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11052098 No.11052098 [DELETED]  [Reply] [Original] [archived.moe]

There we go, all sorted out.

>> No.11052112

>>11052098
Bravo

>> No.11052118

>>11052098
>iq~0

>> No.11052151

They aren't equal. Any proof using 1/3 is invalid because we ALSO can't represent 1/3 appropriately.

>> No.11052184

>>11052151
0.1 in base 3, exactly

>> No.11052194

>>11052151
>They aren't equal.
No they're approximately equal. Close enough.

>> No.11052196

>>11052194
I agree but I will rearend the next fag youtuber to tell me they are equal

>> No.11052264

>>11052151
>>11052194
Are you guys really this stupid?

The repeating decimal means
[eqn]9\times 10^{-1}+9\times 10^{-2}+9\times 10^{-3}+\dots[/eqn]
This is a geometric series
[eqn]9\times 10^{-1}(1+10^{-1}+ 10^{-2}+\dots)=9\times 10^{-1}\left(\frac{1}{1-10^{-1}}\right)=1[/eqn]
I'm sorry but if you are one of those crackpots that doesn't believe in infinite series, you don't get to talk about non-terminating decimals, since that is exactly what they are

>> No.11052329

Gay, 0.9... = 1

>> No.11052331

>>11052264
Brainlet here
Wouldn't the right side of the equations solve to be 00,81?

>> No.11052333

>this thread again
Why are you all such dull stupid faggots.
You'd think with all the self professed 200+ IQ's around here there'd be a spark of some creativity.

>> No.11052390

>>11052329
this. how is if so hard to understand

>> No.11052393

>>11052098
If I have an infinite number of dice and roll all of them an infinite number of times, will there exist a die that rolled a 6 every single time?

>> No.11052399

[math]
\frac{1}{3}=0.1_3 \\
0.1_3 +0.1_3 = 0.2_3 \\
0.2_3 +0.1_3 = 1_3=1_{10}
[/math]

>> No.11052414

>>11052393
Yes, since the opportunity exists. Otherwise the opportunity wouldn't exist

>> No.11052419

>>11052393
Yes

>> No.11052425

>>11052393
>>11052419
Taking this a bit further, you'd have an infinite number of dice that rolled a 6 every single time.

>> No.11052489

https://youtu.be/G_gUE74YVos

>> No.11052498

>>11052399
Based
No, multi-radix based

>> No.11053551

>>11052489
based grimeposter

>> No.11053712

>>11052264
infinity doesn't actually end.

even 10^-1(1/(1-10^-1)) in your equation is only an approximation for the set the infinitesimally small number is just disregarded. but disregarding it to make an equivalence is false, it'll always be an approximate. it's just the limit of the numeric system that mathematicians cheat over

>> No.11054326

>>11053712
>I'm sorry but if you are one of those crackpots that doesn't believe in infinite series, you don't get to talk about non-terminating decimals, since that is exactly what they are

>> No.11054391

>>11053712
>infinity doesn't end
nooo really?
next: water is wet

>> No.11054424

>>11053712
brainlet

>> No.11054430

Define 0.999... to be 1.
QED

>> No.11054541

>>11052098
Suppose 0.99... is strictly less than 1
Therefore 1-0.99... =x where x is strictly greater than 0.
So 1-x=0.99...
Now let's consider 1-0.1x, this expression is at least as large as 1-x, but definitely smaller than 1. So, either it's 1-x<1-0.1x<1 or 1-x=1-0.1x<1. If 1-x=1-0.1x then x=0 which is a contradiction. If 1-x is less than 1-0.1x, then there exists a number between 0.99... and 1, which will call y. Y must be strictly smaller than 1 and strictly larger than 0.99... so there exists numbers 1-Y and Y-0.99.. that sum to x. These numbers must be stricty nonzero and smaller than x, and their absolute difference must be smaller than either, call it z so that 1-z is greater than 1-y and greater than 1-x. You can do this forever and find an infinite amount of numbers larger than 0.99.. and smaller than 1. So either 0.99... is equal to 1 or it's totally meaningless because there's always a number closer to 1 than it.

>> No.11054548

>>11052098

NO.
It is NOT "approximately" 1.
It is EXACTLY one.
There is NO difference between 0.999... and 1.000...

>> No.11054598

Found the guy responsible for the 737MAX's crashing: >>11052098

>> No.11054601

>>11054548
>There is NO difference between 0.999... and 1.000...
So what's 0.999... - 1.000... ?

>> No.11054611

>>11054601
0

>> No.11054614

>>11054611
Prove it. xD

>> No.11054617

>>11054548
>he probably thinks it's okay to say pi is equal to """exactly""" 3, since it's """close enough"""

>> No.11054624

>>11054614
See
>>11052264

>> No.11054628

>>11054624
Nonsense. Only 1=1. You're a brainlet if you believe anything else.

>> No.11054730

>>11054601
>So what's 0.999... - 1.000... ?

Zero.

What is "4 quarters" - "1 dollar bill" ?
Also Zero.

A number can have many different symbol representations.
Just like money can have many different representations.

>> No.11054743

>>11052414
If the opportunity has an infinitely small chance of happening, doe the opportunity exist?

>> No.11054753

>>11052393
>will there exist a die that rolled a 6 every single time?

Yes, in fact an infinite number of them.

>> No.11054755

>>11052098
>>11052264

0.9 < 1
0.09 < 0.1
0.9 + 0.09 < 1 + 0.1

QED

>> No.11054786
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11054786

>>11054326
>>11054391
>>11054424
Ah yes, it is abundantly clear by your responses that you have run out of rational responses to this argument. What's wrong? The reality of infinite sets too difficult for you?

>> No.11054789

>>11052098
Why can't faggots understand this? It's not that hard, are you really that stupid?

>> No.11054824

>>11052393
Countable or uncountable infinities?
If countable infinities, number the dice 1, 2, 3, ….
Let A(n) be the event that die #n rolls a 6 every single time. It has probability 0. Let B(n) be the event that die #n is the first die (in this enumeration) to roll a 6 every single time. It is a subset of A(n), so also has probability 0. The B(n) are all disjoint events. The event that at least one die rolls a 6 every single time is the countable union of the B(n), so also has probability 0. If the number of dice were uncountable the answer would be different.

>> No.11054841

>>11054753
https://en.wikipedia.org/wiki/The_Library_of_Babel

>> No.11054870

>>11054755
Yes continue your argument and you will have proven that 1 < something greater than 1

Wow you really showed me

>>11054786
Why am I required to humor your silly delusions? If you want you can learn from my post, and if not that's your choice then. This isn't an argument between equals

>> No.11055246

1/9 = .111...
2/9 = .222...
3/9 = .333...
4/9 = .444...
5/9 = .555...
6/9 = .666...
7/9 = .777...
8/9 = .888...
9/9 = .999... = 1

>> No.11055404
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11055404

>>11054755
based af

>> No.11055451
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11055451

Disclaimer: I do actually agree with the ignorant, barely literate pajeets in these threads who say that the 1/3=0.33... => 3/3 = 0.999... = 1 is not a valid proof, at least in a sense. Because disagreement over whether 0.999...=1 or not comes from the DEFINITION of what the "..." part means, and manipulations of these expressions before agreeing what it means get you nowhere. In the following, I will give the standard definition of what it means (at least for anyone aware of mathematics) and then prove that 0.99...=1.
Read and understand this proof to get smart:
By the Cauchy sequence definition of real numbers, a real number is an equivalence class of rational sequences a:N->Q, whose n'th member is a_n, with the equivalence relation being a~b <=> |a_n-b_n|-> 0 as n-> infinity. This says that for every rational x>0, there is a natural number N such that for all n>N, |a_n - b_n|<x. You can easily check yourself that a~b and b~c implies a~c, that a~a for all a and that a~b implies b~a. Hence this actually IS an equivalence relation which partitions the sequences into equivalence classes. Now that this is established, we need to define decimal expansions.
<cont.>

>> No.11055454

>>11055451
<cont.>
For an infinitely long decimal expression, we define the real number that it represents by taking a sequence of increasing finite truncations of the decimal expression. In particular, we write 0.9999... to denote the real number represented by the sequence (0, 0.9, 0.99, 0.999, and so on). To make sense of the real number 1, we inject rational numbers into reals by letting the real number q' by (q,q,q,q,....) for a rational number q. Then, in order to prove that the real numbers 1=[(1,1,1,1,...)] (where [x] denotes the equivalence class of the sequence x), and 0.9999...=[(0.9, 0.99, ...)] are equal, it suffices to show that they lie in the same equivalence class (because gain, real numbers are equivalence classes, not elements in those classes themselves). The n'th term in the canonical sequence for 0.999... is 1-(10^-n). The n'th term in the sequence for 1 is 1. Hence it suffices to prove that |1-(10^-n) - 1 | = 10^(-n) -> 0 as n->infinity. Looking back at the definition of a limit, let x>0 be any positive rational number. We want to find an N such that for all n>N, 10^-n < x, or 10^n > 1/x. But that is simple, just take any N such that 10^N > 1/x. Hence, the limit is proved and 0.9999... = 1.
Note that by similar arguments, we also have [(0.97, 0.997, 0.9997,...)]= 1 etc.

Keep in mind that everything I just explained is not complicated. In fact, it's elementary mathematics that is often left as an exercise in introductory analysis books. That means you should be able to understand what I just explained and accept that 0.999..=1.
retards

>> No.11055457
File: 317 KB, 500x375, b9f0210a0eefbccae719772f2f0ce74b.png [View same] [iqdb] [saucenao] [google] [report]
11055457

I understand that my post was probably the first time a lot of people here saw what real numbers actually were. I will take this opportunity to teach you some more. We will continue with the Cauchy definition of real numbers. How do we define the field operations?
Simple. From now on, we will refer to real numbers by arbitrary elements in their equivalence classes. This means you have to prove that the definitions are well defined independent of the choice of element in the equivalence class, but that can be done without too much effort.
The most basic operation is addition. We define (a_n)+(b_n) be (a_n + b_n) (essentially sum each entry in the sequence. so (1,1,1,1,1,1,...) + (1, 1/2, 1/4, 1/8,...) will be (1, 1.5, 1.25, ....). We need to prove that this defines a unique real number independent of choice of sequences (a_n) and (b_n) in their respective equivalence classes. This is easy: assume (a_n) ~ (a'_n) and (b_n) ~ (b'_n). We need to show that (a_n + b_n)~(a'_n + b'_n), or equivalently that |a_n + b_n - a'_n + b'_n | -> 0 as n-> infinity. But |a_n + b_n - a'_n + b'_n | = | (a_n - a'_n) + (b_n - b'_n)| <= |a_n - a'_n| + |b_n - b'_n| (here we used the triangle inequality |a+b| <= |a| + |b|). Hence since |a_n - a'_n| tends to 0, as does |b_n - b'_n| , their sum does too, hence (a_n + b_n)~(a'_n + b'_n) and addition of real numbers is well defined. This is actually not the complete proof yet: we need to establish that addition actually defines a real number by showing that (a_n + b_n) is also a Cauchy sequence, but that proof is similar and left as an exercise to the reader :)
Now that you've seen how addition is defined, try and yourself define: addition, multiplication and division. Not just tell us how to do it, but show that your definition actually works, as I did.

>> No.11055510

>>11052098
>>11055451
>>11055454
>>11055457
There we go, all sorted out.

>> No.11056063

>>11052264
Finally, some sanity

>> No.11056226

>>11052151
0.999... = X
10X = 9.999...
9X = 10X - X = 9
X = 9X/9 = 1
Nigga

>> No.11056340

>>11052194
No they are equal

>> No.11056448

>>11056226
>10X = 9.999...
Multiplying by 10 results in a product ending in 0

>> No.11056469

>>11052151
1/3 is a valid representation though
>>11056226
so many things wrong with this

>> No.11056495

>>11054870
>continue
there is nothing to continue, you are wrong by definition

>> No.11056515

>>11052264
>1+10−1
you can't insert a 1 anywhere retard, it's all 9's

>> No.11056528

>>11056448
Is this the new shitpost?

>> No.11056536

>>11056528
it's correct.
0.9 x 10 = 9.0 =/= 9.9

>> No.11056587

>>11056536
Please take your meds.

>> No.11056699

>>11052098
therefore 0.9999(...) is a natural number

>> No.11056983

>>11056469
theres literally nothing wrong with it
>>11056515
take your meds

>> No.11057122

>>11054870
Yes I understand my concept is difficult for you but I will at least try to treat you as an equal.

>> No.11057160

>>11055457
I would love to understand what you're talking about. It feels like I walked in halfway into a story

>> No.11057231

>>11056699
>therefore 0.9999(...) is a natural number

Yes.
Why does it bother you that the same number can be represented in different ways?

4 quarters = 10 dimes = 20 nickels = 1 dollar
here the same amount of money is represented in 4 different ways but they all represent the same amount of money

0.999... = 10/10 = 1.00.... = 1

The same number represented 4 different ways.

>> No.11057240

>>11057231
u havent done anything to prove it's an equivalency you fucking idiot

>> No.11057263

This thread rages on haha

0.999... is a symbol for 0.99999 and then infinite 9s,.
This is because you cannot represent infinite 9s.
You will run out of paper.
So if you graph 0.999... it will form an infinite curve known as an asymptote. With the line forever approaching 1, but with 1 as the limit.
No matter how close you get to one, the line never touches 1.

The same as how if you weigh out 0.999999 grams on a scale. It doesn't equal 1 gram.
No matter how many decimals you go to, it's still not equal to 1

>> No.11057318

>>11057263
>cannot represent
nope
[math]
1 = \dfrac{3}{3} = 3 \cdot \dfrac{1}{3} = 3 \cdot 0.\bar{3} = 0.\bar{9}
[/math]

>> No.11057322
File: 5 KB, 812x388, infinity.png [View same] [iqdb] [saucenao] [google] [report]
11057322

>>11057263
>No matter how many decimals you go
yeah that's why infinity isn't a number,
by definition it's bigger than all of them

>> No.11057360

>>11052098
0.9 repeating = 1

The bit that's missing between 0.9 repeating and 1 is just the operator. (The equal sign itself contains the missing amount between 0.9 repeating and 1, because these are relative math concepts that can not be compared without an operator. 0.9 repeating |Absolute =| 1 can not exist.
0.9 repeating = 1 is fine, and correct, as the automatic forebearance is that the equal sign provides the missing amount to make the statement true, or the statement is false.

Sorry for you finite, solid math, and non-theoretical cucks that can't actually deduce that on your own.

>> No.11057361

>>11057318
1/3 =/= 0.333....

>> No.11057364

>>11052264
Ok jackass, post an infinite series in long form.
As soon as you do that, I'll believe they exist.

>> No.11057365

>>11057322
The argument is infinitesimal there, not infinity.

>> No.11057369

>>11052151
>they aren't equal
Then what's their mean?

>>11052393
No matter how large the number of rolls becomes, you'll always be able to find an arbitrarily large number of dice who have always come up with a 6.

>> No.11057431

>>11057369
>Then what's their mean?
0.999.... + 0.000...1 / 2

>> No.11057434

>>11057365
>infinitesimal
not a real number

>> No.11057437

>>11057361
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.11057438

>>11057434
neither is infinity

>> No.11057441
File: 28 KB, 488x463, retardClap.png [View same] [iqdb] [saucenao] [google] [report]
11057441

>>11057431
so 0.5

>> No.11057442

>>11057437
>1/inf
>x = y

>> No.11057444

>>11057438
exactly, that's why it works

>> No.11057446

>>11057442
r u ok?
your post reads like you just had a stroke

>> No.11057447

>>11057444
you can't just write 0.999... and say it's an infinite number of 9's

>> No.11057450

0.999... = 1
9.999.../9 = 9/9
9 = 8.999
8.999.../9 = 9/9
0.888... = 1

hmm

>> No.11057460

>>11057450
>9 = 8.999
nope

>> No.11057461

>>11057447
[citation needed]

>> No.11057463

>>11057460
According to >>11052489 it is

>> No.11057464

>>11057447
https://www.wolframalpha.com/input/?i=%280.999...%29+-+1

>> No.11057469

>>11057463
8.999... = 9, yes
lrn2write

>> No.11057482

Alright anon, let's get a Cartesian number plane.
A horizontal plane we call X,
Now this plane ranges from 0 to 1
Plot the point "0" one the plane
Now plot "1" on the plane.
Now plot 0.999...
Is it equal to "1"?
No.
It's a different number.

Just because you can imagine it, doesnt make it real.

>> No.11057486

>>11057450
>8.999.../9 = 0.888...
holy shit that's retarded
https://duckduckgo.com/?q=8.9999999999999999999999999999999999999%2F9&t=h_&ia=calculator

>> No.11057487

>>11057482
>Is it equal to "1"?
yes

>> No.11057489

Lol does 9=10
Hahaha

>> No.11057493

>>11057489
either one could be your iq
really no difference there

>> No.11057503

>>11052264
[math]\sum_{i=1}^{\infty}\frac{9}{10^{i}}=1[/math]
is a much better way to say it

>> No.11057511

>>11057503
[math] \displaystyle
\sum_{i=1}^{\infty} \dfrac{9}{10^{i}}=1
[/math]
Optimized.

>> No.11057519 [DELETED] 

>>11052098

This shit can be solved with basic algebra.

[math]x = \sum_{i=1}^{\infty}\frac{9}{10^{i}} = 0.99\bar{9}[/math]
[math]10x = 10 \times\sum_{i=1}^{\infty}\frac{9}{10^{i}} = 9.99\bar{9}[/math]
[math]10x-x= 9x = 9 \times\sum_{i=1}^{\infty}\frac{9}{10^{i}} = 9.99\bar{9}-x=9.99\bar{9}-0.99\bar{9}[/math]
[math]9x=9[/math]
[math]x=1[/math]

But we started with [math]x = 9.99\bar{9}[/math]
Therefore, [math]9.99\bar{9}=1[/math]

THERE. That's your proof. You don't even need a geometric series to figure this shit out.

>> No.11057526

[math]x = \sum_{i=1}^{\infty}\frac{9}{10^{i}} = 0.99\bar{9}[/math]
[math]10x = 10 \times\sum_{i=1}^{\infty}\frac{9}{10^{i}} = 9.99\bar{9}[/math]
[math]10x-x= 9x = 9 \times\sum_{i=1}^{\infty}\frac{9}{10^{i}} = 9.99\bar{9}-x=9.99\bar{9}-0.99\bar{9}[/math]
[math]9x=9[/math]
[math]x=1[/math]

But we started with [math]x = 0.99\bar{9}[/math]
Therefore, [math]0.99\bar{9}=1[/math]

THERE. That's your proof, plain as day, in algebra no less.

>> No.11057530

>>11057511
So it approaches the limit of 1, but never actually reaches 1.

Hey guys if i have a savings account and I invest $900 000, then 90 000, then 9 000, then 900, then 90, then 9, then 90cents, then 9 cents, then 0.9 cents, then 0.09 cents forever, deciding each amount by ten, do I eventually get a $1 000 000?

Go and learn about limits.
This is why you can't understand infinity.
Stop pretending to be a mathematician if you don't understand limits.

>> No.11057534
File: 112 KB, 953x613, 0.999 = 1.jpg [View same] [iqdb] [saucenao] [google] [report]
11057534

>>11057530
>So it approaches the limit of 1, but never actually reaches 1.

No, it's *exactly* 1. It's not a computer program that iterates. Moreover, it's not even remotely different. Numbers can be expressed in many ways and [math]0.99\bar{9}=1[/math] is just as valid as saying [math]\frac{6}{3}=2[/math]. Just because they *appear* to be different (to you) doesn't mean they actually are. The repeating decimals is just an artifact of our decimal number system. It's a flaw in representing it in logarithmic base. The fact is if we had a base 12 number system that artifact wouldn't even show up.

>> No.11057536

>>11057530
Stop pretending to know infinity if you believe any limit can be proven in this Universe.

We hit entropy death before either one of us can prove a limit, that includes infinity, to be true or false.

You understand mathematics, but we don't exist in your world that infinity can be practically applied.

>> No.11057538

>>11057534
I prefer sexagesimal, but exactly what this guy said.

PS - Ancient Sumerians used a sexagesimal number system.

>> No.11057540

>>11052098

If [math]0.99\bar{9} \ne 1[/math] then there must exist some number [math]x[/math] such that [math]0.99\bar{9} < x < 1[/math]
So, what is [math]x[/math]? Go on. I'll wait.
Here, I'll even use your logic against you. if the 9s go on forever without terminating, then when you subtract so do the 0s in [math]0.00\bar{0}...[/math] Remember, those 0s *never*, *ever* terminate. There is no room for a difference greater than zero which means they have to be the same.

>> No.11057545

Anyone who still thinks 0.999... \neq 1 is such a brainlet they can't comprehend how brainlet they are. I wouldn't bother trying to convince them.

>> No.11057555

0.1 ~= 0.2
0.2 ~= 0.3
...
0.9 ~= 1

Does that mean 0.0 ~= 0.1? And thus 0 = infinity?

>> No.11057577

Hey anon,
If I borrow 1 Bitcoin from you,
And agree to pay back one tenth of what I owe per day,
As I the first day I pay 0.9 Bitcoin, the. 0.09, then 0.009, then 0.0009, then 0.0009, then 0.00009 etc.
How long until the total of 1 Bitcoin is paid paid.

ie how long until the amount in your account becomes equal to 1 Bitcoin?

I can't believe this is still a debate.

You never reach 1, it's a limit. You get closer and closer for ever but never reach.

It's called a limit.

>> No.11057666

>>11057577
Your practical argument is MEGA FLAWED.

Do your research plebian. You can't pay me back past 1 satoshi limit.

Thus, you default on your debt, and owe me more money after interest.

God damn, go to the fucking accounting thread, trash.

>> No.11058107

>>11052098
Perfect because nobody would actually be stupid enough to confuse a numbers limit to what the actual number exactly is.

>> No.11058122

>>11052098
0.999...99*10=9.99...90
9.99...90-0.999...99=8.999...91
8.999...1/9=0.999...
Fuck all this 10x bullshit

>> No.11058128

>>11057530
>approaches
infinity isn't approaching anything, it's way out there already from the get-go.

>> No.11058136

>>11058128
He is talking about the geometric series you fucking red nosed cock retard fuck face mother fucker shit

>> No.11058142

>>11057666
But you just said that 0.999...=1

So I only have to pay you back 0.9999999 Bitcoins and you will have 1 Bitcoin ;););)

.......unless 0.999..=1 is incorrect :0

Which it it....you fucking idiot.

Way too agree with me because you don't understand maths.

>> No.11058147

>>11057240
>prove it's an equivalency

NO, YOU prove they are not.

You are an idiot, you refuse to believe anyone's proof, so if you are so fucking positive they are different numbers then YOU provide a proof.

Prove how 0.999... is a different number than 1

>> No.11058149

>>11058136
yes, we all are, little dipshit

>> No.11058153

>>11058149
Yes so I was right you fuck

>> No.11058154

>>11058153
0.999... = 1
nice to agree

>> No.11058155

>>11058147
0.999...=1-10^-n
1=1-0
unless 0=10^-n which is just retarded

>> No.11058159

>>11058154
check this if you can read subspecie:
>>11058155

>> No.11058163

>>11058155

What is the value of 'n'? You need to fix 'n' to a specific value, then your argument falls apart.

>> No.11058164

>>11058159
1/(10^inf) = 0
no problemo

>> No.11058165

>>11058164
lol hahahahahahahaha ok, so 1/0=10^infinity?

>> No.11058172

>>11058165
1/0 = undefined
10^infinity = inf
so, not the same

>> No.11058173

>>11058163
n is the largest number, it is just to illustrate the difference between 1 and 0.999..., it's infinatly small but existant.

>> No.11058174

>>11058172
so how isn't 1/10^n also not undifined

>> No.11058175

>>11058173
>largest number
no such thing

>> No.11058177

>>11058174
n?

>> No.11058179

>>11052399
absolute madman
never saw it proven that way, for some reason, really nice

>> No.11058182

>>11058173
>n is the largest number

WTF? What is "the largest number"???
Please pick it, then add one to it, and what is the new number called??
"the largest number PLUS one?"

>> No.11058183

>>11058175
yes becuase infinity is undifined but obs that means we still know that the number im talking about is not zero

>> No.11058185

>>11058177
infinity

>> No.11058189

>>11058182
try adding one to infinity you fucking pleb

>> No.11058190

>>11058183
>infinity is undifined
nope

Definition is:
An unbounded quantity that is greater than every real number.

>> No.11058192

>>11058189
but inf isn't a number

>> No.11058193

>>11058190
Omg are you stupid?
Yes it has a definition but it is not a defined NUMBER.

>> No.11058195

>>11058185
1/inf = 0

>> No.11058196

>>11058192
Ok so?

>> No.11058198

>>11058195
no 0 is the limit, do you think 0*infinity=1?

>> No.11058199

>>11058193
so?

>> No.11058201

>>11058196
inf isn't the largest number

>> No.11058203

>>11058199
So it is undefined

>> No.11058206

>>11058198
0*inf is undefined

>> No.11058207

>>11058201
what is?

>> No.11058208

>>11058185
>infinity

infinity is not a number, it is an idea.

There are lots of infinities and they differ greatly in size.
There are in infinite number of natural numbers, but there are far more irrational numbers than natural numbers.

>> No.11058211

>>11058203
>Yes it has a definition
>it is undefined
hurr durr
pick your lane

>> No.11058212

>>11058206
ok so 1/infinity=0 exactly but 1/0=is not infinity and 0*infinity is undifined is what you are saying?

>> No.11058214

>>11058207
>>11058175

>> No.11058216

>>11058208
ok so i can't use it to prove that the diffrence between 1 and 0.999... is real only very small because the number doesn't have a exact value?

>> No.11058219

>>11058212
1/0 undefined
0*infinity undefined
1/inf = 0

>> No.11058220

>>11058211
Ok einstein tell me, what is infinity?
exactly in numbers if it is a defined number?

>> No.11058225

>>11058214
ok so lets say i have a number bigger than all other numbers and it is because i say so, it has this symbol ∞

>> No.11058227

>>11058216
>diffrence between 1 and 0.999...
Infinitesimal, which by definition isn't real

>> No.11058229

>>11058219
Well I can only disagree, if you would divide an apple in to infinitly small parts they would just be that, infinetly small parts, not non existant.

>> No.11058231

>>11058227
wow it's like we are talking about surreal numbers.

>> No.11058233

>>11058225
nope, the definition is at >>11058190

>> No.11058235

>>11058229
ignorance is bliss

>> No.11058237

>>11058233
I don't understand what you are trying to say?
Are you annoyed because I didn't pick you definition you looked up?

>> No.11058238

>>11058235
Funny but you can't prove shit either so really I can say the same thing in your book.

>> No.11058240

>>11058237
Your definition is flawed because it claims that inf is a number.
The definition at >>11058190 results in infinity NOT being a number.

>> No.11058241

>>11058231
>surreal numbers.

Yes, EXACTLY, you have NO physical means of understanding infinity, it is an idea.

ONE is easy to understand you can hold one object, you can easily understand a million or even a billion, but infinite is far beyond common understanding. It is not just a "Really really big number", it is far larger than that.

>> No.11058242
File: 256 KB, 768x960, 1568511972774.jpg [View same] [iqdb] [saucenao] [google] [report]
11058242

>mfw all the people here trying to "prove" 0.99.. = 1 using infinite series and rephrasing the problem in many ways
>mfw they all fail to see that the core of the disagreement stems from whether or not we allow infinitesimals, and that the real numbers by their definition don't allow infinitesimals.
> mfw my 3 effortposts explaining all this in detail and proving that 0.999... = 1, get 0 replies.
>mfw 99% people here don't realize the core of their disagreement stems from difference in definition of what 0.999... is, or lack of definition altogether.
>mfw a sizeable portion of people here think they're arguing about maths and not notation, and think this is what maths is about
just kill me already

>> No.11058244

>>11058240
It is a number, a undifined number.

>> No.11058246

>>11057364
t. low IQ animal who can't grasp basic mathematical abstractions

>> No.11058247

>>11058241
Yes so the distance between 0.999... and 1 is surreal (not real) and therefor maybe it doesn't apply the same rules as 1 and 2

>> No.11058250

>>11058238
sure bud

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

https://www.wolframalpha.com/input/?i=0*inf

>> No.11058251

>>11058244
if it's undefined, it isn't anything

>> No.11058252
File: 42 KB, 591x570, b0a.jpg [View same] [iqdb] [saucenao] [google] [report]
11058252

Alright. I will provide the answer, if I must.

infinity = 1/(1/(1-0.99...))

infinity != 1/0
.'. 1!=0.99....

>> No.11058254

>>11058247
Define what you mean by 0.999..., faggot.

>> No.11058255

>>11058220
>>11058190

>> No.11058256

>>11058247
>so the distance between 0.999... and 1

But there is your flaw, there is NO distance between the two. For two numbers to be different there needs to be a value that they differ by.
So what is the value that 0.999... differs from 1??

>> No.11058260

>>11058254
0.999....
a zero and dot followed by infinite nines.
aka the biggest number smaller than 1

>> No.11058264

>>11058256
0.000...1

>> No.11058268

>>11058264
>0.000...1

That is NOT a number.

>> No.11058269

>>11058250
What is 0^0? Hint it's one by definition, know your cool calculator seems to disagree so maybe its just a program made to show specific awnsers to certain calculations done by the programmers

>> No.11058271

>>11058268
Yes like how infinity isn't and like how 0.999... isn't and how 1/0 isn't and the sqrt(-1)

>> No.11058274

>>11058268
0.000...1 = 0

>> No.11058276

>>11058271
>infinity isn't
ok
> and like how 0.999... isn't
.999... = 1
>1/0 isn't
ok
>sqrt(-1)
i

>> No.11058277

>>11058274
Prove it, seems like you are just assuming

>> No.11058280

>>11058277
0.1 = 10^-1
0.01 = 10^-2
0.001=10^-3
:
0.000...1=10^-inf = 0

>> No.11058282

>>11058269
depends on how the limit is calculated.
doing the limit with x^x is the simplest and gives 1

>> No.11058283

>>11058276
0.999... is as undifined as infinite and 1/0 and i they all are not real

>> No.11058284

>>11058282
?
2^2=4 not 1

>> No.11058287

>>11058283
>2019
>being baffled by a geometric series
kek
https://en.wikipedia.org/wiki/Geometric_series

>> No.11058288

>>11058280
You are just saying it is, you dont prove it.

>> No.11058292

>>11058284
awww it's retarded

>> No.11058295

>>11058288
ok hun

>> No.11058300

>>11058292
Ok whatever you say but 0^0=1 and your calculator that obs doesnt know that maybe could be subjektive like you

>> No.11058303

>>11058300
thanks ESL, that laugh felt good

>> No.11058304

>>11058287
Wow im so baffled i haven’t sen this a houndred Times and it is a theory at most since there is no proof of it.

>> No.11058333

>>11058304
>i can't read so books don't exist

oh i am laffin

>> No.11058408

>>11058274
That’s not an infitesimal. That number terminated with a 1, and by extension is a real number.

>> No.11058416

>>11058408
anything after ... is irrelevant
it's zero

>> No.11058421

>>11058304
Mathematical theorems have very rigorous proofs, idiot.

https://www.purplemath.com/modules/series7.htm

And the geometric series is one of the easier things to prove

>> No.11058428

>>11058416

My point is that notation is logically incorrect. There is no 0.000...1
That “1” at the end is a lie. That, or the “...” is not really infinite. There cannot be both infinite zeros and have the set terminate with a 1. There is no room for that “1” at the end. It’s JUST 0.000...., which is, in fact, 0

>> No.11058450

>>11058288
1/3 = 0.333....
2/3 = 0.666....
3/3 = 0.999....
3/3 = 1

Just because two representations of values *look* different or use different numbers doesn’t mean they *are*. I don’t see anyone arguing that 6/2 =\= 3.
0.999... = 1 is just as valid as valid as 3/3 = 1
If you cannot see this intuitively, you are just being a brainlet. If you cannot believe rigorous proofs provided, you are just in denial and your intuition betrays you.

>> No.11058465

>>11058450
>6/2 =\= 3

[math]
\sqrt[]{(-1)^6} \neq (-1)^3
[/math]

>> No.11058496

>>11058269
>done by the programmers
aka actual mathematicians

>> No.11058747

>>11058465
That’s stupid Square root X is just X^(1/2)

>> No.11058754

>>11058282
Wrong. 0^x is simplest and that limit approaches 0

>> No.11058827

>>11058754
x^x is the purest, "just the function & x"

>> No.11058845

>>11058827
You are incoherent. Plus, we’re not even talking about “purity”, whatever that means, we are talking about simplicity, and a constant raised to a variable is simpler than a variable raised to a variable

>> No.11058873

>>11058242
your post is good and completely correct.

>> No.11058886

>>11058845
bs, that hand-picked zero is biasing it

>> No.11058915

>>11058142
>then 0.00009 etc.

>then 0.00009 etc.
>etc.

You do not go full infinitesimal.

Your argument is brainlet mode.
Get BTFO.

>> No.11058916

>>11058242
Your post is gay and completely heteromathematical.

>> No.11058951
File: 1.52 MB, 2000x2264, 1565750750437.jpg [View same] [iqdb] [saucenao] [google] [report]
11058951

>tfw posting about the inane fundamentals to thwart orthodoxy and make the scientifically indoctrinated enlightened to the nature of logic and reasoning itself. Infinity is stipulated, what other systems can be stipulated, and what unexplored worlds do they give rise to? Perhaps there exists one that approximates reality even closer than the current consensus... who knows?

>>
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