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10360371 No.10360371 [Reply] [Original] [archived.moe]

Alright, alright.

Let's settle this as adults with a compromise, now everybody wins!

>> No.10360444

>>10360371
In certain circumstances such a limit can make a difference (like in 'chaos theory' some attractors have infinitessimal divisions and can strictly be affected by infinitessimal errors), but for any level of error you want 0.999... will equal 1

>> No.10360460
File: 44 KB, 948x264, 1549401917361.png [View same] [iqdb] [saucenao] [google] [report]
10360460

>>10360371
there will be no compromises. this is a mathematical truth

>> No.10360461

>>10360371
Infinitesimals are a trash meme.

>> No.10360476

>>10360460
you drive a hard bargain

>> No.10360483

>>10360460
high iq thread

>> No.10360588

>>10360460
>>10360371
both are true

>> No.10360657
File: 14 KB, 200x300, 1493689384887.jpg [View same] [iqdb] [saucenao] [google] [report]
10360657

>>10360371
not so fast

>> No.10361510

>>10360460
based

>> No.10361516
File: 6 KB, 618x175, SlopeProof.png [View same] [iqdb] [saucenao] [google] [report]
10361516

Infinitesimals are real and a recognized part of mathematics. People who argue that .999... = 1 are arguing from authority and can't really think mathematically on their own.

https://www.youtube.com/watch?v=WYijIV5JrKg

>> No.10361540

>>10361516
I can think mathematically on their own, and I get the thing why mathematician choose the real over hyperreal when constructing topology on hyperreal

>> No.10361543

>>10360371
[math]
1 = \dfrac{3}{3} = 3 \cdot \dfrac{1}{3} = 3 \cdot 0.\bar{3} = 0.\bar{9}
[/math]

>> No.10361554

>>10361543
This is the stupidest proof.

If you didn't notice the assumption that 1/3 = .333... then that is what I mean by "can't think mathematically on their own."

>> No.10361565

>>10361540
>I get the thing why mathematician choose the real over hyperreal when constructing topology on hyperreal

If you choose the Natural over the Real set, you can 'prove' that 1/2 = 0. I can name a situation where this is the correct answer, but that doesn't mean it is reasnable to assume 1/2 = 0 in all cases.

>> No.10361576

>>10361554
https://www.wolframalpha.com/input/?i=1%2F3+-+0.333...

>> No.10361584

>>10361576
I'm your side but nigga wtf

>> No.10361589

>>10361554
hey prof sai got a question

then what is (2-.999...)/.999... ?

>> No.10361591

>>10361584
>I'm your side
ok this is legendary

>> No.10361599

>>10361554
1/3 = 3/10 + 1/30
= 0.3 + 1/30
= 0.33 + 1/300
= 0.333 + 1/3000
:
= 0.3... + 1/inf
= 0.3... + 0
= 0.3...

>> No.10361607

>>10360371
Such a statement can only be proven or disproven with a real-world observation, some way of observing this mathematical truth before us.
0.999... what is that exactly? Well, for every n length stick, there’s another stick beside it that has n-1 length. So, a stick of length 10 is beside a stick of length 9.
9/10, 99/100, 999/1000, and so on. The sticks are defined as being different. The fraction is always n-1/n. The second stick never catches up.

0.999... < 1

>> No.10361611

>>10361599
>1/inf = 0
Right, because a stick of length 1 will some day become absolutely nothing as long as you compare it to a stick of infinite length.

>> No.10361636

>>10361611
https://www.wolframalpha.com/input/?i=1%2Finf

>> No.10361646

>>10361611
>stick of length 1
actually, any real number
(graham's number^graham's number)/inf = 0 too

>> No.10361655

>>10361607
x = 0.9...
10x = 9.9...
9x = 9.0...
x = 1 = 0.9...

>> No.10361656

>>10361655
>a variable can be made equal to a non-terminating ratio
>non-terminating ratios can somehow be added to one another
>non-terminating ratios can be multiplied by integers
I’m gonna need some proof pal

>> No.10361657

>>10361656
What is 9.999.../10 ?
Is it <1, =1 or >1 ?

>> No.10361659

Two walls. 1 is fixed in place. The other wall approaches the first, covering 9/10 distance between them with each movement. The walls will never meet, because 9/10 will never equal 10/10. There will always be a gap between the walls. Keep zooming in, and it will be as if you have made no progress.

>> No.10361662

>>10361659
call it peaches

>> No.10361665

>>10361657
What is 9.999...? How is it any different from the examples given
>>10361607
>>10361659

The 0.999... denotes a ratio that, to me, never becomes equal to 1.

>> No.10361673 [DELETED] 

>>10361665
answer please

>> No.10361675

>>10361665
Is it <1, =1 or >1

>> No.10361676

>>10361675
It never reaches 1. It will always be less than 1

>> No.10361681

>>10361676
ok so you agree that the answer is
0.something

next question:
Is it <0.9, =0.9 or >0.9

>> No.10361688

>>10360588
How the fuck is that true?

>> No.10361691
File: 115 KB, 437x640, Pope Real set.jpg [View same] [iqdb] [saucenao] [google] [report]
10361691

Every proof of 1=.999... ultimately has the same flaw:

The set of Real numbers was specifically designed to exclude non-zero infinitesimals. As a result, any proof involving the Real set assumes the conclusion you are trying to prove. Infinitesimals don't exist in the Reals for the same reason that fractions don't exist in the Integers.

This is the OPPOSITE of a proof.

As the video I linked to above shows, infinitesimals have been important since Issac Newton's time. There was an emotional need to deny them for a while, but for serious maths, that is over now.

Anyone questioning 1=.999... is thinking about infinitesimals. Responding with "proofs" based on real numbers is obnoxious and undermines people's faith in math and science. It needs to stop.

>> No.10361698

>>10361691
>exclude non-zero infinitesimals
duh, that's why we talk about limits if you stick to R

>> No.10361699

>>10361589

.999...

>> No.10361701

>>10361681
It can certainly be greater than 0.9.

>> No.10361705

>>10361701
ok so you agree that the answer is
0.9something

next question:
Is it <0.99, =0.99 or >0.99

>> No.10361706

>>10361698
>that's why we talk about limits if you stick to R

Yes, that is what Dr James Grime says in the video. We invented limits (and the Real set) so that we wouldn't have to talk about infinitesimals any more.

https://www.youtube.com/watch?v=WYijIV5JrKg

>> No.10361708

0.0 = 0
0.3... = 1/3
0.6... = 2/3
0.9... = 3/3 = 1

>> No.10361709

>>10361705
>Is it <0.99, =0.99 or >0.99

Are you trying to use Zeno's paradox as a proof? If you ask an infinite number of questions an endless number of falsehoods will add up to the truth?

>> No.10361710

>>10361708
>0.0 = 0
>0.3... = 1/3
>0.6... = 2/3
>0.9... = 3/3 = 1

Prove it.

>> No.10361712

>>10360371
Suppose

>> No.10361723

>>10361705
This isn’t going anywhere. 0.999... is greater than all terminating values between 0 and 1 but always less than 1.
By definition, 0.999... is a ratio that never approaches 1.

n-1 will never reach n.

>> No.10361725

>>10361709
are you going to answer?

>> No.10361726

0.99 != 1
Our number system cannot properly represent 1/3

>> No.10361730

>>10361725

I'm not the poster you asked, so no.

>> No.10361732

>>10361726

1/3 = .1 (base 3)

>> No.10361749

1 is the LIMIT of 0.999...

It is the same principle as an asymptote. Take the graph 1/x. As x gets infinitely larger, it approaches zero, but never actually touches the x-axis. You can zoom in on the graph for an infinite amount of time and the graph will always be above the x-axis. How is this so hard to understand?

>> No.10361843

>>10361723
are you going to answer?

>> No.10361864

one of my professors asked if we could find a number that was between .9999... and 1. one of the fundamental axioms, between any two unique numbers a and b, there exists a unique c between them.

>> No.10361868

>>10361516
>can't really think mathematically on their own.
>links a memephile video

>> No.10361872

>>10361699
...wut?

How can a number >1 divided by a number <1 be less than 1?

I don't think it's one, but .999... ain't it chief. IMO the expression is irreducible.

>> No.10361878

>>10361864
.999.../10+.9

ez mode

>> No.10361884
File: 17 KB, 400x400, 1508386795971.jpg [View same] [iqdb] [saucenao] [google] [report]
10361884

>>10361864
>one of the fundamental axioms, between any two unique numbers a and b, there exists a unique c between them.
>.999... is a number
>infinity is a number

>> No.10361885

>>10361878
how is that >0.9... ?

>> No.10361886

>>10361884
>infinity is a number
no it isn't

>> No.10361890

>>10361749
the expression [math]\sum_{n=0}^{\infty}a_n[/math] actually means two things: the series itself and its limit (when it converges), while it's usually clear from the context what is meant. it's a completely harmless abuse of notation, and otherwise it wouldn't really make sense to write [math]\sum_{n=0}^{\infty}a_n = 3[/math] for example. whenever you treat the symbol [math]0.999...[/math] as a number (e.g. you compare it to other numbers), it actually stands for [math]1[/math].

>> No.10361904

>>10361886
That's the point. .999.... is just a representation for the limit of a particular series. Just like infinity is.

I brought up infinity because it's the easiest analogy that shows how it can't be compared to a real number.

>> No.10361913

>>10361904
amount of digits =/= value

example: 1.000....

>> No.10361926

>>10361913
The difference is that 1.000 is completely consistent with the series 1+0+0+0...

Are you not aware that treating the series 9/10+9/100+9/1000... as 1 does not always yield the same results?

>> No.10361947

x = 0.9...
10x = 9.9...
9x = 9.0...
x = 1 = 0.9...

>> No.10361968

>>10361947
>10x = 9.9...
>9x = 9.0...
This is wrong.

9x=9 + 9*(.1)*(.1)*(.1)....

Why are mathematicians so bad at understanding infinite series?

>> No.10361972

>>10361968
Sorry,
9x=9 - 9*(.1)*(.1)*(.1)....

>> No.10361975

>>10361968
>mathematicians so bad
unlike shitposters?
kek

>> No.10361981

>>10361975
I'm feeling pretty good about my stance if that's your argument.

>> No.10361996

>>10361981
never met a crazy who wasn't

>> No.10362000

>>10361996
Why are you scared, brainlet?

>> No.10362031

>>10361972
9x=9+0.1^inf
9x=9+0
x=1

>> No.10362044

>>10362031
>9x=9+0.1^inf
>9x=9+0
prove it. Matter of fact

>0.1^inf*10^inf==0*10^inf
>(0.1*10)^inf==0
>(1)^inf==0
>1==0
>false
therefor 0.1^inf!=0

Please tell me you already knew you were making a circular argument and just wanted to waste my time.

>> No.10362054

>>10362044
https://www.wolframalpha.com/input/?i=0.1%5Einf

>> No.10362057

>>10362044
>0*10^inf
0*inf is undefined, mr crazy

>> No.10362094

You brain need some language because your minds are tired of numbers and wibbily letters.
A number that is ultra close to one is less than one and despite how infinitely close to one it is, it is not one! This is also known as 0.999...<1

>> No.10362096

>>10362094
this post would be cooler if i didn't botch the first two words

>> No.10362117

>>10362094
>infinitely close
0 distance, so 0.9...=1

>> No.10362174

>>10360444
nope

>> No.10362178

>>10361656
>non terminating ratios can be multiplied by integers
>he doesn't know that the distributive property is one of the axioms
>mfw

>> No.10362179
File: 112 KB, 953x613, 1542054335766.jpg [View same] [iqdb] [saucenao] [google] [report]
10362179

>> No.10362219

.999...≠1

>> No.10362222

>>10362219
>>10362179

>> No.10362272

>>10362222
The image is correct. The bottom left with green ground :
>A simple proof of induction:
>x = 0.999...
>10x = 9.999...
>10x - x = 9.999... - 0.999...
>9x = 9
False; 9x = 8.999...

>> No.10362276

>>10362272
>correct
*Incorrect*

>> No.10362296

>>10362272 (Addendum, for shitposters)
>x = 0.999..
>9x = 8.999...
because its a infinitely repeating the trailing 1 is never reached. If it wasn't infinite then:
>n = 0.999
>2n = 1.998
>3n = 2.997
>...
>9n = 8.991

>> No.10362314

There are so many proofs of this is it silly people still argue against it.

>> No.10362320

>>10362314
"people"

>> No.10362325

>>10361688
they are both true because they say "less than or equal to" and "greater than or equal to". Since the answer is "exactly equal to" they are both true.

>> No.10362333
File: 7 KB, 274x290, Oy+vey+shekels+mah+shekels+_4525f0b974d66219703e161fa294167b.png [View same] [iqdb] [saucenao] [google] [report]
10362333

so if i am to send you BTC for your proofs, should i send you 1 million x 1 BTC or 1 million x 0.999.. BTC?

>> No.10362342

Imagine not being able to conceptualize why .9999999999... is exactly equal to 1
This is why we look down on engicucks

>> No.10362345

>>10361710
Prove what? that 1/3 is 0.333...?
Just divide by hand yourself.

>> No.10362349

>>10360371
π
>3.14159265
>3.1415927
>3.141593
>3.141590
>3.1416
>3.142
>3.10
>3.0
>3
π = 3

>> No.10362350

>>10361749
There is no "limit" of 0.999...
0.999... is the limit of the sum 9/10**n and if that equals 1, then 0.999... equals 1.

>> No.10362356

>>10362349
Great, you're doing the process backwards

>> No.10362378

>>10361611
>moves goal posts

>> No.10362414

>>10362333
It's the same, so who cares?

>> No.10362418

>0.9... = 1
This is crazy.
0.9... = 1 = 0.9... + 0.1...
1 - 0.1... = 1
0.1... = 0
0.1... + 0.1... = 0
I'm still not buying anyone could believe the above.

>> No.10362421

>>10362418
>0.9... = 1 = 0.9... + 0.1...
What the fuck are you doing?
And don't play the "I was just pretending to be retarded" card.

>> No.10362432

Two real numbers a, b are equal IFF there does not exist a real number c such that a < c < b
Let a = .999999999999999999999999...
Let b = 1
Find a c such that .999999999999999999999999999999... < c < 1
Oh wait, you can't.
Therefore .999... = 1
Its literally that simple and if you don't understand this you are certified retarded

>> No.10362433

>>10362432
>b-b-buh 0.999...995 dude

>> No.10362442

>real numbers
ah yes the cruel joke of modern mathematics.

>> No.10362448

>>10362442
The reals are well defined and objectively exist.
You are a certified retardo

>> No.10362449

>>10362448
if you say so guy

>> No.10362451

>>10362449
It's not "me" saying so there are shitloads of proofs for this.
Tell me 1 reason how the reals aren't well defined or what the problem is with them. "I don't like uncountability or the idea of infinite processes" is not an answer

>> No.10362461

>>10360371
>"An irrational number is a rational number"

Uuuuhhhh... okay buddy

>> No.10362467

>>10362421
Well 0.9... + 0.1... = 1 and if like people are arguing in this thread 0.9... = 1 then 0.1... = 0 so 0.1... + 0.1... = 0 also 1 - 0.1... = 1
This 0.1... = 0 is what everyone is arguing in support of aka every number equals zero.

>> No.10362478

>>10362418
>0.9... = 1 = 0.9... + 0.1...
0.9... = 1 =/= 0.9... + 0.1... = 10/9

>1 - 0.1... = 1
1 - 0.1... =/= 1
1 - 0.1... = 8/9

>0.1... = 0
wew lad

>0.1... + 0.1... = 0
sigh

>> No.10362483

>>10362461
0.9... is an integer

>> No.10362485

>>10362467
>also 1 - 0.1... = 1
That's a mistake, I forgot 0.9... = 1 in this thread so 1 - 0.1... = 0

>> No.10362492

>>10362478
>0.9... = 1 =/= 0.9... + 0.1... = 10/9
0.9... ≠ 1
0.9... + 0.1... = 1
Not according to people in this thread but according to reality.

>> No.10362541

>>10362432
A small contraption is 1 meter long. At one end is an infinitely thin metal sheet.
0.1 meter away from it, is another metal sheet. 0.01 meter away from it is another metal sheet, and so on. The sum of the distances are then 0.9 + 0.09 + 0.009... etc for infinity. For every terminating number, it will be surpassed by the sum. Yet the sum never reaches 1, because each successive sheet will always be 1/10 distance away from the last sheet. The sheets never touch.

>> No.10362570

0.9... =/= 1
Because
0.9... + 0.1... = 1.0...

>symbol test, there should be a guide on what is filtered
Not equal ≠
Therefore ∴
Because ∵

>> No.10362578

>>10362541
>inb4 the sheets magically touch “at infinity”
The gap cannot be eliminated. Each section is only different in size. The 9/10 is consistent, and never reaches 10/10.

0.999... is less than 1

>> No.10362607

ITT a bunch of retards claiming 1≠0.999...
what a sad state of affairs

>> No.10362645

>>10362570
No. On finite lengths of 0.999... adding a 1 to the last digit starts a cascade of carrying over that causes each digit to flip from 9 to 0 and send the 1 to the next digit.
For example 0.9999 + 0.0001 = 0.9990 + 0.001 = 0.9900 + 0.01 ... until the 1 rests at the unit digit and the sum equals 1.0000.
Now if you extend the trail of 9s infinitely, logically you have to add a 1 digit to the last digit which if infinitely far out in order to get 1. You are adding 1 to every digit meaning there is an extra 1 at every digit except the units digit, so your sum gets 1.11... .
The number you have to add is a string of 0s ending with a 1 infinitely far to the right. Now what is that number?

>> No.10362750

>>10362492
>people in this thread
you're confusing that with the voices in your head

>> No.10362756

>>10362570
>0.9... + 0.1... = 1.0...
0.9+0.1=1
0.09+0.01=0.1
etc
0.9... + 0.1... = 1.1...
1 + 1/9 = 10/9

>> No.10362768
File: 216 KB, 473x477, Screenshot_20190206-115733_Google.jpg [View same] [iqdb] [saucenao] [google] [report]
10362768

>>10360460
>>10362174

>> No.10362783

The definition of the reals in terms of the rationals tells us that two reals are equal if their distance is smaller than any positive rational number. 0,000...1 is not a rational number, so 0.999... and 1 are the same real number. They are not the same surreal number, if one wants to explore the consequences of their inequality.

>> No.10362825

Between any two different real numbers, one can take their average, which will be a different real number. So if a<b, then a<(a+b)/2<b. You can't name a number bigger than 0.99999... and smaller than 1. Therefore, 0.99999...=1

>> No.10362849

>>10362825
>>10362541
>>10362578

>> No.10362863

>>10362492
>0.999... + 0.111.. = 1
stoopid

>> No.10362976

0.9 + 0.1 = 1
0.99 + 0.01 = 1
...
0.999...9 + 0.000...1 = 1

>> No.10363000

>>10362976
>0.999...9 + 0.000...1 = 1
1+0=1

>> No.10363016

>>10362976
What's your point?

>> No.10363019
File: 37 KB, 586x578, 1519134466886.png [View same] [iqdb] [saucenao] [google] [report]
10363019

>>10362057
>0*inf is undefined
fucking idiot lmao
0*inf
0*(10*10*10....)
0*10*0*10*0*10...
=0

>>10362054
this isn't a better argument than when it was posted before

If you wanted to say 0 or 1, then why don't you just say 0 or 1 you fucking mongrels. An infinite series is not necessarily the same as a real number just because it converges.

>> No.10363028

>>10362314
*so many incorrect proofs

meanwhile there are extremely simple numerical counterexamples showing it can't possible be equal to 1.

>> No.10363033

>>10362432
>a
>real number
why can't mathlets use brain?

>> No.10363034
File: 98 KB, 500x282, Wrong ding dong.gif [View same] [iqdb] [saucenao] [google] [report]
10363034

>>10363028

>> No.10363039

>>10362578
>t. I can't into limits

>> No.10363048
File: 545 KB, 572x703, 1537485316059.png [View same] [iqdb] [saucenao] [google] [report]
10363048

>>10363034
An anime reaction image? That's your proof?

Look up Bernoulli trials my based brainlet

>> No.10363054

>>10362418
>0.1...
You mean 0.0...1

>> No.10363109

>>10363039
>literally called limit
>he thinks it can be reached
1 + 1/2 + 1/4... can never equal 1, or else it would then surpass 1. When does the gap close? Keep zooming in, keep zooming in, it’s always there. You can’t make it go away using definitions and axioms. This is real life, bucko. Mathematics would be just as useful and consistent if the concept of infinity were thrown out completely.

>> No.10363120

>>10362849
You're a fucking retard and your "argument" using physical beams is literally irrelevant. If this is how you think it's no wonder you can't do math.

>> No.10363124

>>10363109
But even supppsing that an infinite sum can exist, then let us call it what it is: infinite. The sum never ends. You cannot say “at infinity the sun = x” because there is no such thing as “at infinity.” This misconception probably stems from mathematical statements like “as x approaches infinity” etc. But x can never get closer to infinity, it will never “reach” infinity.
0.9 is less than 1 just as 0.999.... is. Take two sticks, one being always one meter less than the other, and stretch them both out at a constant rate for as long as you like, the ratio of their lengths will never equal 1. One will always be in front of the other by one meter.

>> No.10363130

>>10363000
0.000...1 = 0? How can something which obviously is something, be nothing?

>> No.10363134

>>10363120
Not an argument. Math doesn’t require infinity to be useful in our world. The idea that pi can be APPROXIMATED using an infinite sum is neat, but we have to remember that circles don’t actually exist, which is why the number is transcendental. Taking the area under a curve should only require infinite sums of you’ve assumed that the graph is in a transcendent space, unlike everything we encounter in reality.

>> No.10363138

>>10363134
>Math doesn’t require infinity to be useful in our world.
The physical universe is a proper subclass of mathematics so what you're talking about makes literally no sense.
This universe isn't discrete btw it is isomorphic to the Continuum so I have no idea what the motivation for what you're saying is anyway.

>> No.10363140

>>9999999
we already settled this shit a few months ago

>> No.10363146

>>10363140
based & /thread pilled

>> No.10363153

>>10363138
Prove that the “continuum” exists. How can we derive infinity from our discrete perceptions?

>> No.10363167

>>10363153
>How can we derive infinity from our discrete perceptions?
....crickets

>> No.10363177

>>10363130
It is the middle ground between things that are something and nothing.

>> No.10363190

>>10363140
holyshit

>> No.10363210

>>9999999

>> No.10363215

>>10363019
sure, mr crazy
https://www.wolframalpha.com/input/?i=0*inf

>> No.10363223

>>10363130
0.1 = 10^-1
0.01 = 10^-2
0.001 = 10^-3
;
0.000...1 = 10^-inf = 0

>> No.10363228

>>10363223
>1/ INF = 0
>1
>0

If the universe is infinite, humans don’t actually exist.

>> No.10363235

>>10363153
This was proven over a hundred years ago

>> No.10363240

>>10363235
Actually it was disproven 50 years ago. Your move, retard

>> No.10363245

>>10363240
>Actually it was disproven 50 years ago
No it wasn't. This level of delusion.

>> No.10363249

>>10363240
that turned out to be a false alarm

>> No.10363255

If imaginary numbers exist, then why can't infinitesimals?

>> No.10363257

>>10362325
this

>>10361688
let x = 0.9999...
so 10*x = 9.999.....
now subtract 1*x:
10x = 9.999.... | -x
9x = 9 | :9
x = 1

>> No.10363263

>>10363255
no problem, as long as you don't confuse them with real numbers

>> No.10363280

>>10363228
>>10363153
>>10363134
>>10363124
>>10363109
>>10362541
>>10361749
>>10361659
Not a single one of these posts has been refuted

>> No.10363295

>>10363280
because they belong in >>>/x/

>> No.10363297

>>10363295
You only embolden my conviction, and offer no evidence to persuade me. You’re the one who believes in something never yet perceived (infinity) yet you claim I belong on a paranormal board.

>> No.10363304
File: 42 KB, 1920x1872, 1920px-GeometricSquares.svg.png [View same] [iqdb] [saucenao] [google] [report]
10363304

>>10363280
fine i'll refute this one

>>10363109
pic related, there ain't no gaps. pick any point in this unit square, and it's not too hard to find the term in the geometric series would capture that point. therefore the area of this figure is 1 unit squared exactly

>> No.10363313

>>10363297
>me me me
no one cares, anon

>> No.10363316

>>10363304
The purple squares never connect to the corner, or else there would be a finite amount of them. This is only a rehash of the same problem, the logic still applies. It never actually reaches the goal, hence why it’s an INFINITE sum. It never ends.

Btw your English is hardly understandable

>> No.10363396

>>10362645
>Now what is that number?
0.000...1

>> No.10363424

0.9... ≠ 1 ∵ 0.9... + 0.0...1 = 1.0...

>>10362645
Thanks.
>>10363054
I do now, thanks.

>> No.10363482
File: 212 KB, 1281x612, Rafael_Sanzio.jpg [View same] [iqdb] [saucenao] [google] [report]
10363482

You could argue a lot about how [math]0.99 \dots[/math] is unclear, how can the dots be very ambiguous and how can one abuse notation. Well, maybe what is needed is to justify and explain notation and representation. To really understand numbers real analysis is needed, so you will lose your time with someone who only knows up to basic algebra because without any fundaments you can talk very few things about numbers and infinity.

Now, what is [math]0.9999999 \dots [/math] ?

[eqn]0. \bar{9} = \frac{9}{10}+\frac{9}{100}+\frac{9}{1000}+\frac{9}{1000}+\frac{9}{10000} \dots[/eqn]

That is your answer. If you really want to know what the dots notation mean, how to take "infinity" into account, you would want to know calculus first and deal with the infinite series. But without topology and analysis, even without a hint of set theory and its axiomatizations, how would you say anything of what mathematicians understand of infinity, only with your "intuition" and your misleading use of notation. What is [math]0.999 \dots[/math] and does it is equal to [math]1[/math]? Solve this:

[eqn]0. \bar{9} = \sum_{k=1}^{ \infty} \frac{9}{10^k}=x[/eqn]

Where [math]x[/math] is your proved solution. But if you don't know what a convergences test or what is a geometric series is, you will only argue over your intuitive notion of the symbols and you will not be arguing over math at all. Semiotics is a thing but is not the central thing in math.

Nothing in the world, in science, in humanities and even in abstract systems like math should be like you want it to be, in a way that you feel good about. This desire is irrational. You must accept a fair scientific fact, even if you would want things to be different. You should distinguish between what you see and what you want to see and it is not very different if instead of science you are thinking maths.

"All the truths of mathematics are linked to each other, and all means of discovering them are equally admissible" Adrien-Marie Legendre.

>> No.10364120

>>10362179
wrong. if x = 0.999... then 10x is 9.999...0

>> No.10364392
File: 191 KB, 1600x1584, Pole.jpg [View same] [iqdb] [saucenao] [google] [report]
10364392

>>10364120

>> No.10364427

>>10364120
That would be the case if it wouldn't be .9999... with infinite decimals

>> No.10364601

>>10363316
The purple squares always connect to the corner, or else there would be a finite amount of them

>> No.10366156

bump m'gentlemen

>> No.10366575

>>10366156
Why would you do such a thing?

>> No.10366588

>>10361607
>strict inequalities hold in an infinite limit
gonna need to stop you right there
.999... <= 1*

>> No.10366972

>>10363257
Would actually be something more like
10*x=9.999...
subtract 1*x
9x=9.999... -x
If you subtract things from one side but not another you prolly have some form of autism

>> No.10367188
File: 15 KB, 1025x693, math.png [View same] [iqdb] [saucenao] [google] [report]
10367188

>>10360371
Now go eat a dick OP

>> No.10367261

>>10366972
nothing else was done, everything after the | shows what is done in this step
in the line 10x = 9.999... | -x
nothing has been subtracted yet; the next line (9x = 9) is the result of that step

>> No.10367312

1/9 = 0.111111...
2/9 = 0.222222...
1/3 = 0.333333....
4/9 = 0.444444...
5/9 = 0.555555...
2/3 = 0.666666...
7/9 = 0.777777...
8/9 = 0.888888...
9/9 = 0.999999...
But 9/9 = 1

>> No.10367810

[math]
x= \frac{1}{10} \\
0. \overline{9}=9x+9x^2+9x^3+9x^4+ \cdots \\
0. \overline{9}=9x \left (1+x+x^2+x^3+ \cdots \right ) \\
0. \overline{9}=(1-x) \left (1+\mathbf{x}+x^2+\mathbf{x^3}+x^4+ \cdots \right ) \\
0. \overline{9}=1-x+ \mathbf{x-x^2}+x^2-x^3+ \mathbf{x^3-x^4}+x^4-x^5+ \cdots \\
0. \overline{9}=1
[/math]

>> No.10368624

>>10361540
>I can think [...] on their own
I have troubling news for you, anon

>> No.10368662

>>10362349
pi=e, by the fundamental theorem of engineering

>> No.10368742

>>10360460
Based and analysispilled

>> No.10368745

>>10367312
It really boggles the peanut

>> No.10368747

>>10361872
It's not less than 1 you idiot. That's the point.

>> No.10368749

>>10361691
0.9999... doesn't mean 1 minus an infinitesimal, you buffoon. It means the limit of the sequence 0.9, 0.99, 0.999, 0.9999, etc.

>> No.10368753
File: 83 KB, 645x614, 1538528044594.png [View same] [iqdb] [saucenao] [google] [report]
10368753

>>10361749
>limit of a number

>> No.10368758

>>10361926
>does not always yield the same results?
How so?

>> No.10368765

[math]x = \lim_{x \to 0}[/math]
[math]0.\overline{9} + x = 1[/math]

This is my LAST OFFER.

>> No.10370089
File: 8 KB, 320x240, 1548093440688.jpg [View same] [iqdb] [saucenao] [google] [report]
10370089

>>10360371
>1/3 = 0.3333333...
>1/3+1/3+1/3=0.9999999... = 1

>> No.10370092

>>10368765
oh ok x=0 i’m good with that

>> No.10370351

>>10364601
Finitist BTFO

>> No.10370395

Assume there is some fraction that produces 0.9 repeating.

1/x = 0.999...

1 = x * 0.999...

For anything where 1 = xy, the only solutions are that x is plus or minus 1 (it is 1 here) and y is plus or minus 1, (0.999... is our y), it is obvious that 0.999... is not -1, therefore it is 1.

>> No.10370400

>>10370395
>Assume there is some fraction that produces 0.9 repeating.
There isn't.

>> No.10370407

>>10370400
Exactly

>> No.10370465

All men are equal under God.

All numbers are equal under infinity.

There is only 1 god. There is only 1 infinity.

>> No.10370472 [DELETED] 
File: 232 KB, 300x300, 1307889832001.png [View same] [iqdb] [saucenao] [google] [report]
10370472

>>10370395
>>10370400
[math]\sum_{n=1}{\infty} \frac{x}{(x+1)^2} = 0.\overline{9}[/math]

>> No.10370479

>>10370465
Your infinity can't be bijected with its powerset.

>> No.10370480
File: 232 KB, 300x300, 1307889832001.png [View same] [iqdb] [saucenao] [google] [report]
10370480

>>10370400
>>10370395
>>10370407
[math]\sum_{n=1}^{\infty} \frac{x}{(x+1)^n} = 0.\overline{9}[/math]

>> No.10370483

>>10370479
Speak english

>> No.10370789

>>10370465
>There is only 1 infinity.
ridiculous, even in R you have two, +inf and -inf
Under C, you have an infinite amount of infinities

>> No.10370839

>>10370789
There is no negative infinity. Hell, there is no positive infinity. Its not a number so it doesn't adopt numeral properties. If it were to be treated as a number though, then all real numbers are equidistant from it, and thus equidistant to each other in relation to it. If there was a positive infinity, even the largest negative number would be no further from it than the same number ×-1. As no enumeration will ever reach infinity under any circumstance, it doesn't matter which value you begin incrementing from, and all values are equally nothing compared to infinity, including all known and knowable values collectively.

Theres no useful value in a negative infinity. There isn't even really any useful value in positive infinity either. "Something you can never reach even if you try" explicitly defies any sense of value to be extracted from invoking infinity in math.

>> No.10370880 [DELETED] 

>>10370839
infinity is further from the origin than any real number
in R this can happen in two ways, 2D and 3D there are infinite ways
inf is not a number, but it is big, duh
1/inf = 0
inf-inf undefined
lim_x->inf of 1^x, = 1 but 1^inf is undefined
inf isn't a number, but that doesn't mean there aren't some things you can do.

>> No.10370882

>>10370839
infinity is further from the origin than any real number
in R this can happen in two ways, 2D and 3D there are infinite ways
inf is not a number, but it is big, duh
1/inf = 0
inf-inf undefined
lim_x->inf of 1^x = 1, but 1^inf is undefined
inf isn't a number, but that doesn't mean there aren't some things you can do.

>> No.10370906

>>10360371
Recurring decimals hold no meaning in a finite universe. Infinity is a false god

>> No.10370981

>>10370882
There is no origin in relation to infinity.

>> No.10370990

>>10370981
so? Then it works from anywhere.

>> No.10370993 [DELETED] 

>>10370906
[math]
0.333_{10} = 0.1_{3}
[/math]

>> No.10370999

>>10370906
[math]
0.333..._{10} = 0.1_3
[/math]

>>
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