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/sci/ - Science & Math


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11557408 No.11557408 [Reply] [Original]

if 0.99999...=1 so
polygon with an infinitely many segments = circle

>> No.11557414

>>11557408
Mmmm............


Yes.

>> No.11557427

>>11557408
you can prove pi r ^2 using a proof like this so ye essentially. its the polygon with more edges than any non circle.

>> No.11557495

>>11557408
lim( 1 - 1/10^n ) = 1
lim( regular n-sided polygon ) = circle

where's the problem ?

>> No.11557530

>>11557495
what problem?

>> No.11557657

>>11557408
Yes, obviously. Why does no one on this board understand what a fucking limit is?

>> No.11557662

>>11557427
Nice name

>> No.11557668

>>11557657
it's not just this board, the fucking argument has been a staple of internet forums for decades now, i really don't understand what the difficulty is or the attraction to arguing such a boring fucking minute point

>> No.11557673

>>11557408
In the surreal numbers, [math] 0.999...\neq 1,[/math] so could you do some kind of surreal geometry where a polygon with infinitely many segments is not a circle?

>> No.11557690
File: 30 KB, 1280x960, 1x1.png [View same] [iqdb] [saucenao] [google]
11557690

>What's x at y = 0?
>What's the limit?
Limit = value that a function approaches =/= what it is

>> No.11557699

>>11557690
The total ordering and completeness of the reals ensures that the limit is same as the value.

>> No.11557717

https://themathpage.com/aCalc/limits.htm
Go back to school retards

>> No.11557729

>>11557717
>https://themathpage.com/aCalc/limits.htm
Show me where it says that 0.9999... is not 1.

>> No.11557741
File: 27 KB, 641x332, r.png [View same] [iqdb] [saucenao] [google]
11557741

>>11557729
It's literally the definition of a limit.
Look into every single calc book you have

>> No.11557759

>>11557741
>It's literally the definition of a limit.
The definition of a limit is not that 0.9999...=1.
Also, I ask again, show me where it says that 0.9999... is not 1. Because it doesn't say that there.

>> No.11557773

>>11557759
Did you even read it?
The example they provide is essentially the same as what you're asking.

>> No.11557783

>>11557773
>The example they provide is essentially the same as what you're asking.
No. The example says that 0.999999999....9 (i.e. a finite number of 9's) is not 1. That is different to 0.999999...
Learn to read.

>> No.11557794

>>11557408
Fuck off, it's teselatted line of real number, not infinity number polygon.

>> No.11557801

>>11557783
>No. The example says that 0.999999999....9 (i.e. a finite number of 9's) is not 1. That is different to 0.999999...
They're talking about limits and providing example with finite numbers of zeros to show the initial values while x is still relatively small they can't write down the entire list it will eventually because infinite because we're talking about limits here.

>> No.11557808

>>11557801
I forgot these
,

>> No.11557836

>>11557801
That was a completely meaningless, and incoherent sentence. Are you trying to say that since it's true when there's a small number of 9's after the decimal point then it must be if there's an infinite number of 9's after the decimal point? If so, you need to learn how logic works.

>> No.11557854

>>11557836
Define a limit

>> No.11557861

>>11557854
Wave function collapse observed on a macro level

>> No.11557876

>>11557408
if infinity = reciprocal of plank length in meters then yes

>> No.11557880

>>11557861
Alright will that wave function ever touch zero or will it always have a value no matter how small?

>> No.11557927

>>11557801
>they can't write down the entire list it will eventually because infinite
so close to understanding and yet so far

>> No.11557928

>>11557854
Not what this retard >>11557861 said.
The relevant definition is for sequences here. For a sequence of real numbers [math] \{a_n\}, [/math] the limit, if it exists, as [math] n\to\infty [/math] is equal to [math] L\in\mathbb{R} [/math] if and only if for all [math] \epsilon\in\mathbb{R}, [/math] there exists an natural number [math] N [/math] such that for all [math] m>N, [/math] we have [math] a_m-L<\epsilon. [/math]

>> No.11557937

>>11557927
It would make sense if you took a look at the picture. They put down the list of values but didn't provide you with the formula.

>> No.11557939

>>11557801
0.999... IS THE LIMIT, is that so hard to grasp ?

>> No.11557944

>>11557939
1 is the limit since that's what it tends to

>> No.11558002

>>11557944
you have just acknowledged 0.999... = 1. thank you

>> No.11558004

>>11557939
>>11557944
Correct.

>> No.11558008

>>11557928
Yes but sequences are basically the derivative of a limit. Sequences themselves won't
ever end either.

>>11557939
>>11558002
I did not. I explained before that a limit is what the formula will tend to it will never touch the value.

>> No.11558009
File: 136 KB, 1280x960, 1280px-3_utilities_problem_torus.svg.png [View same] [iqdb] [saucenao] [google]
11558009

>>11557530
What?

>> No.11558014

>>11558008
do you agree that 0.999... is a number ?

>> No.11558016

>>11558002
thats what it approaches, but it will never get there

>> No.11558026

>>11558016
see >>11558014

>> No.11558033

>>11558008
>sequences are basically the derivative of a limit.
I don't think you know what a derivative is.
>Sequences themselves won't
ever end either.
So?
I feel like your confusion comes from the fact that you think that the number 0.9999... is a part of the sequence 0.9, 0.99, 0.999, .... However is can't be, because as you pointed out, the sequence won't ever end. But if 0.9999... was a member of the sequence, then we can see that the sequence would have to terminate, since no number could possibly come after 0.9999....

>> No.11558034

>>11558014
Will there be a value if we
1 - .999... = ?

or will it be 0

>> No.11558035

>>11558026
i disagree, infinity is not a valid concept

>> No.11558047

>>11558033
The fact that there is LIM in front of it means that that is what it tends towards.

Try to find the value at the answer using the formula and it'll be undefined every single time because it'll only ever keep getting smaller it'll never reach it.

>> No.11558068

>>11558047
>Try to find the value at the answer using the formula
What value? What formula? You are really exhibiting your lack of understanding here.

>> No.11558069

>>11558034
? = 0
>>11558035
then you reject 0.999... as a concept and there's nothing to discuss

>> No.11558093

>>11558069
I don't reject it as a concept, I think it is impossible. There is a difference. Infinity is not possible, there is not an infinite gradient of options.

>> No.11558101

>>11558068
>You are really exhibiting your lack of understanding here.
I could say the same to you as you're not even trying to understand my point of view or the definition of a limit itself.

>> No.11558117

>>11558101
>my point of view
Explain it coherently then. Also, math is objective. Your point of view is irrelevant to the facts. Furthermore, this is clearly false from >>11558033
>I feel like your confusion comes from the fact that you think that the number 0.9999... is a part of the sequence 0.9, 0.99, 0.999, .... However is can't be, because as you pointed out, the sequence won't ever end. But if 0.9999... was a member of the sequence, then we can see that the sequence would have to terminate, since no number could possibly come after 0.9999....
>the definition of a limit itself
Right here >>11557928

>> No.11558118
File: 415 KB, 1125x849, A9B06F29-D9B9-4F2D-AF4F-74358AA4CA2F.jpg [View same] [iqdb] [saucenao] [google]
11558118

>>11558093
>infinity is not possible
Yes it is. Infinity exists.

>> No.11558138

>>11558117
Yeah you gave me the definition now stick it in your head retard.
When you get your hands on a formula in front of a limit try to find the value of the x at whatever value the limit equals to.

>> No.11558143

>>11558138
>When you get your hands on a formula...
What are you on about? You keep mentioning a formula. What formula? Provide me with the formula you are referring to. Do you even know what a formula is?

>> No.11558153

>>11558143
Any formula that involves a limit that converges.

>> No.11558154

>>11558143
>What are you on about? You keep mentioning a formula. What formula?
I said when you get your hands on a formula, learn to read

>> No.11558155
File: 99 KB, 1080x1080, 1586635146527.jpg [View same] [iqdb] [saucenao] [google]
11558155

n = 0,(9) / * 10
10n = 9,(9) / - n
9n = 9 / * 1/n
n = 1

>> No.11558156

>>11558118
he defines it into existence, it is not valid. show empirical proof of an infinite gradient or an infinite universe and I will concede

>> No.11558163

>>11558154
How is a formula relevant to our discussion. Again, do you even know what a formula is?

>> No.11558167

>>11558156
>he defines it into existence
And that's different to every aspect of math because?
Also,
>an infinite gradient
Literally a vertical line, retard.

>> No.11558168

>>11557699
The function is not defined at y=0. There is no value at that point.

>> No.11558172

>>11558163
Again do you know how to read? Do you know that a limit requires a formula?

>> No.11558175

You idiots know that there are two types of limit right?
The first one is rooted in Zenos' paradox, or 1/2 + 1/4 + 1/8.... = 1. It has to be equal to 1, not ALMOST, otherwise you can't go any where in the real world.
The second type is 1/x ~ 0 as x approaches infinity. It will never be 0.
Retards.
Also, 0.9999 = 1 because it is the first type of limit.

>> No.11558182

>>11558168
>There exists a function that isn't continuous, therefore 0.9999... is not 1.
Are you actually retarded?

>> No.11558189

>>11558167
lines do not exist, there is a bound to them. they are rays at best

>> No.11558192

>>11558172
It doesn't. You'd better learn calculus buddy, because you're really struggling here. Again, and please actually answer this time, do you even know what a formula is? In fact, do you even know what a limit is?

>> No.11558198

>>11558189
>there is a bound to them
>they are rays at best
Retard.

>> No.11558200

>>11558192
Give me a limit without a formula.
Do you know what a word is?

>> No.11558203

>>11558189
based

>> No.11558211

>>11558200
Are you asking for an example of a limit?
Well the one that is relevant is [math] \lim_{n\to\infty}(1-\frac{1}{10^n}), [/math] which, big surprise, evaluates to 1.

>> No.11558216

>>11558156
>he defines it into existence, it is not valid
No shit, anon. What makes an idea “valid” exactly? Do you also get angry when you see a dragon portrayed on a tv show or film because “they don’t exist”? Do you start yelling at people writing comic books that superheroes are not “valid” because humans can’t fly? Do you angrily demand that they show you proof of such a thing. Do you start frothing at the mouth of an artist paints a surreal landscape because such a place isn’t even real? When someone talks about the economy do you get upset and argue with them that it doesn’t exist, since it’s only an abstraction used to describe observable phenomenon? After all, such a thing only exists in our minds, it isn’t a “real” thing. I guess it’s invalid.

>> No.11558225

>>11558211
>(1−110n)
Uh oh what's this?

>> No.11558226
File: 25 KB, 400x400, 1Se9qfoX_400x400.jpg [View same] [iqdb] [saucenao] [google]
11558226

So u guys trying to tell that triangle is basically a circle?

>> No.11558230

>>11558225
A sequence, retard.

>> No.11558231

>>11558175
>The first one is rooted in Zenos' paradox
>It has to be equal to 1
No it doesn't, the guy won't reach the fucking wall unless he breaks the rule.

>> No.11558233

>>11558230
And what else is it?

>> No.11558241

>>11558233
A function, I guess. I know what you're getting at, and you're completely misguided, so I ask you, yet again, do you even know what a formula is?
Regardless, you've derailed the convo. As I've pointed out numerous times, and as we can see from the limit here >>11558211, 0.999....=1.

>> No.11558244

>>11558241
>I know what you're getting at
No you don't, and I think you're very out of touch with reality. So I ask you again do you know what a word is? Do you know what the definition of a limit is?

>> No.11558262

>>11558244
>Still didn't answer my question.
>Derails the convo, again.
Yes I know what a word is.
Yes, I clearly know the definition of a limit, since I wrote it above.
See that, I answered the questions that were asked, that's how you do it, retard.

>> No.11558368

>>11558262
>still didn't understand MY question
>derailed the convo YET AGAIN
You defined it but you don't get what it is.
What does the answer to a limit mean when using a formula?

>> No.11558372

>>11557699
It obviously has flaws then.

>> No.11558393

>>11557759
>Because it doesn't say that there.

It does, but you can't see it because you are blinded by preconceptions.

> "...it will be less than 2."

>> No.11558414

>>11558118
Infinity can exist, but if the "infinitely" (not using infinitesimal on purpose to avoid retardo response about 0) small doesn't, in a quantized universe, 0,999... can't exist.

>> No.11558426

>>11558175
Zeno's paradox is fake and gay. Space is discrete. Even other chaud greek contemporaries btfo Zeno because he was a stupid sodomite.
0,999... is not a real number, space is not a continuum.

>> No.11558449

>>11558372
Point them out then.

>> No.11558458

>>11558368
>>still didn't understand MY question
Your questions were
>So I ask you again do you know what a word is? Do you know what the definition of a limit is?
I literally answered both of them, dumbass.
>What does the answer to a limit mean when using a formula?
What formula are you talking about? Your question makes no sense. What part of a limit contains a formula? And again, do you even know what a formula is?

>> No.11558461

>>11558393
The "it" it is referring to is an element of the sequence. But 0.9999... is not an element of the sequence.

>> No.11558464

>>11558458
I really don't feel like dragging this out so just tell me what the answer to a limit means

>> No.11558469

>>11557408
Well this is true tho. Circle has infinite faces so...

>> No.11558495

>>11558464
>tell me what the answer to a limit means
Rephrase this to something that is coherent, and I will. Are you asking for the definition of a limit? Because I already gave you that above. Are you asking for the specific limit of the sequence where the nth entry is given by [math] 1-\frac1{10^n}, [/math] as n goes to infinity? Because I also gave you the answer to that above. Try to learn enough math and English so that you can construct sentences that actually make sense. This discussion continues to be hindered by your retardation.

>> No.11558507 [DELETED] 

>>11558495
How about you just tell me what the answer of a limit me and in relation to the formula used for it is?

>> No.11558514

>>11558495
How about you just tell me what a limit is in relation to the formula used for it?

>> No.11558516

>>11558507
>How about you just tell me what the answer of a limit me and in relation to the formula used for it is?
That question makes literally no sense.

>> No.11558518

>>11558514
Better, but still not quite making sense. Now either tell me what a formula is, or remove that word as well.

>> No.11558530

>>11558507
>Deleted his own post.
>These are the retarded faggots who mod the boards

>> No.11558531

>>11558518
I know what a formula and I'm assuming you do as well now answer the question.

>> No.11558534

>>11558518
And please answer it in plain English because I'm very retarded as you can tell.

>> No.11558539

>>11558531
Well, you clearly don't, since limits have nothing to do with a formula.

>> No.11558561

>>11558539
Oh so you don't plug a formula in a limit now?
Are you sure you know what a formula is? How about limit?

>> No.11558574

>>11558561
>Oh so you don't plug a formula in a limit
Correct. In fact, you never plug a formula into anything; a formula is something into which you plug things, retard.
>How about limit?
Need I remind you? >>11557928

>> No.11558578

>>11558574
Yes now define it in plain words big boi

>> No.11558587

>>11558574
>you never plug a formula into anything
Oh so it's safe to assume that (1−110n) by itself without anything in front is the same as limn∞(1−110n)?

>> No.11558597

>>11558578
Can't really do it rigorously, but here it is:
For an infinite sequence of real numbers, the limit, if it exists, as n approaches infinity of the nth entry in the sequence is a real number L, if and only if for every positive real number e, there exists a natural number N such that for every natural number, m, greater than N, the absolute value of the mth term of the sequence subtracted from L is less than epsilon.

>> No.11558600

>>11558587
No. Are you actually retarded? Do you think that [math] 1-\frac1{10^n} [/math] is a formula? Why are you even on this board if you don't know what basic words relating to math mean? I mean this genuinely, the fact that you are this retarded is a good reason to just kill yourself. The world would be better off without you, and your parents would be a lot happier.

>> No.11558611

>>11558597
>as n approaches infinity of the nth entry in the sequence is a real number L
>if and only if for every positive real number e, there exists a natural number N such that for every natural number, m, greater than N, the absolute value of the mth term of the sequence subtracted from L is less than epsilon.
And does this mean that any of the terms will ever equal the answer to the limit?

>> No.11558615

>>11558611
No, none of the terms in the sequence will be equal to the limit. What is your point?

>> No.11558616

>>11558600
>not a formula
Are you even trying anymore?

>> No.11558619

>>11558615
Yes, so what does the answer to a limit mean?

>> No.11558631

>>11558619
>the answer to a limit
hmmm... We can have answers to questions... A limit is not a question though. Again, you are not making any sense.
>>11558616
It isn't. I've already asked you if you know what a formula is. You haven't answered, but you perpetually demonstrate that you don't at all.

>> No.11558651

>>11558631
Let me ask again what does the number at the end of the = sign of a limit function mean?
If you can't answer this I seriously hope you don't go into anything science or math related.
>Again, you are not making any sense.
I feel the same about you. How about you try to do a quick google search and answer my question?

>> No.11558657

>>11558651
>I feel the same about you. How about you try to do a quick google search and answer my question?
Because your question doesn't make sense, retard.
>Let me ask again what does the number at the end of the = sign of a limit function mean?
This is the first time you're asking this. And the answer is literally given in the definition of a limit, which you would know if you had half a wit. Let's call this number L. Then, as I wrote here >>11558597
>for every positive real number e, there exists a natural number N such that for every natural number, m, greater than N, the absolute value of the mth term of the sequence subtracted from L is less than epsilon.

>> No.11558667
File: 16 KB, 1083x162, wikiwoohoo.png [View same] [iqdb] [saucenao] [google]
11558667

>>11558657
>Because your question doesn't make sense, retard.
You know you could just say "I'm too retarded to figure this out or even attempt to try to" it's a very simple question.
Here i'll make this simple for you, does the value of the function ever reach the answer of the limit?

I even pulled up Wikepedia for you, can I get a thank you?

>> No.11558682

>>11558667
>And he finally rephrases it so that it makes sense.
Took you long enough.
>does the value of the function ever reach the answer of the limit?
In general, the answer is maybe but not necessarily.

>> No.11558691

>>11558682
>and he still doesn't understand shit
>In general, the answer is maybe but not necessarily.
It does not that is the answer

>> No.11558697

>>11558691
>It does not that is the answer
[math] \lim_{x\to1}0=0. [/math] Explain this then.

>> No.11558700

>>11558682
>And he finally rephrases it so that it makes sense.
Do you seriously not know what the word answer means?

>> No.11558706

>>11558697
That's not a formula that's a term retard, there is literally no reason to take the limit of that since it's implied in the term.

>> No.11558707

>>11558697
All you have to do is admit that you were retarded and are no enlightened and stop answering. Please, do you still not understand what limits are?

>> No.11558713

>>11557668
>moot
And I agree

>> No.11558716
File: 8 KB, 480x360, hqdefault.jpg [View same] [iqdb] [saucenao] [google]
11558716

HEY YOU TWO, SHUT THE F*CK UP!

>> No.11558722

>>11558700
I know what it means, it didn't make sense in the context. As I pointed out, a limit is not a question, so it does not make sense to talk about the "answer to a limit".
>>11558706
>That's not a formula
No shit. As I've told you already, you don't plug formulas into limits. Also, it is obviously a function, it is the zero function.
>there is literally no reason to take the limit of that
There indeed is a reason, since I just used it as an example to prove your statement wrong.
>>11558707
>do you still not understand what limits are?
I obviously do. What part of them do you think I don't understand.

>> No.11558731

>>11558216
Looks like we have a person who uses their left brain in here. Most of the autist on this board are fucking Spock.

>> No.11558743

>>11558534
This is some top notch bait.

>> No.11558746

Oh man he >>11558619 just BTFOd
>>11558631 kek thanks guys

>> No.11558786

Read about synthetic differential geometry, or smooth infinitesimal analysis.

Yes, this was a real problem when you were in kindergarten. Now it's solved. Get over it.

>> No.11558829

>>11558016
Point nine repeating is NOT a process. You don't add the infinite nines one by one, they're already there.

>> No.11558979

>>11558530
You do know you can delete your own posts without being a janny or a moderator, right anon?

>> No.11559255

>>11557944
I agree. In the limit process, 0.999 equals 1.
But the number 0.999 does not equal 1.
Context matters.

>> No.11559554

>>11557408
A circle is a limit of a sequence of polygons. A circle is not a polygon. .999999999... Is a sequence whose limit is 1. Next troll, please.

>> No.11560350

>>11559255
so you agree that 0.999... is a number
how do you take a limit of a number ?
and obtain a different number on top of it ?

>> No.11560953

>>11560350
.99999... Is not a number. It is a sequence. See >>11560350 you absolute braindead mong.

>> No.11561073

>>11560953

>>11559255
>But the number 0.999 does not equal 1.
>number 0.999

so now it's not a number ?

>> No.11561078

>>11558426
>Space is discrete
source: my ass

>> No.11561083

>>11560953
"1.000... is not a number, it's a seek-wince"
hurrr durr

>> No.11561097

>>11561083
0 is not a unit, ,000... is stupid.

>> No.11561101

>>11560953
Meant to say "see >>11559554." And yes, .999 is a number, it is the sum of a finite sequence of rationals, and it itself exists as a rational number.
>>11561073
No.
>>11561083
The expression you wrote is a sequence, and it's a boring one at that. 1 + 0/10 + 0/100...
You want to know how I know none of you even know who Rudin is? Fuck off.

>> No.11561108

>>11561097
nooo yuuu stuuupiiid
>fine debate

>> No.11561109

>>11561101
>Fuck off.
>>11561108

>> No.11561115
File: 1 KB, 108x49, nnn.png [View same] [iqdb] [saucenao] [google]
11561115

Both
.333...
and
.999...
Aren't numbers just like 3.14... or 2.718 aren't numbers since they keep going till infinity


.333... isn't 1/3 but we know that it is the only decimal way to express the fraction 1/3.
.333... will NEVER become 1/3 because 1/3 is already whole while .333. is trying to get smaller and smaller to reach the perfect 1/3.

Remember it's not a number it's a concept. we could also represent it as a series.

.9, . 09, .009, .0009etc
pic rel

>> No.11561127

>>11561115
tldr: infinity is infinite basically also how would you go about proving that .000...1 = 0?

>> No.11561131

>>11561109
Or stay. I can break apart these damnable threads all day. Seems reporting doesn't do shit anyways.

>> No.11561134

>>11561115
2.718 stops after 3 decimal places...

>> No.11561137
File: 7 KB, 616x383, Regular_2-apeirogon.png [View same] [iqdb] [saucenao] [google]
11561137

>>11557408
A circle is defined as having no sides, so it doesn't have infinite sides. The upper limit of the number of polygonal sides either *looks* like a circle or a line, depending on whether the area/perimeter or side lengths of the polygons stay constant, respectively.

>> No.11561139

>>11561134
It's Euler's number I forgot the ellypses here you go >>...

>> No.11561142

>>11557408
Yes obviously.

>> No.11561192

Why do we need 5 fucking threads about this stupid bullshit?

>> No.11561465

>>11557427
Correct, it's the regular polygon. Otherwise you get a class of continuous curves.

>> No.11561587

>>11558182
Are you? His argument is correct, dumbfuck. The same issue applies in both cases: The limit of f(x) as x approaches n is not necessarily equal to f(n).
There are a lot of different .9...s and none of them are equal to 1.

>> No.11561597

>>11557759
The definition of limit proves it, retard. Learn to fucking extrapolate. You clearly don't understand basic calculus or hyperreals.

>> No.11561619

>>11557673
In the surreal numbers, 0.999... also equals 1 you brainlet.

>> No.11561625

>>11558829
This. Holy fuck. How hard is it to understand that 0.999... is not a "process" or whatever bullshit pseuds believe.

>> No.11561632
File: 97 KB, 1654x2339, proof.jpg [View same] [iqdb] [saucenao] [google]
11561632

>>11557408
x = 0.999...
10x = 9.999...
9 + 0.999... = 9.999...
9 + x = 10x
10x - x = 9
9x = 9
x = 1

>> No.11561640

>>11560953
It's not a fucking sequence you fucking mong. A decimal expression denotes a REAL NUMBER not a SEQUENCE you stupid piece of shit.

>> No.11561652

>>11561192
Because some fucktards are too fucktarded to understand hyperreals so they post fucktard claims like '.9...=1'

>> No.11561655

>>11561632
lim(n-∞)10^-n≠10^-∞
Nice try though

>> No.11561663

>>11561632

Now prove .00...1 = 0

>> No.11561666

>>11561655
0.999... = 1

>> No.11561671

>>11561663
>.00...1
Your notation is self-contradictory. You're simultaneously asserting that every digit after the decimal point is 0 while at the same time asserting that some digit is 1.

>> No.11561678

>>11561671
>durr hurr I haz smol brain

>> No.11561742

>>11561678
>Me brain tooo smol 4 countre argoment, so acccus u of smolness

>> No.11561991

>>11557668
>boring fucking minute point
Yes, its only mathematics.
Now run off and fix a lawnmower, like the good little mechanic that you are.

>> No.11561994

>>11558226
More than that. They are saying that a line is a circle.

>> No.11562043

>>11558731
An autist would never try to argue that [math]0.999\dots \neq 1[/math], since he has put a lot of work into understanding the fundamentals of mathematics (as we have made them), and understands them perfectly well.
Those are probably humanities majors, that attempt to argue with words they don't even understand.

>> No.11562318

>>11561640
Yo, its the retard! Hey retard! How ya doin', retard?
https://mathworld.wolfram.com/DecimalExpansion.html

>> No.11562356

>>11562318
Also, file name in OP is Russian... Guess I got trololololed.

>> No.11562515

>>11561742
>durr hurr me can't read and no try to understand shit

>> No.11562524

>>11557408
Yeah but I know that one circle is a circle and the other one is an infinite amount of polygons.

>> No.11562527

>>11561994
A line is a circle with an infinite radius of curvature. Everyone says that.

>> No.11562681

>>11562527
Not here apparently

>> No.11562746

>>11561139
You can't express Euler's number as a repeating decimal you absolute mong.

>> No.11562757

>>11561587
See >>11557699, you braindead retard.
>The total ordering and completeness of the reals ensures that the limit is same as the value.
His argument has zero relevance to the discussion.

>> No.11562762

>>11561597
>You clearly don't understand basic calculus
Following the definition of a limit, we have [math] 0.9999... = \lim_{n\to\infty}(1-\frac1{10^n})=1. [/math]
>or hyperreals
Retard, we're talking about real numbers, you stupid cunt.

>> No.11562774

>>11562318
You absolute retard.

The SEQUENCE of digits DENOTES a real number.

What you're doing is like saying 1 + 1 is not a number because
>hurrr akshually it's a string of symbols
You stupid FUCK.

>> No.11562793

>>11561655
So which line of the proof do you disagree with?

>> No.11562833

>>11561619
No it doesn't, you retarded fuck.
[math] 0.999... = 1-\epsilon = \{0|\}-\{0|1,\frac12,\frac14,...\}=\{-\epsilon,1|0,\frac12,\frac34,...\}\neq \{0|\}=1. [/math]

>> No.11563008

>>11562833
That's absolutely NOT what the notation 0.999... means in the surreals.
Read https://arxiv.org/abs/1307.7392 before spouting nonsense.
0.999... still means [math]\sum_{n=1}^\infty \frac{9}{10^k}[/math] in the surreals, which equals 1. The surreal [math]\infty[/math] is NOT [math]\omega[/math], it's "larger" than all surreal numbers (Dedekind-MacNeille completion) just like [math]\infty[/math] is "larger" than all real numbers in the context of the latter. Do not confuse it with [math]\sum_{n=1}^\omega \frac{9}{10^k}[/math], which equals [math]1-\frac{1}{10^\omega}[/math].

>> No.11563012

>>11563008
*where the last expression is indeed 1 minus an infinitesimal

>> No.11563035

>>11563008
>Literally arguing over semantics.
How, pray tell, would you express [math] \sum_{n=1}{\omega}\frac{9}{10^n} [/math] as a decimal?

>> No.11563037

>>11563035
[math] \sum_{n=1}^{\omega}\frac{9}{10^n} [/math]

>> No.11563049

>>11563035
>>11563037
The usual decimal notation is insufficient in that case because it doesn’t allow you to specify what’s going on at arbitrary, say, transfinite ordinal positions. At that point you might as well write it explicitly as a sum. Of course, the decimal expansion still exists (it’s just a map from every surreal positive integer to a digit) but it’s just not describable with the usual notation unless you extend it in some clever way.

Forgot to mention to look specifically at the paragraph right below Definition 5 (surreal version of infinity).

>> No.11563051

>>11563049
*from every ordinal, i.e. an ordinal-indexed “sequence” (these are also called nets).

>> No.11563065

>>11563051
Also: The reason why 0.999... denotes 9s filling ALL decimal places (including those at transfinite positions) is because it’s defined as the *infinite limit* of the partial sums, and in the surreals this *infinite limit* extend pass all the surreals, so you keep a nice correspondence between real and surreal arithmetic (e.g. you can plainly state that 1 + 1/2 + 1/4 + 1/8 + ... = 2 just like in the reals without having to introduce “modulo infinitesimal” fudge factors). That is, ... denotes the appropriate notion of “forever and ever” in the surreals, which doesn’t stop at the lowly [math]\omega[/math].

>> No.11563111

>>11561663
0.1=10^-1
0.01=10^-2
0.001=10^-3
:
0.0...1=10^-inf=0

>> No.11563129

>>11557699
This is not true.
Thats only true if the function is continuous at the limit point.
Completeness and ordering is related but in a different way.

>> No.11563143

>>11557408
>polygon
Only certain ones

>> No.11563262

>>11562774
Well, I hate to break it to you, but you posted another expression, not a number. Actually, I don't hate it. You're a raging cunt and you don't understand basic analysis.

>> No.11563265

>>11563262
>1 + 1 is not a number
Thanks for the insight, retard.
>you don't understand basic analysis
Funny coming from the guy who doesn't know that a decimal expansion denotes a real number.

>> No.11563293

>>11561632
x = inf
take away x on both sides
0 = inf
o shit dog!

>> No.11563675

>>11563049
>>11563051
>>11563065
Yeah, okay, you win. Thanks for the info. Sorry for being a retard.

>> No.11563739

>>11563675
actually, it's okay Anon. On further consideration, it would seem that I am the wrong one, on all fronts. Please take my token of humble apology for being such an ignorant brainlet. You are right on all counts, disregard any previous refutations.

>> No.11563750

>>11557408
But it's not =1, it's on average basically more or less could be just 1 for the lazy sake of it, even though ultimately it's still 0.9999...

>> No.11563761

>>11563750
uneducated opinion

>> No.11563764

>>11563761
Yeah, but it's still the truth.

>> No.11563768

>>11563764
literally not. It's just an artifact of our decimal notation.

>> No.11563772

>>11557408
>0.999...
lmao would an absolutely joke that is, would you clearly girl time to make it be home? Retard

>> No.11563773

>>11563293
inf isn't a number as x=inf claims

>> No.11563776
File: 244 KB, 1280x720, maxresdefault.jpg [View same] [iqdb] [saucenao] [google]
11563776

>>11563768
>breh ima just add whatever I need
What are you? A Chinese engineer?

>> No.11563791

We are literally taught this in middle school, even in the U.S. How anyone doesn't know math this basic is beyond me.

>> No.11563795

>>11563791
To be fair, almost all of what is taught pre-university is non-rigorous bullshit.

>> No.11563806

>>11563764
uneducated opinion

>> No.11563820

Why do people from the English-speaking realm use the [math]0.999...[/math] notation instead of [math]0.\overline{9}[/math]?

While we are at it, how do you even pronounce, say, [math]0.123\overline{456}[/math]?
Over here we insert a word where the repeating section starts, but in English you append a "repeating" after all.
It doesn't become clear where the repeating part starts.

>> No.11563850

>>11563820
you need latex to typeset the bar

occam's razor

>> No.11563876

>>11563806
Which makes it even more valid.

>> No.11563881

>>11563820
In school we use the bar notation, but I think it just comes down to trying to type it with just a standard keyboard

>> No.11563895

>>11563881
>>11563850
Oh, so this is just an Internet thing. Okay.
Now what about the pronunciation?

0.123 {pause} 456 repeating?

>> No.11564137

>>11563895
We literally have no way of saying it that I'm aware of. If you wanted to say that you'd probably say "0.123456 with 456 repeating" or something. I've never heard that sort of decimal spoken in years, so not entirely sure.

>> No.11564713

>>11563675
Sorry I called you a brainlet, that's just my /sci/ signature.
>>11563739
Impersonator.

>> No.11564738

>>11563675
>>11564713
impersonator

>> No.11565238

>>11563265
Oh, back for more? A decimal expansion as I linked previously is a series. Linking it again so you actually take the time to read it.
https://mathworld.wolfram.com/DecimalExpansion.html
The interesting part about real numbers is that it is a perfect set, so any convergent series over the reals converges to another point in the reals. So you can write a convergent series and say "This is a series!" But you cannot say "This series is equal to x!" You would say "This series converges to x!" Proving .999... converges to 1 is a task so trivial even a precalculus student could do it, but rigorously it requires knowledge of Real analysis. Any questions?

>> No.11565283

>>11563820
I don't know, why do people use commas to delimit decimals and full-stops to visualize steps of thousands?

>> No.11565288

>>11565238
>you cannot say "This series is equal to x!"
Yes you can.

>> No.11565293

>>11565238
You are confusing the infinite series with the infinite SEQUENCE of partial sums.
[math]\sum_{n=1}^\infty \frac{9}{10^n} = 1[/math]
End of story. Invent your own retarded notation if you want to say something else.

>> No.11565311

>>11565293
Sum of an infinite series is equivalent to the limit of partial sums. Your notation cleverly skips steps in an attempt to argue the same point as mine whilst appearing to be on the opposing side.
>>11565288
You can if you are showing series to be equivalent with one another by rearrangement, given that they are absolutely convergent.

>> No.11565314

>>11565283
Isn't that how everyone used to do it, until the English-speaking world made the other way round the world-wide standard?
Similar to how you arbitrarily skip milliard, billiard, trilliard, etc. and make a fucking mess of the naming system of big numbers as a result.
I'm glad at least Fahrenheit, pound and feet failed in that regard.

>> No.11565665

Actually there is two types of 0.999999999


there is

(decimal(1/3)) * decimal(3)

and there is 0.9999999......... (repeate forever)

the first one happens because decimal limitations

at base 6 (0 to 5) you have the integer base (with 0 and positive numbers) where the biggest % of all its single digit division is not division by 0 or repeating digits

>> No.11565671

>>11565311
No, you can say a series equals a value.

>> No.11565678

>>11565671
just like you can say 1 + 1 equals 2

>> No.11565679

>>11565665
>at base 6 (0 to 5) you have the integer base (with 0 and positive numbers) where the biggest % of all its single digit division is not division by 0 or repeating digits

Counting base 6 would hard

>> No.11565683

>>11565679
>Counting base 6 would hard
Actually not, just use one hand.

Dont lift a finger and its 0
Lift two finger and its 1
[....]
Lift 5 fingers and its 5


ANd if you think about it we should be using base 11 (assuming we care about using whole hand), because not lifting any finger would be 0 and you would be able to have digit 10 and will have the final digit of each amount of fingers lifter be the same.

>> No.11565936

>>11565679
counting base 6 is actually easier than counting base 10. you can't represent numbers greater than 10 in base 10 on your fingers without making the finger order important, but it's easy in base 6: left hand is the 1s place and right hand is the 6s place. you can go all the way up to 35. It's arguably the best base for finger counting for humans, except maybe the concept of numerals developed much later than the concept of counting, so it could not have evolved naturally.

>> No.11566370

>>11565671
The limit of a series equals a value.
>>11565678
Try and keep up.

>> No.11566386

>>11566370
No, the limit of the SEQUENCE OF PARTIAL SUMS equals a value.

>> No.11566401 [DELETED] 
File: 148 KB, 500x747, bestwtf-com-draw-a-square-around-it-perimeter-4-draw-a-32716410.png [View same] [iqdb] [saucenao] [google]
11566401

Also if 0.99999999...=0 so π=4

>> No.11566406
File: 148 KB, 500x747, bestwtf-com-draw-a-square-around-it-perimeter-4-draw-a-32716410.png [View same] [iqdb] [saucenao] [google]
11566406

Also if 0.9999999...=1 so π=4

>> No.11566445

>>11558449
I can't, I have flaws too.

>> No.11566452

>>11566406
>π=4
π<=4

>> No.11566470

>>11566386
Correct. Forgot to say "sum." See >>11565311
Thanks for affirming my original point.

>> No.11566701

>>11565238
series is a sequence of partial sums
sum is the limit
the symbol [math]\sum_{k=1}^{\infty}a_n[/math] stands for both depending on the context
infinite decimal expansions always mean the sum

>> No.11566702

>>11566701
>l ∑∞k=1an∑k=1∞an
"n" and "k" should be the same letter

>> No.11567659

>>11566406
If you're using the taxicab metric like an autistic retard, then yes.

>> No.11569004

>>11557408
Ummmm, yah.
That's the "joke," midwit.

>> No.11570174

>>11562527
that means that for every line there is an equal and opposite line

>> No.11570196

>>11566406
corners removed are arbitrary

>> No.11570264

>>11558118
>0.c1c2c3
WTF I had no idea you could do that.

>> No.11570276

>>11558093
>Infinity is not possible
Time is infinite.

>> No.11570284

>>11570264
it's just the string of digits, there's nothing going on

>> No.11570287

>>11561991
>like the good little mechanic that you are t science man
loser

>> No.11570290

>>11570276
does infinity have a starting point?

>> No.11570411

>>11557408
Floor 0,999... =0
Floor 1=1
0~=1
ergo 0.999...~=1
Once more logic triumphs over mathematical delusions.

>> No.11570415

>>11570411
"Floor" isn't continuous...

>> No.11570417

>>11570415
>grasping at straws
Mathfags always trying to justify nonsense conclusions rather than changing their axioma's.

>> No.11570419

>>11570417
Your conclusion was nonsense.
Floor isn't continuous so your dedcution was fallacious.

>axioma's
Which axioms would you prefer?

>> No.11570420

>>11558829
>Point nine repeating is NOT a process.
Wrong.

>> No.11570422

>>11558829
>Point nine repeating is NOT a process.
False. Every real number is (the representative) of an equivalence class of Cauchy sequences.

>> No.11570427

>>11570419
>Floor isn't continuous
It is though. You are simply saying it isn't because otherwise your ridiculous 0.999...=1 world comes crashing down.

>Which axioms would you prefer?
They are fine as long as mathfags admit they are arbitrary appeals to intuition and therefore when conclusions following from them are contrary to intuition it suggests there is a flaw in the initial assumptions. Mathematical truth is a choice.

>> No.11570430

>>11570427
>It is though.
lol

>They are fine as long as mathfags admit they are arbitrary appeals to intuition and therefore when conclusions following from them are contrary to intuition it suggests there is a flaw in the initial assumptions. Mathematical truth is a choice.
Intuition is a REALLY bad judge.
I prefer proof, by far.

>> No.11570433

>>11570427
>It is though.
?

>> No.11570434

>>11570411
circular reasoning. prove floor(0.999...) = 0 without assuming 0.999... < 1.
>inb4 muh intuition

>> No.11570435

>>11570427
just like gender is a social construct, we get it.

>> No.11570452

>>11570435
>>11570434
>>11570433
Mathfags not willing to admit their assumptions create their truth.

>circular reasoning
You realize we are discussing math right? Would you prefer some inductive reasoning?

>> No.11570454

>>11570452
>You realize we are discussing math right?
There is no circular reasoning in math. EVERYTHING is derived from axioms.

>> No.11570457

>>11570454
Purely deductive reasoning is always circular. Everything is derived from axioms and already there and implied to begin with.

>> No.11570458

>>11570457
If something is derived from axioms it LITERALLY can not be circular...
Please google what circular reasoning means...

>> No.11570461
File: 50 KB, 563x564, b9845787a3a10f62bcfa5f126a4b1b3e.jpg [View same] [iqdb] [saucenao] [google]
11570461

>>11570457
Circular proof is when you assume the conclusion. Perhaps when you do maths, it's circular: that we can believe. But good mathematics is not circular.

>> No.11570465

>>11570452
> assumption
like which? I am admitting anything if it makes you stop posting and go kill yourself. Or better, not posting anymore.

>> No.11570476
File: 16 KB, 795x846, floor.png [View same] [iqdb] [saucenao] [google]
11570476

>>11570452
dude, you literally said that pic related is a continuous function. I think it's too late to be pretending like you know anything about math, logic or philosophy of science...

>> No.11570492

>>11563675
Anon still had a very interesting point, is there some form of surreal geometry where there is a regular polygon with omega sides that is not the same as a circle?

>> No.11570513

>>11570420
Wrong.

>> No.11570515

>>11558189
kek

>> No.11570517

>>11570411
Wrong. floor(0.999...) = 1.

>> No.11570518

>>11570492
A hyperreal circle would look like a circle. But it would not be the same as a real circle.

>> No.11570542

>>11570513
>>11570517
Why do you bother arguing with mathematically illiterate people? They're clearly too arrogant to ever pick up a textbook on basic analysis and read. With them, it's not about understanding, there is no confusion in their mind, they just want to win the argument, that's all.

>> No.11570558

>>11570290
N does

>> No.11570564

>>11570542
I am not that anon. But I think that when you are an educator you hope to bring someone who is uneducated to a state of being at least somewhat educated. I do see your point though.

>> No.11570572

>>11563049
>transfinite ordinal positions
What is this, anon?

>> No.11570598

>>11570476
for which topology though :^)

>> No.11570613

>>11570598
>>professor, I'm not so sure the step with (x+1)^2 is justified, can you explain ?
>anon, what are you talking about, this is just the high-school formula for...
>>I mean, I can see it IS true if we assume the characteristic to be different from 2
you're that kind of person, aren't you

>> No.11570632

>>11570613
But anon, that's a valid question.

>> No.11570638

>>11570632
The other anon stereotyped you. It changes your question from being a valid one to an invalid one. Rules of /sci/.

>> No.11570649

>>11557408
define "=".
define "is circle".

if we say that a = b means a - b = 0, then we can ask whether 1 - 0.999... = 0 is true or not.
or, if we rephrase it
> is infinitely small value equals zero?
(depending on previous definition of what 'equals' means.)

if we say that point is zero-dimensional, and the circle is a bunch of points, then the question becomes
> is line segment which is infinitely small a zero-dimensional point?

if yes, then the polygon comprising of infinitely small segments and a circle comprising of points become the same, depending on definitions.

so define "=", circle, point.

>> No.11570666

>>11570649
>define "=", circle, point
I believe that you are too naive to think that there is any way OP will be able to answer such a request coherently.
If you have a pond with ducks near your place, go feed them instead. Do not feed the trolls on /sci/.

>> No.11570691

[lim n->§] x= 1/10^n + 1/10^(n+1) +1/10(n+2)...
x= [1/10^(n-1)*1/10]*(1+1/10+1/10^2+...)
10^(n-1)*x = 1/10*(1+1/10+1/10^2+...)
§ = 0.111111

>> No.11570712

>>11570613
I thought the notorious face at the end was enough to convey how serious this question was. But even if I posted this just for the sake of being a faggot, >>11570632 is right that it is often a very valid question.

>> No.11570722

>>11570712
If you are actually the OP, then. What do you mean by a "segment", at least loosely explained if not precisely?

>> No.11570723

>>11557408
heh

>> No.11570738

>>11570722
Note that OP being a faggot does not mean every faggot is OP.

>> No.11570799

>>11570666
define "troll"

>> No.11571327

>>11570422
...Which is not a process, retard.

>> No.11571344

>>11570572
He means e.g. the [math] \omega [/math]th decimal point is not able to be represented using the decimal notation.

>> No.11572667

>>11570417
And the mathematically illiterate screech about "nonsense conclusions" instead of putting any effort into understanding the math involved.

>> No.11572669

>>11557408
0.9... =/= 1
It is functionally identical to 1, but it is not equal to 1 and is only functionally identical due to the imperfect nature of math
A polygon with infinitely many segments =/= a circle
It is functionally identical to a circle, but it is not a circle

>> No.11572678

>>11566406

The limit of 4 is 3.14159....
The limit of .9999... is 1

Numbers and processes are not equal to their limits.

>> No.11572685

>>11570427
>Floor is continuous
What the fuck? No it isn't! It's literally an introductory problem in undergraduate analysis to DISPROVE that floor functions are continuous.

>> No.11572693

>>11572669
Stop using words you don't understand.

>> No.11572708

>>11572678
Numbers don't HAVE LIMITS YOU BITCH. Numbers are the limits of convergent series!!!! .999... Is a CONVERGENT SERIES and 1 IS ITS LIMIT. 3.14159... IS CONVERGENT AS WELL AND PI IS THE SYMBOL ASSIGNED TO ITS LIMIT.

>> No.11572777

Your math is good but your geometry is horrible

>> No.11572848

>>11572708
>Numbers are the limits of convergent series!!!!

... and the limit of the series 4, 4, 4, 4, 4, 4, ... is Pi.

And similarly, the limit of the series
.9
.99
.999
.9999
.99999
...
Is one. But that doesn't make .999... equal one. Because it is a number, not a limit, >you bitch.

>> No.11572851

>>11572848
>But that doesn't make .999... equal one. Because it is a number, not a limit, >you bitch.
Wrong. The number .999... is defined to be the limit of that sequence.

>... and the limit of the series 4, 4, 4, 4, 4, 4, ... is Pi.
No.

>> No.11572904
File: 115 KB, 437x640, Pope Real set.jpg [View same] [iqdb] [saucenao] [google]
11572904

>>11572851
>is defined to be

By whom. You?

You need to face it. The set of Real numbers is DEFINED by the exclusion of infinitesimals. So using them to prove .999... = 1, is the same as using Whole numbers to prove that 1/2 = 0.

There is nothing real about Real numbers. If you are counting electrons, one half DOES equal zero. But that doesn't prove that 1/2 never exists, and neither can you use the limits of the Real set to say that infinitesimals don't exist.

>... and the limit of the series 4, 4, 4, 4, 4, 4, ... is Pi.
> No.
Why not? Try and explain the mistake, instead of just endlessly appealing to your misunderstanding of authority.

>> No.11573014

>>11572904
>Why not?
Pick delta to be .5 you absolute fucking braindead piece of shit troll moron.

>> No.11573033

>>11557408
>He doesn't know that a circle is made up of tangents
Did you even high school?

>> No.11573075

>>11573033
>a circle is equal to the union of its tangent spaces
this is beyond wrong. get off my fucking board you pseud.

>> No.11573348

>>11561671
Its just 1 - 0.999...

>> No.11573360

>>11573348
No it isn't, 1-0.999...=0

>> No.11573915

>>11572904
>Why not? Try and explain the mistake, instead of just endlessly appealing to your misunderstanding of authority.
convergence of functions, even uniform, doesn't imply convergence of derivatives

>> No.11574283

>>11572904
>There is nothing real about Real numbers.
You are probably right about that. 1/2 certainly "exists", though.
Irrational numbers is where it gets tricky. Those are probably pure fiction. Extremely useful fiction, but ultimately fiction.
What he says, is, that infinitesimals don't exist in the number system we use on a daily basis. In that system 0.999... = 1 without even the shroud of a doubt.

If you want 0.999... to not be 1, define your own number system, but good luck making that as free of contradictions as the Reals.

>> No.11574949
File: 577 KB, 2000x1384, 1587020202655.jpg [View same] [iqdb] [saucenao] [google]
11574949

I fucking love Stephen Wolfram!

https://writings.stephenwolfram.com/2020/04/finally-we-may-have-a-path-to-the-fundamental-theory-of-physics-and-its-beautiful/

youtube.com/watch?v=8bdA_g1F06M

>> No.11575130
File: 78 KB, 725x353, 1:3 ≠ .3333....png [View same] [iqdb] [saucenao] [google]
11575130

>>11574283
>in the number system we use on a daily basis

Nobody uses real numbers on a daily basis.

Computers natively use a quirky version of whole numbers, and can be taught to use floating point numbers that resemble the set of Rationals numbers up to a point.

But ask a computer to calculate an irrational number and it will invariably stop. If it doesn't run out of memory, it will run out of some other finite resource.

Many things about numbers in computers are utterly incompatible with the real set:

Negative Zero
Machine infinity
Largest and smallest possible numbers. (Both positive and negative.)
Many (most?) numbers do not change when one is added to them, due to exponential notation.

And it is not just computers. If you have two halves of cell phones, you do NOT have a working phone. And I already mentioned half of an electron. And no one ever USED more than 12 digits of Pi to calculate an actual circle. (As opposed to doing it to test math itself.).

The volume of the universe is 4.6×10^185 cubic Planck lengths. Any number larger then this is as meaningless as 0/0.

...So claiming that the Real set is somehow the only set that matters is nonsense. It is just the only set that gives the answer you want.

>>11574283
>If you want 0.999... to not be 1, define your own number system, but good luck making that as free of contradictions as the Reals.

This has been done at least three times:
Surreal numbers
Hyperreal numbers
Base Infinity:

.999... = 1®-1
...999. = 1;-1®
.000...1 = ®1

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

>> No.11575146

>>11575130
>But ask a computer to calculate an irrational number and it will invariably stop
This is nonsense. Computers can operate on irrational numbers perfectly fine (and by fine I mean exactly) without running out of memory.
They just can't print out all of it's digits, well obviously...

>Many things about numbers in computers are utterly incompatible with the real set:
Fun fact. It's provably impossible to have a (reasonable) finite precision floating point system that actually becomes a field.

>> No.11575383

>>11575130
>Nobody uses real numbers on a daily basis.
For fuck's sake, natural numbers and rational numbers are (subsets of the) real numbers.
Don't tell me you don't use those on a daily basis.(*)
There are ways to represent (certain) irrational numbers in computers - not approximating them using floats or doubles, but actually directly working with them. (Naturally not all of them.) That's not what any sane person would ever do for non-scientific purposes, though. Use a double and you'll probably be fine. (For currency use integers.)

Most of the problems you list are due to limitations in variable size.
You may just as well say: All numbers are the same for computers, since practically all of them are past the largest representable number.
And you don't need the Reals for all those problems. The whole numbers already do that.

>The volume of the (observable) universe is 4.6×10^185 cubic Planck lengths.
FTFY, and thanks for that number. I'll believe that for now without checking.
Seems in the right ballpark, though.

>This has been done at least three times:
I wasn't claiming it had not been done. I was merely saying that we are talking about the Reals.

(*): I do realize one could make the same argument with complex numbers ("The Reals are the complex numbers with b=0."), but I'd argue those are a slightly different beast.

>> No.11575424

>>11575383
>I was merely saying that we are talking about the Reals.

And I'm saying we are not. If we are talking about infinitesimals then by definition we are not talking about Reals.

>>11575383
>natural numbers and rational numbers are (subsets of the) real numbers.

And Reals are a subset of the Hyperreals. What is your point?
Nobody uses irrational numbers on a daily basis.

>>11575146
>Computers can operate on irrational numbers perfectly fine (and by fine I mean exactly) without running out of memory.

Give example. And I don't mean assuming a variable is irrational, and then printing the name of the variable. That isolates the computer to the rational side of the equation.

>> No.11575455

>>11575424
>Give example.
[math]\sqrt{2}\cdot\sqrt{2}[/math]
A high quality CAS won't go and convert those into floating point numbers to arrive at some 1.999999-esque solution, but arrive at an exact solution.
It calculates with the irrational number "sqrt(2)", not with an approximation. Is that what you mean with "printing the name of the variable"?

>> No.11575858
File: 77 KB, 665x422, A towering intelegence!.jpg [View same] [iqdb] [saucenao] [google]
11575858

>>11575455

There are maybe 10 or 50 irrational numbers that a computer could be taught to deal with to some limited extent, but the vast majority of them are uncomputable.

But that is besides the point. Watch the numberphile video. He directly says that the Real set was invented as a method of ignoring infinitesimals.

===============
So imagine you have this idea for 1/2, but I "prove" that 1/2 can't exist by invoking the rules of Whole numbers. And when you try to tell me that you are thinking beyond the Wholes, I simply insist that you aren't because all these other irrelevant activities happen in the Wholes. Does this sound like reasonable behavior?

That is why this .999... discussion can never end. You have trapped yourself in this circle of Real Numbers, and refuse to think outside of it, even though Surreals and Hyperreals are well established concepts in mathematics.

>> No.11576769

>>11561994

don't tell him

>>11562527
shhh

>> No.11577092

>>11575858
Aren't you slightly missing the point there?
I will admit, that I had not looked into the Hyperreals and Surreals before, but isn't even in the Hyperreals .999... = 1?
The number just below 1, you are talking about is [math]1-\epsilon[/math], and you wouldn't write that as .999...
Feels a lot like the complex numbers to be honest, except you naturally can't talk about fractions of [math]\epsilon[/math].

>> No.11577242

>>11575858
>So imagine you have this idea for 1/2, but I "prove" that 1/2 can't exist by invoking the rules of Whole numbers. And when you try to tell me that you are thinking beyond the Wholes, I simply insist that you aren't because all these other irrelevant activities happen in the Wholes. Does this sound like reasonable behavior?
where exactly is the analogy ? you have an idea for 0.999... and someone is using real numbers to prove that it can't exist ? I'm just not seeing it.

>> No.11577293

dont't mind me

>> No.11577298

just bumplimiting this fucking thread

>> No.11577909

>>11577092
>but isn't even in the Hyperreals .999... = 1?

It is clearest in Hackenstrings:
https://combinatorialgames.wordpress.com/2012/08/19/ii-4-hackenstrings-and-0-999-vs-1/

> the difference between “LRLLL…” and “L” is the infinitesimal “LRRR…”.

> where exactly is the analogy?
1/2 does not exist in whole numbers. That doesn't mean 1/2 does not exist.
Infinitesimals do not exist in whole numbers. That doesn't mean infinitesimals do not exist.

No one who ever argued that .999... ≠ 1 ever mentioned the Real set. It is the opposition that keeps locking the discussion into that set in order to make their proofs work. That makes EVERY .999... = 1 proof circular logic: The Real set is DEFINED by excluding infinitesimals, which are the central subject of the question. So anything you do from there is irrelevant. 1+2=1 if you ignore the "2". 0.999... = 1 if you ignore the infinitesimal.

>> No.11577940

>>11577909
>1/2 does not exist in whole numbers. That doesn't mean 1/2 does not exist.
>Infinitesimals do not exist in whole numbers. That doesn't mean infinitesimals do not exist.
however 0.999... does exist in R

>> No.11577993

>>11577909
.999... isn't "LRLLL...", though, it's "L".
"LRLLL..." is an entirely different thing, similar to [math]1-\epsilon[/math].

By the way,
>I do not have a copy of it.
has the author of that blog never heard about archive.org?

>> No.11578012

>>11577909
Stop misusing hyperreals to argue your idiotic conclusions.

>> No.11578507
File: 58 KB, 850x306, Handling critisism rude person.png [View same] [iqdb] [saucenao] [google]
11578507

>>11577940
>however 0.999... does exist in R

The symbols 1/2 exist in Whole numbers. It is the commonly accepted meaning that does not.

>>11577993
>"LRLLL..." is an entirely different thing, similar to 1−ϵ1−ϵ.

The author says otherwise. It is exactly the same thing, similar to 1−ϵ.

>>11578012
>Stop misusing hyperreals to argue your idiotic conclusions.

See pic.

>> No.11578559

>>11578507
0.999... exists in real numbers and it has a commonly accepted meaning.
you cannot say the same about 1/2 and integers.

>> No.11578581

>>11578507
Stop using webcomics to justify being a dumbass who misuses hyperreals to argue your idiotic conclusions.

>> No.11578589

>>11578507
This comic relies on the potentially false premise that the art in question is worth any consideration.

>> No.11578724

>>11578507
[math]L = 1 = 0.999...\\
LRLLL... = 1 - \epsilon \neq 1\\
\Rightarrow LRLLL... \neq 0.999...[/math]

>> No.11579512

>>11578724

You really don't understand the concept of circular logic, do you?

>> No.11579563

>>11557759
The conceptualization is limited to the axiomatic system.
Generally the limit is accepted as a part of the generally accepted conceptualization which underlies math practiced in most universities.
However you could theoretically take your own axioms and have a system that doesn't accept the limit and therefore 0.999... would be still 0.999

>> No.11579859

.999... = 1 and i can prove it
imagine you have a bottle that contains exactly 1.0L of water. you pour that bottle EQUALLY into three cups. now each cup has .333... L of water. then, you pour each cup back into the original bottle. the bottle now contains

.333...
+.333...
+.333...
----------
= .999... L of water
but we never lost any water, so therefore:
.999 = 1

>> No.11580243

>>11579859

Now go back up this thread and find the 4 times this has already been refuted.