/3 than any other number. It is by definition the closest number to 1/3, including 1/3. That is, .333... IS 1/3.

Likewise as others have pointed out, .999... is the closest possible number to 1, including 1. Because .999... IS 1.

File: true.gif (901KB, 625x334px) Image search: [Google]

901KB, 625x334px

>>739486471

yeah its the queens English Yankees

>>739486452
So 0.999... isnt real?

File: an option to consider.jpg (50KB, 800x530px) Image search: [Google]

50KB, 800x530px

>>739486120

You do reach that full meter once you accept that the concept of infinity can't be approximated to phrases like "no matter how many times" or "can't be achieved" or "they never reach".

>>739486416
pi is a well known number.

The operation you are trying to do is universally known as UNDEFINED. Like dividing by 0. You just can't use it, and much less try to justify that its value is between 0,999... and 1.

If I am wrong prove it.

>>739486520
No, they don't. Real numbers do in fact include infinitely long decimals --- in fact, that's part of the definition and the major part of the proof that the real numbers are a different cardinality than the natural numbers.

>>739486673
You want your cake on a plate and in your mouth at the same time.

You cannot assume infinity is real for the purpose of defining a question then reject its use in the solution.

>>739486755
So is 0.999... a real number?

>>739486757
Infinity is real as a concept. That's just like saying sums don't exist because 2 - + = ?

OP I've struggled with the question since I was like 8.

I honestly don't believe 0.99999999999 = 1
or 0.33333333333333 = 1/3rd.

They come close, like Icarus flying too close to the sun but never making it.

>>739486860
Yes. 0.999... is a real number and equal to 1.

There's nothing to discuss here. You're right.

>>739486860
>>739486976
Or I should say, 0.999... is another way of writing the real number 1. They aren't distinct numbers.

>>739486580
No. If 3/3 is 1.0, and you end up with a bunch of nines, no amount of nines (even an infinite amount) will bring it magically to 1.0. I can be ROUNDED to 1.0 but it will not BE 1.0.

Take half of a number.
1/2.
Add 1/3.
Continue.

1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + 1/10 etc. ≠ 1.0

File: 1500487987452.gif (106KB, 625x626px) Image search: [Google]

106KB, 625x626px

>>739486976

>>739477744
you are literally the most retarded person on this planet.

File: horse shit.gif (2MB, 281x209px) Image search: [Google]

2MB, 281x209px

>>739486976

>>739487097
was meant for
>>739486906

>>739477498
in reality there are quanta
your infinite mathematical nonsense works only on paper

>>739486976
So assuming that an infinite number of 9s opens the use of infinity... 1-(1/inf)

Is closer to 1 than 0.999...

File: 1497636485644.png (677KB, 843x637px) Image search: [Google]

677KB, 843x637px

>>739486757

We CAN assume infinity to be real, and we DO USE it for the solution. See>>739481872

You keep arguing with infinity being somehow finite, at some point stopping 0.999... short of 1, or (1/∞) stopping somewhere before 0. You are the person with the dick in your ass and mouth at the same time.

>>739487202
how do you want us to not call you a retard after such retarded posts?

>>739486613
>You do reach that full meter

No, I do not. I come one more step closer to 1, but I'll never in fact reach it.

>>739487226
So is infinity in use or not?

Cant assume that 0.999.... has an infinite number of 9s without conceeding that

>>739487226
infinity isn't real.
for all x such that x in Reals, x-x = 0.
\inf - \inf is undefined.

>>739487274
Assuming an infinite stream of 9s assumes that there always remains a 9 at the end.

Coming back from 1 via its reciprocal is infact, closer

>>739487437
Then its safe to assume that the magical infinite number of 9s is also not real?

>>739487461
"at the end"

"infinite" means there is no end, you silly silly retard

>>739485933
>>739487202
Infinity is not a member of the set of real numbers R. Thus when you are using the set of real numbers R, any use of the number "infinity" is undefined since infinity is not there. This is similar to how, when considering real numbers, you don't use complex numbers, quaternions, or anything similar.

However, if you look instead at the real projective line, which is the union of the set of real numbers with a point infinity, division by infinity is defined (for most numbers). Specifically, 1/infinity is defined as 0. Likewise while division by zero is impossible using just the real line, the real projective line allows 1/0=infinity.

You also have the extended real line, which is a different way of considering infinity. There, you have both a positive and a negative infinity. Which also have 1/+inf = 0, and 1/-inf = 0.

Note that these aren't compatible, just similar.

Thus, in the normal real line, 1-(1/infinity) is impossible since there is no infinity. But even when you use a set of numbers that allows it --- 1/infinity is equal to 0, and thus 1-(1/infinity) = 1-0 = 1.

>>739487526
Sure. But there 8s always another 9. Never 1

File: 1497635107952.jpg (33KB, 399x469px) Image search: [Google]

33KB, 399x469px

>>739487334

Do you try hard to misunderstand on purpose? Did you actually try and employ the geometric series to understand what people are talking about here?

Infinity is in use for both writing 0.999... and for the proof that it is in fact equal to 1.


I have to post a pic with every reply because my browser broke.

>>739485706
So the decimal system failed to explain the complete narative then?

>>739487578
So is 0.999... real?

It assumes an infinity in its definition

>>739487596
>But there 8s always another 9

another 9 where?

>>739486202
Because 1/inf = 0.
In calculus, you literally equate anything over infinity to zero.

>>739487599
If 9 repeats forever it can never equal 1

Fancy maths cant defy basic logic

>>739487683
After the decimal. There will always be another 9. Always. Infinitely.

>>739487787
then tell me a number between 0,999... and 1

1-(1/inf) is actually 1 in the worst of the cases.

>>739487308
In a finite amount of time, assuming it takes the same amount of time each step, no, you won't. But that's not what we are talking about.

You might consider Zeno's Paradox. Suppose someone shoots an arrow at you. In order to reach you, it first must travel half the distance. Then, it must travel half of what remains. This continues infinitely. By your logic, if it travels half each step, it will never reach you. So you tell me: if I shoot an arrow at you, will it ever hit you?

File: 1494981029724.gif (2MB, 249x200px) Image search: [Google]

2MB, 249x200px

>>739487787

Infinity and fancy words like "forever" defy basic logic.

>>739487893
You andwered your own question.

If you admit infinity is real then the reciproval is the gap. If you deny infinity then your question is flawed because you used infinity in the framing of it.

>>739487501
yes

but 1.00... and .99... are equally valid ways of representing the same number.
There's no real reason to use one over the other.
get it, real?

>>739478569
Agreed. 1 =/= 0.999... Using the 1/3 example is a fallacy because 1/3 doesn't truly equal 0.333... The repeating into infinity thing is just a convenience for turning a fraction onto a decimal number on a fraction that can't be truly represented that way.

Flip this all to a number base 3 and it works flawlessly, but you're fucked on halves.

>>739488026
infinity isn't real.
no real number's reciprocal is zero.

>>739488101
Then any reccuring number isnt real

>>739482077
My Professor once said, people dont understant that even infinities still have different sizes.

Your approach is the best to at least make people think that 0.99999.... =/= 1.
9.9999...-0.9999.... =/= 9.

Another solution that is flawed is the one where you divide the liter of water into 3 and get 3 times 0.3333.... liter of water. 0.3333... isn't a real number, i dont mean it's imaginary. But for comparisson, try filling a cointainer with π liters or sqrt(2) liters of water. You can only do it approximately, but never really do it.

Every time you get 0.9999...=1 you used some kind of approximation.

Dont get me wrong, in practical use, you can always assume 0.9999...=1. But in reallity 0.9999... only approaches 1 infinitely but never reaches it.

File: 1462534250064.gif (74KB, 312x390px) Image search: [Google]

74KB, 312x390px

>>739488026

If you assume infinity is real, then the reciprocal is 0. To be anything else than 0, infinity would have to be finite.

Because the image does not show the entire number you would have to approximate what the number is. There for this could be approximated to 1
If you had the app act number than it would be just that, exact and would not be equal to 1.
If you had half a brain you would know it could be one or another or neither.

>>739488146
wat no.

pi is real.
it's reciprocal is between .2 and .4

>>739479088
Didn't know /b/ was posting these treads in 1984 when this shitty image seems to have originated. I can't read the cyan on yellow background. CGA much?

>>739488026
No one here is "denying" infinity. The only person that seems confused about it is you.

0,999... is an infinite amount of 9s after the 0.

Because it's infinite, there can't be any number until it reaches 1. So, because of that, every mathematical operation is the same for 0.999... than for 1. Thus, leaving 0.999... = 1.

Whatever you're trying to do with infinity is just bullshit. Infinity is not a number.

Imagine if someone tells you "hey, what is 90º + angle? if you don't have an answer that means angles don't exist". You probably would think that person is retarded. And that's exactly what I'm thinking about you right now.

>>739488154
If you assume infinity is real then there will always be another 9 after the decimal?

>>739488151
>isn't a real number
you mean it isn't a rational number.
real means something else in math that includes pi and sqrt(2)

>You can only do it approximately
you can never get /exactly/ 2 liters either...

>>739488321
>Because it's infinite, there can't be any number until it reaches 1

If its infinite it never reaches 1

Surely

File: 1472213058704.jpg (848KB, 1800x1405px) Image search: [Google]

848KB, 1800x1405px

>>739488151

The approach of dividing a liter into three parts iss actually valid, because it's a though experiment and as such not bound by real world phenomena. Meaning no water evaporates, no residuals cling to the containers and division can be assumed to be exact.

>>739488481
The approach of dividing anything into 3 parts is best not completed in base10

>>739488437
>it never reaches 1
in a finite length of digits, you're right.
but waterside cadets.

>>739478550
You are a fucking mongoloid.
If you have 1 third or 1/3 litre that's not 0.333333333.
I sincerely hope you die a painful death

>>739488437
So there should be a number between 0.999... and 1, right?

>>739488668
Yes the reciprocal of the infinity you used to stack up an endless line of 9s

I'll make this as simple as I can for you dumbasses. You draw a line at 10 degrees which will be equal to 1. You are going to try to draw a parallel line but the closest you can get is 9.9 degrees. Well, you don't have a parallel line. Given enough distance you will have lines that intersect. So, 9.9 does not equal 1. Go fuck yourselves.

if 1 and .9... are different numbers,
represent them in binary.

>>739488391
whoops, ya i meant irrational

>>739488391
>>739488481
and yeah that part with the water is kinda retarded, what i meant to say is that the number never ends and you would always have to add bits of water but never actually make it

I stick with "it's an approximation" and it will never be more than that.

>>739488811
>9.9 = 9.999...

you're an idiot

File: 1290516050001.jpg (118KB, 640x480px) Image search: [Google]

118KB, 640x480px

>>739488527
>best

Yes, fractions serve a better purpose for most divisions. Does in no way invalidate repeating decimals.

>>739488884
Not sure is weak b8 or weak brain. Either way you're an idiot.

They are not equal ever they are real close tho.

>>739488100

fuck me i swore i wouldn't reply but:

the base makes no differences to the operations - the numbers are literally identical no matter what base they're written in.

>>739488730
>the infinity you used

you can't be this stupid, really...

please, go to school again, I'm done with your bullshit

>>739477498
2 is not 2
Discuss.

>>739488884
It doesn't matter how many 9s there are. My point still stands.

>>739488884
just try to go on with what he said. lines at 10° and 9,999999...° will intersect sooner or later

>>739488916
Yeah it does because the exact same argument 0.999... =! 1

Applies to 0.333... =! 1/3

0.333... only tends to 1/3
It never quite makes it.

>>739489011
2 =/= 2 because of the reciprocal of the 2 you used and if you used a 2 then 2's don't exist

>>739488811
This guy is a right guy

close enough

File: 1377225180283.gif (2MB, 500x375px) Image search: [Google]

2MB, 500x375px

>>739489084
This guy gets it

>>739487661
0.999... is real, but you don't need "infinity" at any point to define it. You need an infinitely long decimal expansion, but not infinity. Why is this? Because the decimal system is only somewhat accurate to write numbers.

For example, consider a base 12 system rather than a base 10 system. There, 1/3=.4. In base 12, 1/3 does not repeat. But in base 10 it does. This is because 3 is not a factor of 10, but is a factor of 12. Likewise in base 12, 1/5 *does* repeat, because 5 is not a factor of 12 but is of 10. (1/5 in base 12 is 0.249724972497... if my math checks out.)

For 0.999... specifically, this is just an alternate way of writing the real number known as 1, in the same way that 1=1.0=1.00=1.000, and so on are all alternative ways of writing 1.

Strictly speaking, ANY real number that has a continually repeating string of numbers in its decimal expansion is a rational number and can be represented as a fraction instead of a decimal.

>>739489185
marsclimateorbiter.jpg

>>739488811
This makes the most sense

>>739488996
Represent one third in base 10. You can't.

>>739478850
What number lies between 0.999... and 1?
If there is none, then both numbers are equal (we are taking real numbers).

>>739477498
You could just use the approximation sign ≈ and stop being a cunt. Good luck passing any STEM courses being that dense, you cunt.
>>739477498

>>739488874
>meant irrational
1/3 is rational
rational means the ratio of two integers

>I stick with "it's an approximation" and it will never be more than that.
there are rigorous ways to map countably infinite series of digits to real numbers,
but they require 1 = .9999...

File: IMG_1269.jpg (28KB, 480x269px) Image search: [Google]

28KB, 480x269px

>>739477498
Actually, the Leibniz identity of indiscernibles says they are the same.

>>739489391
I'm asking this since the post started an no-one could answer something logical.

>>739488811
9.9 does not equal 9.9999....

>>739489444
It actually states the opposite you candy ass

>>739487032
1/2 + 1/3 + 1/4 + ... doesn't equal 1, it diverges. You can see that pretty quickly --- it exceeds 1 after the first three decimals and only gets bigger from there. However, 1/2 + 1/4 + 1/8 + ... does equal 1.

>>739489575
No, if 9.99999... and 1 share the same predicates, then they are the same. So you are the only jabroni here.

>>739477498
retard semantics=retard sematicos

>>739489391
There cannot be a number between the two because 9.999... goes on with infinite digits, it will always be one more 9. It doesn't mean they are the same. What about 0? It's the same as saying "Name a number between 0 and 0.000...1. It must be the same if you can't." But it isn't the same. 0 isn't a number it is a symbol given to things of no value, but clearly the 0.000...1 has at least a little value, right? Then they are not the same.

stupid fucks 1 = .999...

take 1.0 glass of water

split it into 3 equal parts

how do you represent each part? .333 repeating

put them back together
1 = .999 repeating you dumb fucks

the repeating is just how you represent fractions in decimals. three thirds of a glass isn't infinitely less than one glass. it's just one fucking glass

>>739489435
fuck... but sqrt(2) and pi aren't. i wanted to compare them going on infinitely with 0.999... going on infinitely.

>they require 1 = .9999...
this is what we are trying to prove first. and mapping infinite series of digits to real numbers is only used for practical application. i said i wont stop you when you assume 0.9999... = 1 if you do it for practical uses, i wont even stop you from sayin g = 9,81 = 10. But if you go into theory and say 0.9999...*c = c i will not agree anymore

>>739489678
*.999....

>>739489827

no

if you have an infinite number of zeroes then the value is zero

also it's nonsensical to think of numbers coming after an infinite string - it's not a meaningful statement

>>739488811
If you draw a line at 10 degrees and another line at 9.999... degrees they would never actually cross. There would always be another 9 holding it back.

This is actually an interesting evidence for them being the same value...

>>739488100
>Flip this all to a number base 3 and it works flawlessly, but you're fucked on halves.
>you're fucked on halves
huh. i never thought of that. how WOULD you represent a 0.5 in base 3?

>>739488996
retard

>>739477498

1 does NOT equal 0.9999999...

Programmer proof: imagine if you have a computer with infinite memory, who has these two values in memory.

X = 1;
Y = 0.999999999999...;

Now, if we convert it to strings we quickly see the following:

XString = X.ToString(); // Contains "1"
YString = Y.ToString(); // Contains "0.9999..."

If we compare them, the comparer will quickly determine that they are NOT EQUAL on the first character on the string as 0 does NOT EQUAL 1.

Dumbfucks.

>>739489678
If by predicates you mean that they are both numbers, I suppose I smell what you're cooking. However, that's just a bunch or brahma bullshit

>>739490048

divide 1 by 2 just like in base 10

>>739477498
its correct but not reality compatible.
PI is endless and crucial for circular mathematics, meaning it would be impossible to calculate with circles or spheres

>>739489969
Hopefully you will take geometry when summer is over

>>739490087
this b8 is such shit one could almost argue it's good b8... but really it's just shit. i'm embarassed for you

>>739490087
Where can I buy a computer with infinate memory?

>>739487945
Wait your telling me the turtle doesn't win?

>>739489944
Watch Vsauce's video on Supertasks. Say in 2 minutes you flick a light on and off, taking half as long as you did to turn it off the last time. so in the two minute time span, you flick it on, wait 1 minute, flick it off. Then half a minute, quarter minute, eighth minute, sixteenth minute, etc. You WILL eventually hit the 2 minute mark but what state will the light be in? It has to be in one state or the other. Not both, not neither, one or the other, meaning that you can have an "infinite" amount of 0's and the final digit be a 1.

>>739490087
So 0.5 does not equal 1/2 because it starts with a 1?

what a dickhead

>>739490210
Its winter in the southern hemisphere faggot

>>739489410
there are rigorous ways to map countably infinite series of digits to real numbers

>>739486380
In math world I can.

>>739490123
go ahead and type it not as a fraction then, faggot

>>739490320
You still be a retard wherever you are. Except Africa. You'd just be slow there.

>>739490315
jfc, you're a moron

>>739490389

0.111111111111...

stupid motherfucker

>>739490422
You would still suck at
1. Logic
2. Debate
3. Life

Not sure on the order, but tou get the point

>>739478030
>approaches
its not a limit

>>739490505

and if you added 1/2 plus 1/2 in base 3 you get

0.22222222222 repeating

stupid fucks would say "less than 1 by infinite amount" still but they'd be wrong as fuck

>>739490505
EXACTLY, it doesn't fucking work, dumbass. It's still infinitely repeating digits. The same problem we have with dividing 1 by 3 in base 10.

>>739490523
If you think that /b/ is a litmus test for debate or logic skills it is clearly you that doesn't have a life.

>>739490758

It works just fine. it's a representation and non-stupid fucks know what it means

>>739490919
0.22222222222222 doesn't fucking equal 2 retard.

>>739490919
It means that an infinitely repeating sequence of numbers suddenly stops and morphs into an entirely different number.

Some.people seem to struggle with the fact that infinite means repeat forever.

>>739482366
You can't use the x value on one side of the equation and the variable on the other... write either
10x-x=9.999...-x
Or
10x-0.999...=9.999...-0.999...
But you don't do this, and do you know why? Because 9.999... =/= 10

>>739490919
>>739490505
jfc, you're a stupid fuck. missed the point entirely

>>739491092

the infinite repeating is just how you represent a fraction. it is the same thing as the fraction.

you take 1 cup and split it into equal thirds.

you can represent that in fractions: 1/3
or you can represent it in decimals: 0.3 repeating

if you add those back together, you still have 1 motherfucking cup.

we're talking about decimal representations of fractions here, not infinite sequences

>>739491402

no you.

explain then idiot

>>739478030
that exactly, thread solved

This is some high brow trolling

>>739491437
But if the representation of the fraction is an infinite series of 9s then that series needs to either actually be infinite or not.

If it is represented as infinite 9s then it is never 1. Just basic logic

>>739477498
Yeah, no shit they aren't the same, but it's gud 'nuf, so we don't care and neither should you.

Guys it's very easy,
1/n for n->infinity equals zero, so 1-1/n equals 1. Its a simple limit. In a way it's intuitive as you are subtracting an impossibly small number from 1. For all else this is how the formalism works, and mathematical analysis for that matter; if you want to discuss the phylosophycal background to the problem then it's another thing, wchich is not of concern to math analisys. If you want to seek further reading on the topic you can read any analysis text or look for limits and such.

ITT people not understanding the concept of infinity

>>739477498
Where's an Asian when you need one.

File: IMG_1444.jpg (24KB, 353x353px) Image search: [Google]

24KB, 353x353px

I'll take the bait. They represent the same value not the same number.

>>739491839
Now you fucked up.

>>739491672

represent 1/3 in decimal for me?

the way you do it is .3 repeating, with the line over the 3 and shit

the decimal way to represent 1/3 is .3 repeat and it means the exactly one thing, 1/3

>>739491750
I only did 4 university math units... 20 years ago... but from memory limits define the way things behave as they hypothetically approach a value. They never actually hit that value.

I fail to see how they make something approaching 1 hit it.

Let us go back to basics by realizing what 0.999... means. It is true that infinity is NOT a real number. Thus you cannot just throw in infinity and expect it to work like a real number. One of the few places where you can actually use infinity is when defining limits, i.e., you are allowed to write something like the following:
lim [...]
n→∞
For convenience, when writing limits, we sometimes inline the infinity, especially in sums (also called infinite series). For instance we may write the following:
∞
∑ [...]
i = 0
which is defined to be the same as writing:
n
lim ∑ [...]
n→∞ i = 0
We use ellipsis to refer to the infinite series obtained by repeating one or more decimals. In this case, 0.999... is the same as writing
∞
∑ 9 / (10^i)
i = 1
thus, by definition of the syntax, we have the following:

n
0.999... = lim ∑ 9 / (10^i)
n→∞ i = 0
If you know how to work with limits, you will find that the limit does indeed exist and that the limit is 1. Thus 0.999...=1.

>>739482077
>>739482212
>>739482240
>>739482281
>>739482342
>>739482410
>>739482411
>>739482472
>>739482511
>>739482528
>>739482557
>>739482625
>>739482666
>>739482774
>>739482801
>>739482939
>>739483041
>>739483173
>>739483181
>>739483513
>>739483597
>>739483855
>>739485058
>>739485083
>>739485321
>>739485324
>>739486380
>>739486401
>>739486405
>>739486409
>>739486416
>>739486580
>>739486613
>>739486673
>>739486755
>>739486757
>>739486896
>>739486976
>>739487032
>>739491075
>>739491092
>>739491437
>>739491538

It's proven and accepted in the mathematical community that 0.999... = 1
Why are people even trying to argue against it? It's literally accepted as fact by all the greatest mathematicians in the whole world.

If you truly believe you have some sort of proof that it isn't true then stop wasting time convincing other 14 year old edgelords on /b/ and go become a 'The famous mathematician that proved the world wrong'

File: 1457346829320.webm (1MB, 720x480px) Image search: [Google]

1MB, 720x480px

>>739477498

>Discuss.

There is no number that fits between 0.999... and 1. Therefor they are the same by definition.

Op is a fag https://youtu.be/ZrAfMDAqzLg

9.99999999999999/10 thread

>>739492044
you cant even show that it is this way, its just a convention of all mathematicans. There are more rules e.g. u cant divide by 0 or that pi actually was once almost changed to 3,15 but still stayed on 3,14..
btw how long did it take for all those tags?

>>739479524
Not how infinity works

File: get fucked cat.jpg (7KB, 251x251px) Image search: [Google]

7KB, 251x251px

>>739481872
>>739482240
>>739485750
>>739482502

>googled the solution to a well known problem
>claim to be clever

not true, 0.99999... Is only 1 if it is rounded. This is a realy stupid thread

>>739492705
finally someone else.

>>739477498
0.99999999999999...
Simply cannot exist.
Problem solved.

>>739492965
/thread/

1/0.999....=1.00000........1 and not 1, therefore 0.999... is not 1

>>739489072
>0.333... only tends to 1/3

No. It is not a process, it is a concept. The illustration by process serves only to, wait for it, approximate the concept.

>>739492965
>i can't imagine it
>it can't be

QED amiright.

0.999.... == 1 - 1/∞

>>739477498
Only a Jew would pretend that 0.99999 shekels is 1 shekel. Anyone who thinks 0.99999 is 1 is a Jew.

File: 1499205820317.png (435KB, 609x456px) Image search: [Google]

435KB, 609x456px

>>739481685

>>739493300
Get smarter m9

Repeating decimals are just representations of numbers, exactly the same way fractions are representations of numbers. Any fraction can be represented in decimal notation and vice versa.

So .333... means the same thing as 1/3 by definition.

The repeating is just how you represent that number that could be equally well represented by the fraction 1/3.

What is a third of a cup written as a decimal? 0.3...

What do you get if you add three thirds of a cup together? One stupid fucking cup

THERE IS NO NUMBER BETWEEN 0.99... AND 1, THEREFOR IS THE SAME NUMBER,

>>739492161

0.999... Means that there are an infinite amount of 9s. Because infinity is not a specified amount, we can not realy give a concrete number between 0.999... And 0. However if we imagine that it was a concrete number it would still end with a 9 and this means that 1/0.999.... = 1.00.....1 and therefore 0.999... Is not equal to 1 and the number in between 0.999.. And 1 would be 0.999...+0.000....9

>>739493711
Again, according to that logic, 0.000...1 has no value because there is no number between it and 0.

ffs two number are only defined as different if there is a number inbetween them. Since there is no number inbetween .99999999999... and 1 they are the same.

Both answers are correct, bc there is a infinitly small difference between 0.9999...9 & 1.
But in real numbers infinitly small numbers don´t exist, whereas in hyperreal numbers such numbers do exist. Thus everyone is right.

>>739493889

It's a decimal notation of a number that could be represented as a fraction. If it was written as a fraction you wouldn't be so autistic about the infinite part. It's not "an infinite amount of 9's" it's a number that you can represent however you want. as a fraction or as a decimal or as a base-3 number or whatever the fuck you want. three thirds of a cup is one cup whether you write it with repeating digits or fractions.

>>739493954
thats another number,not OP, i always ask myself about that number ANYWAY

>>739494153
How is 0.999... not an infinite amount of 9's?

>>739493484
Id like to change my answer to the non kike one please.

>>739494211

the number doesn't have any aspect of infinity to it, just its representation in decimal

>>739493138
There is no number with infinite periodic decimal places and a digit at the end. By definition, an infinite number of digits has no end.