https://strawpoll.com/fz4g5wxa

[Anonymous No.11517686]

0.999...=1?????

https://strawpoll.com/fz4g5wxa

Vote in this poll so we can settle it once and for all and the same thread doesn’t get made every day

[Anonymous No.11517698]

>>11517686
I vote that OP gargles with his cum

[Anonymous No.11517718]

>0.999...=1

If you buy this, you don't think for yourself and just go with whatever authority says. The arguments are so obviously circular that anyone should be able to see through them.

[Anonymous No.11517721]

>>11517718
>any one

[Anonymous No.11517740]

>he can't prove it so he vote it

[Anonymous No.11517751]

>>11517740
>he doesn't onederstand

[Anonymous No.11517758]

>>11517718

Amen Brother, day of the discrete Universe when?

[Anonymous No.11517764]

>>11517686
saying 0.999999... = 1 is the same as saying lim(x->inf) (inf-1)/inf = 1

[Anonymous No.11517774]

>>11517764
>lim(x->inf) (inf-1)/inf = 1
this tells everything of your iq

[Anonymous No.11517779]

>>11517764

Yes, and saying 2+2 = 5 is another way of saying 5-2 = 2.

[Anonymous No.11517791]

>>11517764
ah fuck lim(x->inf) (x-1)/x

[Anonymous No.11517805]

>>11517791
[math] \displaystyle \lim_{x \rightarrow \infty } \dfrac{x-1}{x}
= \lim_{x \rightarrow \infty } 1+ \frac{1}{x}=1+0=1
[/math]

yeah I'm good

[Anonymous No.11517807]

>>11517791
[math] \displaystyle \lim_{x \rightarrow \infty } \dfrac{x-1}{x}
= \lim_{x \rightarrow \infty } 1- \frac{1}{x}=1+0=1
[/math]


yeah I'm good

[Anonymous No.11517810]

>>11517805
wtf are you doing nigger

[Anonymous No.11517811]

>>11517791
[math] \displaystyle \lim_{x \rightarrow \infty } \dfrac{x-1}{x}
= \lim_{x \rightarrow \infty } 1- \frac{1}{x}=1-0=1
[/math]
yeah I'm good

[Anonymous No.11517815]

>>11517791
[math] \displaystyle \lim_{x \rightarrow \infty } \dfrac{x-1}{x}
= \lim_{x \rightarrow \infty } 1- \frac{1}{x}=1-0=1
[/math]

yeah I'm good

[Anonymous No.11517818]

>>11517791
[math] \displaystyle \lim_{x \rightarrow \infty } \dfrac{x-1}{x}
= \lim_{x \rightarrow \infty } 1- \frac{1}{x}=1-0=1
[/math]
yeah I'm good

[Anonymous No.11517820]

>>11517815
If you say
>lim(x->inf) 1/x = 0
you’re implying that
>e = lim(x->inf) (1+1/x)^x
>e = lim(x->inf) (1)^x
>e = 1

[Anonymous No.11517821]

>>11517820
no u

[Anonymous No.11517837]

>>11517820
https://youtu.be/8HpvEANFQ7Q?t=5m

[Anonymous No.11517842]

1.001 * 0.999 = 1

[Anonymous No.11517850]

>>11517815
my point is that 0.99999... is the same as saying the limit when the amount of decimal places approaches infinity which is 1. any number of decimal places is not equal to 1 but that notation means what it approaches to as you add more and more decimal places

[Anonymous No.11517857]

>>11517850
if there are infinite decimal places then it doesn't matter how many more decimal 9's you tag onto the end. You'll never come close to even a fraction of the amount required to approach 1.

[Anonymous No.11517859]

>>11517686
[math] 0.999\ldots [/math] is a shorthand for the decimal expansion of the neutral element 1 of the multiplicative group on [math] \mathbb{R}\setminus \{0\} [/math]. So explain how this question makes any sense?

[Anonymous No.11517861]

>>11517820
you have to also imagine the power increasing and being equal to that denominator, the power amplifies the difference between the numerator which is being added by one and the denominator.

[Anonymous No.11517869]

>>11517857
>if there are infinite decimal places then it doesn't matter how many more decimal 9's you tag onto the end.
>infinite decimal places
>the end

[Anonymous No.11517873]

>>11517857
if there are finite decimal places then it doesn't matter how many more decimal 9's you tag onto the end. You'll never come close to even a fraction of the amount required to approach 1.
with infinite, it's exactly 1

[Anonymous No.11517889]

>>11517686
0.999... is not a real number, 9/9 is on the other hand
just like [math]sqrt(3)[/math] is not 1.7 or 1.7... or whatever invalid decimal representation you want to have

[Anonymous No.11517902]

>>11517686

[Anonymous No.11517905]

>>11517764
saying 0.999... = 1 is the same as saying [math]\lim_{n\to\infty}\sum_{k=1}^n\tfrac{9}{10^k} = 1[/math]

[Anonymous No.11517908]

>>11517873
Infinity explicitly doesn't mean what you think it means if that is what you believe.

[Anonymous No.11517911]

>>11517889
>1 is not a real number

[Anonymous No.11517915]

>>11517908
What does he believe it means and how is it wrong?

[Anonymous No.11517916]

>>11517908
it's what I know

[Anonymous No.11517917]

>>11517911
kek

[Anonymous No.11517919]

>>11517889
>3^.5 isn't a real number
[citation needed]

[Anonymous No.11517925]

>>11517869
You misunderstand.

4 decimal places
[0.xxxx]
[0.9xxx]
[0.99xx]
[0.999x]
[0.9999]
You can fill all decimal places with 9's

infinite decimal places
[0.xxx...]
[0.9xx...]
[0.99x...]
[0.999x...]
[0.9999x...]
[0.99999x...]
[0.999999x...]
you can't fill all decimal places with 9's.

[Anonymous No.11517943]

>>11517925
>you can't fill all decimal places with 9's.
Sure you can: 0.999...

[Anonymous No.11518041]

>>11517925
infinite fills anything
retard

[Anonymous No.11518120]

>>11517943
>>you can't fill all decimal places with 9's.
>Sure you can: 0.999...

Do you seriously think that this argument is going to persuade anyone? One reason that this debate goes on forever is that people who support the equality think that anything they say must be "right" just because it conforms with the established answer.

[Anonymous No.11518135]

>>11517686
9 is the furthest number from 1 in the alphabet so thats retarded.

[Anonymous No.11518141]

[Anonymous No.11518155]

Reminder that there is no smallest unit of spacetime and that the universe is infinite in expansion.

[Anonymous No.11518170]

>>11518155
>Reminder that there is no smallest unit of spacetime and that the universe is infinite in expansion.

Yes there is. It is called the Planck length. The universe is about 4.6×10^185 of these. So outside that range, the set of Real Numbers detaches from reality to become an angels-on-the-head-of-a-pin subject.

[Anonymous No.11518185]

>>11518170
the planck length is not the smallest unit of spacetime

[Anonymous No.11518200]

>>11518185

Yes it is.

[Anonymous No.11518207]

>>11518200
>planck length * 0.1

[Anonymous No.11518216]

>>11518207

> Planck length * 0.1
> Electron * 0.1

Both meaningless.

[Anonymous No.11518335]

>>11518120
>you can write infinite decimals as [0.xxx...]
>but not [0.999...] because I say so
Do you seriously think that this non-argument is going to persuade anyone?

>One reason that this debate goes on forever is that people who support the equality think that anything they say must be "right" just because it conforms with the established answer.
Funny how you don't realize that the "debate" is due solely to contrarians and trolls.

[Anonymous No.11518346]

Since all repeating decimals are rational that means .999... should have a finite rational form. That number is 1/1

[Anonymous No.11518360]

Ok 45% brainlets what's [math]1-0.999\ldots=[/math]

[Anonymous No.11518400]

>>11518360
0

[Anonymous No.11518405]

>>11518360

> Ok 45% brainlets what's 1−0.999…=
0®1

[Anonymous No.11518407]

>>11518360
0

[Anonymous No.11518417]

>>11518335
>Do you seriously think that this non-argument is going to persuade anyone?

Then why does it make any more sense in reverse:
>you can write infinite decimals as [0.999...]
>but not [0.xxx...1] because I say so

If you can achieve .999... as a finished result, then why can't you append anything after it?

[Anonymous No.11518426]

>>11518360
0.000...1, an infinitesimal. learn2hyperreals brainlet

[Anonymous No.11518433]

>>11518426
>0.000...1
0 in real numbers

[Anonymous No.11518449]

>>11518417
>Then why does it make any more sense in reverse:
>>you can write infinite decimals as [0.999...]
>>but not [0.xxx...1] because I say so
Maybe because [0.xxx...1] is not [0.xxx...] you illiterate brainlet?

You can write it when dealing with hypereals, otherwise there is nothing after infinity because it has no end.

[Anonymous No.11518472]

>>11518417
>If you can achieve .999... as a finished result, then why can't you append anything after it?
I guarantee that a lot of stuff which you now find confusing would make perfect sense if you stopped thinking about everything in terms of terminating or non-terminating processes actually happening in the real time

[Anonymous No.11518485]

If .999... =/= 1, then by definition, there exists some real number x such that .999... < x < 1. What is x?

[Anonymous No.11518487]

>>11518417
>infinite
>has a terminating digit
Pick one, retard.

[Anonymous No.11518490]

>>11518485
schizos be like
>there's no integer between 1 and 2 so by your logic 1 = 2

[Anonymous No.11518499]

>>11518490
retards be like
>integers and real numbers are the same

[Anonymous No.11518500]

>>11518490
I'm talking about real numbers, not integers, fucktard.

[Anonymous No.11518501]

>>11518490
Thought it was quite reasonable to be honest.

[Anonymous No.11518502]

>>11517686
>settle it once and for all
>/sci/ence and math
>arguing semantics

all my shiggy-diggy

[Anonymous No.11518709]

>>11518485
There isn't. 0.999... is the upper limit of real numbers less than 1

[Anonymous No.11518728]

>>11518485
0.0000....1

[Anonymous No.11518740]

>>11518360
0

[Anonymous No.11518743]

>>11518426
That’s just lim 1/10^x as x approaches infinity, which is 0.

[Anonymous No.11518757]

>>11518728
not a real number

[Anonymous No.11518763]

Which of the following is true or false?

[eqn]\frac{1}{3}=0.333\ldots[/eqn]

[eqn]3\times\frac{1}{3}=1[/eqn]

[eqn]3\times0.333\ldots=0.999\ldots[/eqn]

[eqn]0.999\ldots=1[/eqn]

[Anonymous No.11518764]

>>11518757
How is that?
You can add infinitely 9s at the end but not 0s in between?

[Anonymous No.11518772]

>>11518764
if 0.00...01 is a real number and 0.00...01 > 0, then also 1/0.00...01 > 0. you can thus apply the decadic logarithm. log(1/0.00...01) is also a real number, therefore it's bounded by some integer

log(1/0.00...01) < N

working backwards gives

0.00....01 > 1/10^N

therefore there can be only a finite number of zeros before the 1

[Anonymous No.11518778]

>>11517758
The universe is already discrete. The problem is that some people live in the “””world of ideas”””

[Anonymous No.11518792]

>>11518743
Do you not know the definition of limit?
Fucking shit

[Anonymous No.11518848]

>>11518200
No, it's the smallest measurable distance. Proper distances can't be smaller, but observer dependant distances, like the wavelength of light, can be.

[Anonymous No.11518872]

>>11518764
>You can add infinitely 9s at the end
There is no end to add to.

>but not 0s in between?
There is no end to be in between.

[Anonymous No.11518873]

>>11518792
Yes.

[Anonymous No.11518905]

1/3 * 3 = 1
1/3 = 0.3333...
0.3333... * 3 = 0.9999...
0.9999... = 1
wow that was some high level math here

[Anonymous No.11518909]

> majority of people on this board think 0.9999... is not 1.
Holy shit this board is actually retarded. The posters here are not pretending to be low IQ for the laughs, theyre genuine retards. Now I can finally leave in peace.

[Anonymous No.11518919]

>>11518905
your point? it's the simplest and most elementary possible example. what else would you suggest showing to these trolls and brainlets? seriously

bit pretentious using [eqn]L^AT_EX[/eqn] but idgaf

[Anonymous No.11518933]

>>11518764
>>11518772
this argument works to show 0.999... = 1 actually
if you assume the difference 1 - 0.999... to be non-zero, then 1 - 0.999.. > 0 and by the same argument you can find an integer N such that

1 - 0.999... > 1/10^N.

however clearly 0.999... > 0.99..9 with exactly N nines which gives

1 - 0.999... < 1 - 0.99...9 = 1/10^N

which is a contradiction. therefore the difference must be zero.

[Anonymous No.11519004]

>>11517686
The inability many people today who view themselves as being "scientific" as well as math fans (left-brain prisoners) have in comprehending that .999 isn't the same as 1, is completely connected to their inability to grasp eternity and infinity. Their minds have basically been programmed to believe eternity and infinity are impossibilites. Over the course of the last 10 or so centuries of indoctrination into an alien world-view, they've "learned" to be unable to comprehend it.

This difficulty they have with eternity/infinity shows up in many different fields, from math to astrophysics.

This mental handicap is inherited directly from the (((Abrahamic))) religions, more specifically Christinsanity for us Westernerns. In it's origin, the inability to understand infinity and eternity is 100% Judaic in thought/philosophy. In contrast, the non-Jewish man; the Pagan man, at least the /European/ Pagan man, never had any problem with infinity and eternity. Christinsanity introduced into the minds of people the idea of life and the world/universe being linear, starting from point A and ending with a point B, whereas in the Native European world-view everything is infinite, a circle.

That's why many people today can't understand that .999 repeating forever will never reach 1 -- they refuse to accept the idea of an infinite/eternal repetition. Saying "it's 1" is their method of escaping from the uncomfortable (and to them insurmountable) challenge which the concept of infinity/eternity is to thier Judaically-induced mental disease.

[Anonymous No.11519017]

>>11519004
>.999 repeating forever will never reach 1
numbers don't reach or approach anything. they stand perfectly still.

[Anonymous No.11519024]

>>11519017
0.99, or 0.999999, or 0.9999999999999999999, or n infinite number of 9s if you want, isn't 1. No matter how many 9s you put it, it will never be 1.

[Anonymous No.11519028]

>>11519004
see >>11518905

[Anonymous No.11519031]

>>11519017
0.99, or 0.999999, or 0.9999999999999999999, or an infinite number of 9s if you want, isn't 1. No matter how many 9s you put in, it will never be 1.

[Anonymous No.11519043]

>>11519031
>0.99
true
>0.999999
also true
>0.9999999999999999999
still true
>an infinite number of 9s if you want, isn't 1
not true

[Anonymous No.11519083]

>>11517686
You people have to be trolling
[eqn]x=0.\dot{9} \\ 10x=9.\dot{9} \\9x= 10x-x= 9.\dot{9} -0.\dot{9} =9\\ \therefore x=1[/eqn]

[Anonymous No.11519101]

.999... < 1

how could the answer be anything else?

people who say 0.999... = 1 are the same people who say 2+2=5

[Anonymous No.11519109]

>>11519101
>.999... < 1
can you prove it ?

[Anonymous No.11519112]

>>11519109
its already proven

[Anonymous No.11519126]

>>11519112
post the proof then

[Anonymous No.11519139]

>>11519004
>The inability many people today who view themselves as being "scientific" as well as math fans (left-brain prisoners) have in comprehending that .999 isn't the same as 1, is completely connected to their inability to grasp eternity and infinity. Their minds have basically been programmed to believe eternity and infinity are impossibilites. Over the course of the last 10 or so centuries of indoctrination into an alien world-view, they've "learned" to be unable to comprehend it.

>This difficulty they have with eternity/infinity shows up in many different fields, from math to astrophysics.

>This mental handicap is inherited directly from the (((Abrahamic))) religions, more specifically Christinsanity for us Westernerns. In it's origin, the inability to understand infinity and eternity is 100% Judaic in thought/philosophy. In contrast, the non-Jewish man; the Pagan man, at least the /European/ Pagan man, never had any problem with infinity and eternity. Christinsanity introduced into the minds of people the idea of life and the world/universe being linear, starting from point A and ending with a point B, whereas in the Native European world-view everything is infinite, a circle.

>That's why many people today can't understand that .999 repeating forever will never reach 1 -- they refuse to accept the idea of an infinite/eternal repetition. Saying "it's 1" is their method of escaping from the uncomfortable (and to them insurmountable) challenge which the concept of infinity/eternity is to thier Judaically-induced mental disease.

[Anonymous No.11519152]

>>11518485
this is the average person who thinks 0.999... = 1
>>11519004
this is the average person who thinks 0.999... ≠ 1

[Anonymous No.11519157]

if .999... = 1

does 9.999... = 10?

[Anonymous No.11519166]

>>11519157
yes, and there's no "if"

10 = 9.999...

[Anonymous No.11519221]

my mind has been changed

[Anonymous No.11519230]

does .333... = 4?

[Anonymous No.11519259]

>>11519230
Yes.

[Anonymous No.11519300]

>>11519230

It also equals 0.34.

And it equals 0.43.

Maths, man, its so beautiful, it just blows my mind.

[Anonymous No.11519301]

>>11518763
>Which of the following is true or false?
>13=0.333…

The first one.

[Anonymous No.11519308]

>>11519157

>>11519259
No you fucking mongrel, .333... approaches 1/3. 3.999... approaches 4.

9.999... = 10 because both 10 * .999... = 9.999... and 10 * 1 = 10

[Anonymous No.11519320]

x = 0.999....
10x = 9.999...
9.999... = 9 + 0.999... = 9 + x
10x = 9 + x
9x = 9
x = 1

[Anonymous No.11519348]

>>11519230
no, but in base 4
0.333... is 1

[Anonymous No.11519355]

> only 21% think it equals 1
Brehs...

[Anonymous No.11519363]

>>11517686
its not = to 1 but it is ~ 1

[Anonymous No.11519377]

>>11519355
trolls trolling midwits and spergs

this thread is great. will try some of the material on a neurotic sperg next time i see one

[Anonymous No.11519391]

>>11519377
> trolls trolling
I sure hope so

[Anonymous No.11519437]

Right, I am fucking sick of this bullshit. Lets get straight to the fucking crunch, you FUCKING STUPID MORONS, just shut the fuck up and LISTEN for just once in your goddamned stupid motherfucking lives.

Take something as simple as 1 + 1 = 2. There is absolutely nothing to say this is true other than logical intuition. Its not a Universal truth we have discovered. No, it not, arseholes. It is not written across the skies in huge flaming letters by some God. Its a human construct. Nothing more. Now, if you cant get your head around that simple fact you are a drooling moron and you will do the world a favor be keeping your FAT STUPID FUCKING mouth shut while the rest of us move on out of the dark ages.

The entire discipline of Mathematics is built upon such fundamental constructs which rely upon human intuition as he ultimate foundation to all logic. That's right. At the heart of all reason, all logic, there is intuition. Nothing more. Anyone who thinks otherwise is a self deceiving cretin. A fucking parrot. A God cursed sodomite and fool.

Now. Intuition tells us that 0.9999... will never reach 1 because it JUST FUCKING WONT! It will go on being FUCKING 0.9999 for FUCKING EVER! Got that, you brainless Satan spawned scum? FUCK! 0.999... DOES NOT EQUAL 1 and it FUCKING FUCKING FUCKING NEVER WILL! CHRIST! FUCK!

Thanks for listening. I am sure you are properly enlightened now. I have no doubt you will go about daily life with a sense of joy, this heavy intellectual load having being lifted from your scrawny acne-pocked shoulders.

[Anonymous No.11519458]

>>11517686
It is obviously equal to 1, it doesn't matter what the poll results are. Math is not a Democracy.

[Anonymous No.11519471]

>>11517698
Based.

[Anonymous No.11519581]

I like to imagine infinibrainlets believe in an infinity'th decimal place digit and that this decimal place is arbitrarily base-9 instead of base-10.

[Anonymous No.11519703]

>>11519320

Christ, there is nothing so annoying as seeing this bullshit get posted again and again as "proof".

They start with a false premise, then self reference it, to make a conclusion based off a false premise. Yeah, and they do it all with a straight face. The sheer audacity is astonishing. Real knuckle dragging logic there. Same sort of reasoning skills that got "witches" put in a suit of armor and thrown in the village lake.

You know. One day these 0.999... = 1 fuckwits are going to have to atone for their intellectual crimes. One day we will herd them up, hog tie them on top of stack of firewood and let the flames cleanse them of their goddamned heresy. We will stand around with our children, watching, eating hotdogs, maybe throwing some rotten tomatoes at them while we laugh as the flames grow higher and their screams grow louder. Good times to be had.

[Anonymous No.11519712]

>>11519703
They’re right, though.

[Anonymous No.11519715]

>>11519712
Fetch the firewood, I've found one right here.

[Anonymous No.11519728]

>>11519083
Fucking finally, I was going to post this. I mean this is high school level shit.

[Anonymous No.11519735]

>>11519728
Found another knuckle dragging moron for the bonfire.

[Anonymous No.11519763]

>>11519083
are you autistic?
x = 0.9999...
10x = 9.99999....0
10x - 9 is not equal to x, 0.9999...0 is not equal to 0.9999........
9x = 9.99999....0 - 0.99999....
9x = 8.99999999......1

[Anonymous No.11519810]

[Anonymous No.11519816]

>>11519810
>that one p retard who keeps copy pasting his retard formula that no one ever replies to

[Anonymous No.11520022]

>>11519355
Don't worry, I brought it back up to 50% for you.

[Anonymous No.11520037]

I'll big bang pill you fuckers.

The big bang started with space occupying almost ZERO "space." Imagine the smallest possible number that isn't zero. Not .01, not .001, repeat that for infinity. That was the size of spzce for the big bang.

Mass was the opposite. Mass started at the biggest possible number that wasn't 1. Think .99999 infinitely.

The big bang caused space to start infinitely getting bigger and spread the almost infinite mass through it. The energy from this slowly created every universe.

Enjoy being enlightened.

[Anonymous No.11520038]

>>11518763
False
True
True
False

[Anonymous No.11520046]

[Anonymous No.11520052]

>>11520046
Anyone that actually thinks that is 1 is LARPing or is a low-IQ schizo.

[Anonymous No.11520060]

>>11519763
>10x = 9.99999....0
I say this with all sincerity, look up a beginner calculus text book and look up what a recurring decimal is

[Anonymous No.11520105]

Infinity doesn't exist so infinity 9's don't exist so a finite n amount of 9's much exist which means [math]\frac{1}{10^n}[/math] exists as the smallest number between 0.999... and 1.

anyone who believes otherwise has water in their skull.

[Anonymous No.11520198]

>>11519437
>FUCKING STUPID
1 + 1 = 2
>FAT STUPID FUCKING
>JUST FUCKING WONT!
>enlightened now.

but 1/inf=0

[Anonymous No.11520205]

>>11517718
based

[Anonymous No.11520217]

>>11520198
1/california = 0
1/potato = 0
1/pokemon = 0
1/carl sagan = 0
1/mercury = 0

[Anonymous No.11520220]

>>11520046
I don't give a fuck about this stupid argument but someone is 100% botting for the equal side
It was at like 75% not equal the whole time and even slipped into the 80s

[Anonymous No.11520223]

>>11520217
3-3=0
inf-inf undefined
inf-3=inf
1/3=0.333...
1/inf=0

[Anonymous No.11520232]

>>11520038
>False
So what's 1/3 in decimal notation?

[Anonymous No.11520235]

>>11520052
So all mathematicians?

[Anonymous No.11520244]

>>11520235
yes. i know more than all of them.
so of course i dedicate my life to 4chan 24/7 shitposting.

[Anonymous No.11520250]

>>11520232
[math]0.333\ldots\frac{1}{3}[/math]

[Anonymous No.11520257]

>>11520244
24/7=3.428571 428571...

[Anonymous No.11520261]

>>11520250
What's that [math]1/3[/math] at the end?

[Anonymous No.11520262]

>>11520223
inf-inf = 0
inf/inf = 1
inf + n = undefined (and no longer inf)
inf + inf = undefined (and no longer inf_
inf - n = undefined (and no longer inf)
n / inf = undefined

these need to be true for "a set of all numbers" to exist, whose size is "infinite".

if n/inf = 0, but inf/inf is not 1, then no numbers exist in the infinite set of all numbers. and any set that has known elements, but is claimed to be infinite, must inherently actually be finite.

if inf/inf = 1 though, it becomes possible for all numbers to exist in the set regardless of what n/inf evaluates as, so n/inf might as well evaluate as undefined, as it makes no sense for all and any n, divided by inf, to be 0.

[Anonymous No.11520283]

>>11520262
inf-inf = undefined
inf/inf = undefined
inf + n = inf
inf + inf = inf
inf - n = inf
n / inf = 0

Z aleph-0
R aleph-1

[Anonymous No.11520293]

>>11520232
mathematicians seems to think
[math]\frac{1}{3} = \underbrace{0.333 \underbrace{\dots}_{\infty-1}}_{\text{base-10}} \underbrace{\underbrace{3}_{\infty}}_{\text{base-9}} [/math]
unironically.

granted none of them are smart enough to say it as concisely as this, but if you look at the way they treat repeating decimals and infinity, this is the general blueprint of how their minds seem to understand it.

[Anonymous No.11520300]

>>11520293
Nah, $[math]0.a_1 a_2 a_3 \dots = \lim_{N \rightarrow \infty} \sum_{n=1}^N \frac{a_n}{10^n}[/math]$.

It really is that simple.

[Anonymous No.11520313]

>>11520283
set of 100 = 100 size
integers
[math][0,1,2,3,\dots,100][/math]
if you pick a number and another number is picked randomly, there's a 1% ([math]\frac{1}{100}[/math]) chance your picked number is the randomly chosen number. If you say any number you pick must exist in the full range ([math]\frac{100}{100}[/math]), you have a 100% chance that the randomly chosen number exists in that range.

set of all integers = infinite size
[math][0,1,2,3,4,5,\dots][/math]
randomly pick a number in the set of all numbers.
if
>[math]\frac{1}{\infty}[/math] = 0
that means there's a 0% chance of the number you picked is also the randomly chosen number.
if
>[math]\frac{\infty}{\infty} \neq 1[/math]
that means there's still a 0% chance of the randomly chosen number existing within the range of [math]0 \rightarrow \infty[/math]
this means
>infinite sets do not exist
or
>infinite sets exist, but no elements inside them can be known, for knowing even 1 element within an infinite set would thereby make it finite.

are you sure you want to continue believing what you wrote >>11520283 here?

[Anonymous No.11520327]

>>11517889
weak bait

[Anonymous No.11520339]

>>11518155
>universe is infinite in expansion
why?

[Anonymous No.11520355]

>>11520313
>infinity tricky
news at 10: water is wet

[Anonymous No.11520357]

>>11520313
>this means
>>infinite sets do not exist
nope

[Anonymous No.11520368]

>>11520355
>tricky
it's not a natural object, it's entirely fabricated. Its not "tricky"; it's just so terribly and poorly defined that 90% of the definitions for it can be used against it to equally show it can't exist as described.
It's the quintessential function of getting caught in a lie.

[Anonymous No.11520371]

>>11520368
>natural object,
math isn't physics

[Anonymous No.11520373]

>>11520371
your brain is bound by physics, so think again.

[Anonymous No.11520377]

>>11520368
>it's just so terribly and poorly defined
Definition: ∞ is a symbol which satisfies x < ∞ for all real numbers x.

Literally nothing more.

Wow that was hard.

[Anonymous No.11520385]

If two real numbers are distinct, then we can find another number between them.

Give me one x with 0.999... < x < 1

[Anonymous No.11520386]

>>11520377
are you sure you can't find anything wrong with that definition?
For example, are there any implicit or explicit permissions or disallowances that x can be incremented to ∞?
is ∞ a number itself?
if it's not a number, it's assumed we can't do arithmetic with it as if it were a number, such as assigning it to limits or using it in an equation in place of a number, like [math]\frac{1}{\infty}[/math].

[Anonymous No.11520389]

>>11520373
i just imagined hopping from the moon to mars
and now you did too
> bound by physics
nah

[Anonymous No.11520390]

>>11520385
[math]\sum_{n=1}^{\infty}\frac{9}{10^n} = 0.999\dots_n < \sum_{n=1}^{\infty}\frac{10}{11^n} = 0.999\dots_n[/math]

helps if you know how to use infinity or at least know what it's describing.

[Anonymous No.11520393]

>>11520389
>i imagined it therefore its real
if only that's how this world behaved.
take your meds.

[Anonymous No.11520394]

>>11520313
that's 101, not 100 lol

[Anonymous No.11520398]

>>11520386
>if it's not a number, it's assumed we can't do arithmetic with it as if it were a number,
3-3=0
inf-inf undefined
1/inf=0
>as if it were a number,
it is clumsier, but some things you can do

[Anonymous No.11520402]

>>11520393
think harder
math isn't physics

[Anonymous No.11520403]

>>11520386
https://en.wikipedia.org/wiki/Real_projective_line
https://en.wikipedia.org/wiki/Extended_real_number_line
https://en.wikipedia.org/wiki/Riemann_sphere

Stop being a confident idiot and read a book for once in your life.

[Anonymous No.11520411]

>>11520394
you're right my bad.
[math][0,1,2,3,\dots,99][/math]

[Anonymous No.11520417]

>>11520403
>https://en.wikipedia.org/wiki/Riemann_sphere
lmao what the fuck is that image. i get its a wikipedia image and wikipedia is moderated by retards but come on.
1 is halfway between 0 and infinity.

[Anonymous No.11520420]

>>11520417
>i'm stupid
doesn't make it wrong

[Anonymous No.11520421]

>>11520398
>keeps shitposting 1/inf = 0
get a life bozo.

[Anonymous No.11520422]

>>11520386
>are you sure you can't find anything wrong with that definition
yes
>For example, are there any implicit or explicit permissions or disallowances that x can be incremented to ∞?
what exactly do you mean by "increment" ? x+y will never equal ∞, because if x,y are real, then so is x+y. therefore x+y < ∞. or do you mean like x -> ∞ written in limits ?
>is ∞ a number itself?
this is just semantics. "a number" is literally just an element of R. ∞ is not an element of R, therefore it"s not a number.
that doesn't stop me from making my own set myR = R ∪ {∞} and calling myNumbers elements of myR. then ∞ is a myNumber
>if it's not a number, it's assumed we can't do arithmetic with it as if it were a number, such as assigning it to limits or using it in an equation in place of a number, like
again, whether we can do arithmeics with ∞ is just matter of definition. you're now in a situation where you've introduced a new object, ∞ and implicitly there's no arithmetics for it. you need to define it. but obviously you would like to do it in a way which is consistent with the arithmetics that you know, for example defining ∞ + 5 = 13 would be silly.
it turns out that you can define SOME stuff such as x+∞ = ∞ and 1/∞, but not ∞/∞ or ∞-∞. let me remind you that this is the same for zero. zero is a number, BUT you can't do 0/0 because it wouldn't be consistend with the laws of arithmetics.

[Anonymous No.11520441]

>>11520420
infinity is wrong. It has 1 use, and it's not as a number.
It's to describe the size of the set of all integers.
[math][\underbrace{0,1,2,3,4,5,\dots}_{\infty} ][/math]
it has no well defined application outside of this, and this is just the axiom of infinity. Because of it's sole usage here, this is functionally truly no different than it being the "Axiom of Endlessness" or "Axiom of Unlimited", cause it's no different than saying
[math][\underbrace{0,1,2,3,4,5,\dots}_{\text{unlimited}} ][/math].
Nothing about it defines it can be used as an actual number, meaning
[math]\infty - \infty = undefined \\ \frac{n}{\infty} = undefined \\ \infty * n = undefined \\ \infty \pm n = undefined \\ 0^{\infty} = undefined[/math]

if you want to define any of these, you have to show where they are defined to work as such, and whether or not that definition relies on the presence of the axiom of infinity; otherwise provide examples where a case must be defined to solve a problem, thus providing a proof.

[Anonymous No.11520452]

>>11520421
https://www.wolframalpha.com/input/?i=1%2Finf

[Anonymous No.11520456]

>>11520452
https://www.wolframalpha.com/input/?i=infinity
>>Infinity is an unbounded quantity greater than every real (and every whole) number.
https://www.wolframalpha.com/input/?i=quantity
>>a Quantity is how much there is or how many there are of something that you can quantify
https://www.wolframalpha.com/input/?i=quantify
>>to Quantify is to express as a number or measure or quantity
https://www.wolframalpha.com/input/?i=is+infinity+a+number%3F
>is infinity a number?
>>∞ is not a number
https://www.wolframalpha.com/input/?i=Does+1%2F%28not+a+number%29+%3D+1%2Finfinity%3F
>is "1/(not a number) = 1/∞" true?
>>no

wolfram is not your friend here.

[Anonymous No.11520458]

>>11520441
>>11520244

[Anonymous No.11520460]

>>11520441
>infinity is wrong. It has 1 use, and it's not as a number.
wrong
>It's to describe the size of the set of all integers.
size of integers is [math]\aleph_0[/math]. it's a bit different thing than ∞
>it has no well defined application outside of this
wrong
>Nothing about it defines it can be used as an actual number, meaning
this is actually true, but still you can define some of the operations to stay consistent with usual arithmetics, because it's useful in some context

[Anonymous No.11520463]

>>11520456
>unbounded quantity
>unbounded
lrn2read

[Anonymous No.11520464]

>>11520460
show me the usefulness of [math]\frac{1}{\infty}=0[/math]

[Anonymous No.11520469]

>>11520464
>11517815

[Anonymous No.11520472]

>>11520464
>>11517815

[Anonymous No.11520475]

>>11517820
That doesn't follow at all. Undergrads please fuck off.

[Anonymous No.11520484]

>>11520469
2 things terribly wrong with that.
1, you can't actually increment to ∞ from x

2, it provides a finalized value of 0's at the end of the decimal, much like [math]\frac{1}{4} = 0.25000\dots[/math]
so
>0.999 as three nines. [math]\frac{1}{10^3}[/math] = 0.001
>a smallest part exists for n
>0.999... has inf nines. [math]\frac{1}{10^{\infty}} = 0; no smallest part can be added; but also necessarily if 0.999=1, the ∞'th decimal place must be base-9 instead of base-10.

lots wrong with that thinking.

[Anonymous No.11520489]

>>11520464
I didn't say specifically 1/∞. the sum ∞+x is plenty useful in measure theory for example. 1/∞ = 0 does make some theorems about limits to be true in a slightly more general situations though.
it's "useful" in the way that it makes life easier notation-wise, because the symbol itself ∞ is pretty much just a notation. everything could be formulated without it, but there's no reason not to do it.

[Anonymous No.11520493]

>>11520489
>but there's no reason not to do it.
*not to use it

[Anonymous No.11520499]

>>11518200
No it isn’t. You’ve been taken in by pop-sci memes.

[Anonymous No.11520501]

>>11520484
>i never graduated
big surprise

[Anonymous No.11520505]

>>11520484
>>11520472

if x->∞ is a possibility that allows [math]\frac{1}{\infty}[/math]. and that equals 0, then [math]\sum_{n=1}^{\infty}\frac{9}{10^n} = 0.999\dots[/math] must therefore have a sub-infinite amount of 9's, which means it must have a finite amount of 9's for n < ∞, since there is no 9 at the ∞'th decimal place because the ∞'th decimal place is 0 from [math]\frac{9}{10^{\infty}}[/math]

[Anonymous No.11520515]

>>11520505
there's no ∞-th decimal place, man. where did you get that from

[Anonymous No.11520516]

>>11520501
>projecting
you gotta learn to mix it up.
>i dont have an argument
>lets pretend infinite is finite
>shitlatexman
>posts wolfram definition of infinity
>lrn2read unbounded
>bus masturbation

hope to fuck you never do anything even remotely illegal cause if some random anon can pin you down, sure as shit any government organization can.

[Anonymous No.11520526]

>>11520505
>∑∞n=1910n=0.999… must therefore have a sub-infinite amount
-limit to infinity, not even trying to slide all the way to inf using reals
-inf exists, but can't be reached by incrementing reals
doesn't mean that the cat isn't captured in the epsilon-delta box

[Anonymous No.11520527]

>>11520515
its an extension of the motive behind >>11517815
>x -> ∞
>1 / x
and this post somehow being valid proof that 1/∞ = 0 is a valuable concept.

everything possible is wrong with the line of thinking. it necessarily requires there be an n such that x + n = ∞, and it also means that when 1/∞ = 0, there is a terminating zero at the end of real decimals, being the ∞'th decimal.

[Anonymous No.11520535]

>>11520516
said by schizo hos doesn't have a single reference in the world supporting him

[Anonymous No.11520537]

>>11520535
my references are plain logic, you mongoloid buttmaster.

[Anonymous No.11520539]

>>11520516
said by schizo who doesn't have a single reference in the world to support him

[Anonymous No.11520541]

>>11520516
>>11520537
this guy is legit retarded. I mean actual brain damage.

[Anonymous No.11520542]

>>11520539
>>11520535
>said by schizo hos doesn't have a single reference in the world supporting him
https://www.youtube.com/watch?v=cjio2Yrim4w

[Anonymous No.11520543]

>>11520537
says every nutjob ever

[Anonymous No.11520546]

>>11520464
Read up on the Riemann sphere. It’s a beautiful structure that makes a lot of theorems and properties of complex functions (e.g. relating poles and zeros) more elegant and symmetric.
https://en.wikipedia.org/wiki/Riemann_sphere#Applications

[Anonymous No.11520547]

>>11520542
>an anime song
LOL

[Anonymous No.11520549]

>>11520547
keep tryin' lil' nigga
u will get there 1 day
just believe in urself

[Anonymous No.11520552]

>>11520549
1/inf=0

[Anonymous No.11520554]

>>11520537
>plain logic
1/3 > 0.3
1/3 > 0.33
...
1/3 > 0.333....

[Anonymous No.11520557]

>>11520554
now you're gettin it.
[math]\frac{1}{3} > 0.\overline{333}[/math]
this is a true statement.

[Anonymous No.11520566]

[math] \displaystyle
p=0.1 \\
\dfrac{1}{1-0.1}=\frac{10}{9} = 1 + \frac{1}{9} \\
\sum_{j=0}^\infty 0.1^j= 1 + \sum_{j=1}^\infty 0.1^j \\
9+1=9+9\sum_{j=1}^\infty 0.1^j \\
1=9\sum_{j=1}^\infty 0.1^j \\
\dfrac{1}{3} = 3 \sum_{j=1}^ \infty 0.1^j = 0.333...
[/math]

[Anonymous No.11520571]

>>11520566
https://www.wolframalpha.com/input/?i=sum%5B0.1%2C+%7Bn%2C1%2Cinfty%7D%5D

[Anonymous No.11520576]

>>11520571
kek
lrn2read

[Anonymous No.11520578]

https://www.wolframalpha.com/input/?i=is+0.999...+equal+to+1

SAY WHAT ???

[Anonymous No.11520585]

>>11520566
>[math]9 + 1 = 9+9\sum_{j=1}^{\infty}0.1^j[/math]
excuse me?
all you've done in the middle of your method is say that 1 = 0.999...
even though you did it using an infinite sum that explicitly prints out 9's and nothing but 9's.
are you retarded?

[Anonymous No.11520600]

>>11520585
please show the actual error
i could use a laugh

[Anonymous No.11520635]

If 1/3 =/= 0.333...
Doesn't that just mean that fractions and decimals aren't the same thing and we base our answer on a false assumption?

[Anonymous No.11520656]

>>11520600
one of the strongest proofs for [math]0.999\dots \neq 1[/math] is through the use of an infinite sum you mongoloid. The identity of the sum perfectly equates to the decimal result of the sum.
[math]\sum_{n=1}^{\infty} \frac{9}{10^n} = 0.999\dots[/math] explicitly. The sum's intent is to print 9's into the expanding decimal places, and that's exactly what it does linearly.
n1, 0.9
n2, 0.99
n3, 0.999

if you take any other number <9 in that fraction, you get a repeating decimal of that number. (1/10^n) produces 0.111...
(2/10^n) produces 0.222...
(3/10^n) produces 0.333...
and this 0.333... value is the same exact value you can get when trying to convert [math]\frac{1}{3}[/math] to decimal.
However that conversion process from [math]\frac{1}{3}[/math] Fractional to [math]0.333\dots[/math] Decimal is not an exact method via division, so the Decimal is not EQUAL to the Fractional.

1/3 > 0.3
1/3 > 0.33
1/3 > 0.333
>...
1/3 > 0.333...

this is plainly the case. there no ambiguity here, it's logical and sensible.
π > 3
π > 3.1
π > 3.14
π > 3.141
>...
π > 3.1415926535...

terminating 0's are required for an identity in Fraction to equal an identity in Decimal.
>1/2 = 0.5000...
>1/4 = 0.25000...
>1/8 = 0.125000...
otherwise there needs to be no possible solutions of ambiguity to provide a difference.
in the case of 0.999... != 1, there is the above noted 9/10^n sum solution which cleanly equates the value as a distinct number, same with the 3/10^n sum solution which cleanly equates the 0.333... in a way that 1/3 does not cleanly equate it, lacking terminal 0's.

come on man, this is in every thread.

[Anonymous No.11520669]

>>11520635
fractions and decimals aren't the same thing. This is obvious, and it's known. Fractional is a word, describing the language of fractions. there are some values which cannot be cleanly expressed as either a Fraction or Decimal too, such a π (pi).

[Anonymous No.11520672]

>>11520656
>and this 0.333... value is the same exact value you can get when trying to convert 1313 to decimal.
>However that conversion process from 1313 Fractional to 0.333…0.333… Decimal is not an exact method via division, so the Decimal is not EQUAL to the Fractional.
why are you using your own interpretation of what decimal expansion means ?

[Anonymous No.11520682]

>>11520672
>0.3
>0.33
>0.333
>0.3333
>the decimal is expanding

I'm not. You're using some bizarro interpretation of what infinity means, though.

[Anonymous No.11520683]

>>11520656
uh, is this about line #1
or perhaps #2 ?

your wall-of-text schizo raving is off-putting, drop it

[Anonymous No.11520690]

>>11520682
where does 0.333... sit on the number line ?

[Anonymous No.11520694]

>>11520683
you obviously weren't the author of the post if you're not following, and if you're not following then all of this is over your head anyway.

[Anonymous No.11520700]

>>11520694
>i have no argument

[Anonymous No.11520718]

>>11520690
somewhere between 0.3 and [math]\frac{1}{3}[/math]
if infinity is a concept that's allowed to exist in the numberline (aka, there are "infinite" decimal numbers between any integer), there's no sense in saying it's closer to one or the other, since whether it has infinite 3's or one 3, [math]\frac{\infty}{2}[/math] is undefined; so 0.333... is no closer to [math]\frac{1}{3}[/math] than it is to 0.3

infinity is retarded and it lets anyone do retarded things validly with it, and is also why it must be banished from math if not better defined to a much better degree than it has.

[Anonymous No.11520723]

>>11517686 >>11517698 >>11517718 >>11517721 >>11517740 >>11517751 >>11517758 >>11517764 >>11517774 >>11517779 >>11517791 >>11517810 >>11517815 >>11517818 >>11517820 >>11517821 >>11517837 >>11517842 >>11517850 >>11517857 >>11517859 >>11517861 >>11517869 >>11517873 >>11517889 >>11517902 >>11517905 >>11517908 >>11517911 >>11517915 >>11517916 >>11517917 >>11517919 >>11517925 >>11517943 >>11518041 >>11518120 >>11518135 >>11518141 >>11518155 >>11518170 >>11518185 >>11518200 >>11518207 >>11518216 >>11518335 >>11518346 >>11518360 >>11518400 >>11518405 >>11518407 >>11518417 >>11518426 >>11518433 >>11518449 >>11518472 >>11518485 >>11518487 >>11518490 >>11518499 >>11518500 >>11518501 >>11518502 >>11518709 >>11518728 >>11518740 >>11518743 >>11518757 >>11518763 >>11518764 >>11518772 >>11518778 >>11518792 >>11518848 >>11518872 >>11518873 >>11518905 >>11518909 >>11518919 >>11518933 >>11519004 >>11519017 >>11519028 >>11519031 >>11519043 >>11519083 >>11519101 >>11519109 >>11519112 >>11519126 >>11519139 >>11519152 >>11519157 >>11519166 >>11519221 >>11519230 >>11519259 >>11519300 >>11519301 >>11519308 >>11519320 >>11519348 >>11519355 >>11519363 >>11519377 >>11519391 >>11519437 >>11519458 >>11519471 >>11519581 >>11519703 >>11519712 >>11519715 >>11519728 >>11519735 >>11519763 >>11519810 >>11519816 >>11520022 >>11520037 >>11520038 >>11520046 >>11520052 >>11520060 >>11520105 >>11520198 >>11520205 >>11520217 >>11520220 >>11520223 >>11520232 >>11520235 >>11520244 >>11520250 >>11520257 >>11520261 >>11520262 >>11520283 >>11520293 >>11520300 >>11520313 >>11520327 >>11520339 >>11520355 >>11520357 >>11520368 >>11520371 >>11520373 >>11520377 >>11520385 >>11520386 >>11520389 >>11520390 >>11520393 >>11520394 >>11520398 >>11520402 >>11520403 >>11520411 >>11520417 >>11520420 >>11520421 >>11520422 >>11520441 >>11520452 >>11520456 >>11520458 >>11520460 >>11520463 >>11520464 >>11520472 >>11520475 >>11520484 >>11520489 >>11520493 >>11520499 >>11520501 >>11520505
Alright motherfuckers. Here it is.

[Anonymous No.11520736]

>>11520723
>using a limit, the definition of which is used for approximation, as a method of defining equality
>approximation is equality
pls stop

[Anonymous No.11520740]

1-.9=.1-.09=.01-.009=.001
Here we see a 1 that never goes away, but it is a 1 that is never fully constructed as it always becomes a 0 because the series does not terminate. We can find the number for any digit at any point is 0. Any number after 9 that isn't 9 brings the infinite series to a limit =/= 1, but .999... contains only 9. It reaches 1 at precisely infinity

[Anonymous No.11520741]

>>11520736
Nope. That's the definition of the limit of a sequence. Period.

[Anonymous No.11520748]

>>11520741
>using infinity in a way undefined by the axiom of infinity

[Anonymous No.11520750]

>>11520748
Which line are you objecting to?

[Anonymous No.11520759]

>>11520740
>reaching infinity
not possible.

[Anonymous No.11520760]

>>11520740
>1-.9 = .1-.09
topkek

[Anonymous No.11520761]

>>11520718
>infinity is retarded and it lets anyone do retarded things validly with it, and is also why it must be banished from math if not better defined to a much better degree than it has.
you don't know how infinity is defined
you don't know how real numbers are defined
you don't know how decimals are defined
you don't know how limits are defined
I'll be very generous and give you the benefit of the doubt whether you know how fractions are defined

>>11520736
>>using a limit, the definition of which is used for approximation, as a method of defining equality
>>approximation is equality
wrong. a limit is precisely a tool to turn approximation into equality.

[Anonymous No.11520769]

>>11520736
approximation has nothing to do with it
>>11520748
the axiom of infinity has nothing to do with it

[Anonymous No.11520771]

>>11520761
>>using a limit, the definition of which is used for approximation, as a method of defining equality
>>approximation is equality
>wrong. a limit is precisely a tool to turn approximation into equality.
bro...

[Anonymous No.11520774]

>>11520771
>>11520700

[Anonymous No.11520785]

>>11520759
It is already reached in the notation...

[Anonymous No.11520806]

>>11520785
the notation is wrong because reaching infinity isn't possible.

we also have the "[math]\frac{1}{\infty}=0[/math]" problem.
Your 0.999... can't be reproduced by [math]\sum_{n=1}^{\infty}\frac{9}{10^n}[/math], because your 0.999... number has 9's in every decimal, but the sum has 0's in the ∞'th decimal(s).

[Anonymous No.11520814]

>>11520771
well, since you're using the symbol for an infinite sum, you DO know that [math]\sum_{k=1}^{\infty}\tfrac{9}{10^k} = \lim_{n \to \infty}\sum_{k=1}^n\tfrac{9}{10^k}[/math], right ?

[Anonymous No.11520822]

>>11520814
[math]\sum_{k=1}^{\infty}\tfrac{9}{10^k} = \lim_{n \to \infty}\sum_{k=1}^n\tfrac{9}{10^k}[/math]

[Anonymous No.11520823]

>>11520806
>the sum has 0's in the ∞'th decimal(s)

[Anonymous No.11520826]

>>11520814
>>11520822
>tfrac

[Anonymous No.11520853]

>>11520823
this is a line of shitposting where I asked someone to show usefulness for why [math]\frac{1}{\infty}=0[/math] should be considered a true statement.
for which they presented >>11517815
which necessarily requires x in [eqn]\lim_{x\rightarrow\infty}[/eqn] to increment from the reals to infinity (I know, retarded), but also providing for "infinity'th" decimal place when x=infinity.

I guess now is a good a time as any to say this proof was retarded and there is still no displayed reason for why [math]\frac{1}{\infty}=0[/math] rather than [math]=undefined[/math]

[Anonymous No.11520861]

>>11520823
this is a line of shitposting where I asked someone to show usefulness for why 1∞=0 should be considered a true statement.
for which they presented >>11517815
which necessarily requires x in [math]\lim_{x \rightarrow \infty}[/math] to increment from the reals to infinity (I know, retarded), but also providing for "infinity'th" decimal place when x=infinity.

I guess now is a good a time as any to say this proof was retarded and there is still no displayed reason for why [math]\frac{1}{\infty}=0[/math] rather than [math] = undefined[/math]

protip, cant mix EQN and MATH.

[Anonymous No.11520921]

>>11520861
[citation needed]

[Anonymous No.11520926]

>>11520861
I don't really see how defining 1/∞ = 0 and using it as >>11517815 should be imply anything about ∞-th decimal

[Anonymous No.11520963]

>>11520814
>well, since you're using the symbol for an infinite sum, you DO know that [math]\sum_{k=1}^{\infty}\frac{9}{10^k} = \lim_{n \to \infty}\sum_{k=1}^n\frac{9}{10^k}[/math]
they're essentially the same, yes.
The function of the sum is a loop which uses the limit in place of n. Putting an actual limit function in front of it more defines the loop of sums. Whereas the sum produces a single list of partial sums, your limit sum would produce infinite lists of partial sums with infinite degrees of redundancy
>[math]\sum_{k=1}^{\infty}\frac{9}{10^k} = [/math]
>[0.9, 0.99, 0.999, ... ]

>[math] \lim_{n \to \infty} \sum_{k=1}^n \frac{9}{10^k} = [/math]
>[ [0.9], [0.9, 0.99], [0.9, 0.99, 0.999], [0.9, 0.99, 0.999, ... ] ...]

[Anonymous No.11521004]

>>11520926
lets reapply it here
[math]\sum_{x=1}^{\infty} \frac{9}{10^x}[/math]

x is strictly tied to decimal places. if x=1, then there is also 1 decimal place.
>x=1; 1st decimal
>x=2; 2nd decimal
if x=∞, this is equivalent to the ∞'th decimal place.

I personally do not agree with the notion that x can actually increment to ∞ at all, so I don't require an ∞'th decimal to exist. I think this limit function invoking ∞ is not a valid justification for why [math]\frac{1}{\infty}=0[/math] because of the implications.

If there are any better justifications for why [math]\frac{1}{\infty}=0[/math] ought to be a valid statement, i'm willing to hear them. That's what i'm looking for.
cause if there are no valid reasons, then [math]\frac{1}{\infty}=undefined[/math] is how it really ought to be.

[Anonymous No.11521148]

>>11521004
>>11520926
in case it weren't clear, the saying that sum somehow arrives at [math]\frac{1}{\infty}[/math], or rather pointing this identity towards that sum, is really implicitly defining a case where [math]\frac{9}{10^x} = \frac{1}{\infty}[/math], which is the case for [math]\frac{9}{10^{\infty}}[/math], or rather requires x=∞; which further requires the nonsense of incrementing x from real integers to ∞ as if ∞ itself were an integer.

[Anonymous No.11521355]

>>11521004
>>11521148
[citation needed]

[Anonymous No.11521394]

1/9 = 0.111...
+
8/9 = 0.888...
=
9/9 = 0.999...

[Anonymous No.11521409]

>>11521355
>requiring citation for the application of logic

[Anonymous No.11521446]

>>11521409
if it's valid, many more would agree with you

[Anonymous No.11521447]

>>11521004
>>11521148
Is this your chain of thoughts?

>1/inf = 0
>we have performed an arithmetic operation with inf
>therefore inf must be a number
>therefore we can perform all sorts of arithmetics with it and plug it into limits without giving it a thought

Yeah, no.

[Anonymous No.11521452]

>>11521447
>inf must be a number
nope

[Anonymous No.11521457]

>>11521447
>all sorts of
nope
some sorts of

[Anonymous No.11521477]

>>11521452
>>11521457
I'm asking if this is >>11521004's logic. Declaring 1/inf = 0 doesn't magically change definition of infinite sums or adds inf-th decimals to numbers.

[Anonymous No.11521486]

>>11521477
no comment
talk to >>11521004
idgaf what he thinks

[Anonymous No.11521493]

>>11517686
>ITT: People who don't understand what ... means.

[Anonymous No.11521511]

Imagine being so dumb that you can be deceived into believing anything less than 1 is the same as one. Newsflash retards; regardless how many 9's you use it will never be the same as 1.

[Anonymous No.11521513]

-inf and +inf are both elements of the extended real numbers. Some arithmetic operations are defined for this set, namely:

>a/+inf = 0 , a/-inf = 0 , for all real numbers a.

One of the many applications of the extended reals is the monotone convergence theorem of measure theory:

>If a sequence of real numbers is increasing and bounded above, then its supremum is the limit.

You'll need this result for all of calculus if you want the rigor of axiomatic set theory by way of the standard constructions, although this decision is arbitrary and does not require any justification.

[A̛n͟o̧ǹ͝y̶m̶̸͠ous͞ No.11521525]

>>11520861
>>11520921
>>11520926
>>11520963
>>11521004
>>11521148
>>11521355
>>11521394
>>11521409
>>11521446
>>11521447
>>11521452
>>11521457
>>11521477
>>11521486
>>11521493
>>11521511
>>11521513
[math]\mathbb{COOF}[/math]

[Anonymous No.11521548]

>>11521525
OH SHIT

[A͢n͟o͡҉n͠y̧͠mou̷s̛͏ No.11521552]

[A͏n͜o͞ny̧͠m͡o̧͢u̸̶s No.11521572]

>>11520861
>>11520921
>>11520926
>>11520963
>>11521004
>>11521148
>>11521355
>>11521394
>>11521409
>>11521446
>>11521447
>>11521452
>>11521457
>>11521477
>>11521486
>>11521493
>>11521511
>>11521513
coof coof anonchan i dont feel too good

[Anonymous No.11521579]

>>11521511
let's pretend infinite is finite

[Anonymous No.11521604]

You are all infected. To each other, biologically. To the Earth, socially. To the rest of the universe, mathematically.

[Anonymous No.11521605]

>>11521447
Are you retarded? Can't you read?

All i did was ask for why [math]\frac{1}{\infty}=0[/math] needs to be defined that way, and for an example of how that statement is useful. I was redirected to a limit function x->inf that had the fraction [math]\frac{1}{x}[/math] involved.

All i did was show that this doesn't support "[math]\frac{1}{\infty}=0[/math]" at all because of the logical complications in which it can be applied as relative to the fucking retarded limit equation.

[Anonymous No.11521619]

Is anyone going to provide any reasoning or proof for why [math]\frac{1}{\infty}=0[/math] is a useful equation?

If not, [math]\frac{1}{\infty}[/math] = undefined, as it should be.

[Anonymous No.11521640]

>>11521619
[citation needed]

[Anonymous No.11521733]

>>11521640
Without infinity being well defined, neither are it's usages, which is important related to the thread op since many people seem to misunderstand what "0.999..." means.

[A͡n̶͡on͜ym͡o͟͞u̶̕͝s No.11521802]

>>11521733
[math]\sum_{k=1}^{\infty} \frac{9}{10^k} = \lim_{n \to \infty}\sum_{k=1}^{n}\frac{9}{10^k} = \lim_{n\to\infty} \frac{9}{10}\frac{1-\frac{1}{10^n}}{1-\frac{1}{10}} = \frac{9}{10}\frac{1-\frac{1}{\infty}}{1-\frac{1}{10}} = \frac{9}{10}\frac{1-0}{1-\frac{1}{10}} = 1[/math]

[Anonymous No.11521843]

>>11520557
4 > 1
4 > 2
...
4 > 4

[Anonymous No.11521846]

>>11520656
>>11521843

[Anonymous No.11522033]

>>11521733
it's big
duh
1/inf=0

[Anonymous No.11522091]

Test

[Anonymous No.11522103]

>>11520339
Asking "why are the laws of physics how they are" is difficult to answer and exists in the realm of philosophy.

[Anonymous No.11522318]

>>11522311
Have we actually confirmed that replying to an infected user gets you infected?? Because I'm coming up on 30 minutes now...

[Anonymous No.11522321]

>>11521802
Circular logic

[An̶o̢͜n͜y͜m͠ǫ̸̀u̢s No.11522338]

>>11522321
where

[An͢͡on̵͡ymous No.11522438]

>>11522321
projection

[Anonymous No.11522543]

I think .9999 doesn't equal 1, but 1/3 * 3 does, and that 1/3 isn't actually equal to .3333.

Maybe some fractions just shouldn't be decimals. Or maybe there's some form of number we haven't created to make this whole thing true. Can't we just make up something to make the solution work like a phycisist?

[An̶҉o̵n̡̨y͜mo͠u͢͠s̴ No.11522597]

>>11522543
>I think
try harder

[An͜o̕n͠y҉m̛o̶ư͏̀͠s No.11522610]

>>11522543
>think
try to read and think about proofs of 0.999... = 1. and I mean actual proofs, not that 10x = 9.999... bullshit.
then try reading and thinking about proofs of 0.999... != 1. oh wait, there are none. only schizo rambling.

[Anonymous No.11522626]

>/sci/ doesn't understand basic limits
Please tell me this is a high effort troll
Either that or calculus 1 is really a good brainlet filter, now i understand why my uni has it as a mandatory first semester class for everyone together with a bunch of other math classes.

[Anonymous No.11522667]

>>11522515

Are you sure you're not just an asymptomatic carrier?

[An҉ò̴n҉̵͟ý̨mò͠us No.11522668]

[math]
\boxed{0 < p < 1} \\
1 = p + (1-p) ~~~~~~ \overset{1}{ \overbrace{[=====p=====|==(1-p)==]}} \\
\text{divide p using x} ~~~~~~ \overset{1}{ \overbrace{ \underset{p}{[ \underbrace{=====x=====|==(p-x)==}]} ~~ + ~~ (1-p)}} \\
\\
\text{solve x and (p-x), when length ratios must be the same} \\
\dfrac{x}{p-x}= \dfrac{p}{1-p} \Rightarrow x- xp = p^2 - xp \Rightarrow \underline{x=p^2} \Rightarrow \underline{(p-x)=p(1-p)} \\
\overset{1}{ \overbrace{ \underset{p}{[ \underbrace{=====p^2=====|==p(1-p)==}]} ~~ + ~~ (1-p)}} \\
\\
\overset{1}{ \overbrace{ \underset{p^2}{[ \underbrace{=====p^3=====|==p^2(1-p)==}]} ~~+ p(1-p)+(1-p)}} \\
\overset{1}{ \overbrace{ \underset{p^3}{[ \underbrace{=====p^4=====|==p^3(1-p)==}]} ~~+ p^2(1-p)+p(1-p)+(1-p)}} \\
(1-p)+p(1-p)+p^2(1-p)+p^3(1-p)+ \cdots =1 ~~~~ \left | ~ \times \frac{1}{1-p} \right . \\
1+p+p^2+p^3+ \cdots = \dfrac{1}{1-p}
[/math]

[An͜ǫ̶̸́nym̀o҉́u̶s͡ No.11522711]

don't know

[Ano͏̷n͠y̡̛m͘̕ous҉́́ No.11522714]

>>11522668
very nice butters. very nice

[Anonymous No.11522749]

>>11517820
You don't understand how to take limits. You made a typical first year undergrad mistake.

[Anonymous No.11522765]

>>11520736
You really have low comprehension of mathematical analysis.

[Anonymous No.11522793]

>>11522626
Do all US unis use the same courses? I see people here referring to calculus 1, calculus 2 etc but in the UK all institutions have their own courses

[Anonymous No.11522820]

>recuperate is the correct spelling

[Anonymous No.11522821]

>>11520723
A mathematical analytical argument isn't going to convince someone with no understanding of mathematical analysis that 0.999... = 1, for if one did have any comprehension of basic analysis, that 0.99... = 1 is immediately clear (using a reasonable definition of 0.99... of course, which any math student will assume means the limit of the partial sums 9/10 + 9/10^2 + ... 9/10^n). This happens in every single. You get people going around asserting facts using their shitty deduction abilities in fields for which they have no knowledge or experience, but still have somehow convinced themselves that they have expert knowledge. Same as anti vaxxers. Instead of feeling dismayed and trying to convince them, relish in the fact you're not a fucking idiot, perhaps even smart, and laugh at these people.

[Anonymous No.11522996]

>>11522765
You are trying way too hard to defend irrelevant pretend-math.
The only shit comprehension here are mathematicians for allowing the infinity meme to go on this long. Shameful brainlets.

[Anonymous No.11523005]

>>11522793
I'm from eastern europe, so probably it's different from US and western europe, it's just the first uni calculus course so they call it that.

[Anonymous No.11523008]

>>11522821
You're trying too hard.

Academia is not a real job. Just cause you got suckered into learning worthlesd information that literally has no use beyong trying to sucker others into learning it via becoming a teacher, doesn't mean you're right.

Shameful brainlet.

[A̶͟n͞o͜nym̨̛͡o̧u͠s͜ No.11523038]

>>11523008
>Just cause you got suckered into learning worthlesd information that literally has no use beyong trying to sucker others into learning it via becoming a teacher, doesn't mean you're right.
that's exactly what it means

[Anonymous No.11523098]

dont coof @ me brainlet.

[An̕͝on͠͝y̛mo͠us No.11523123]

>>11523098
>>11523038
>>11523008
>>11523005
>>11522996
>>11522821
>>11522793
>>11522765
>>11522749
>>11522714
>>11522711
1/3 = .333...
1/3 + 1/3 + 1/3 = .999...

[Anonymous No.11523174]

>>11523123
>haha calculator print long number brrrr

[ 1 ], [ ÷ ], [ 3 ], [ = ]
[ 0 . 3 3 3 3 3 3 3 ]

but in real math, [math]\frac{1}{3} >
0.333\dots [/math]

[An̸on͘͠҉̴y̶m͜oư̢s͠ No.11523191]

>>11523174
https://www.wolframalpha.com/input/?i=is+0.333...+equal+to+1%2F3

[Anonymous No.11523221]

>wolframalpha isn't a calculator
haha brrrrrrrrrr

[Anonymous No.11523262]

>>11517686
Oh my god you people are fucking retarded. It's just a limit.

[Anonymous No.11523319]

>>11523262
limits are only viable without infinity
or rather, convergence is.
divergence will remain expanding regardless of anything.
but if there an implicit notion of infinite allowable terms between any two integers, then limits of convergence are complete nonsense.
put it another way:
A: [ 0 , 1 , 2 , 3 , 4 , ... ] -> ∞
mapped to
B: [ 0 . 9 , 9 , 9 , 9 , ... ] -> 1
has the same meaning.
A cannot reach infinity, much less get close to it.
B cannot reach 1, much less get close to it.
because infinity is insurmountable.

if there were a finite function there rather than infinite, then you could approach.
For example, with a limit of 7 decimals.
[ 0 . 9 0 0 0 0 0 0 ]
[ 0 . 9 9 0 0 0 0 0 ]
[ 0 . 9 9 9 0 0 0 0 ]
[ 0 . 9 9 9 9 0 0 0 ]
[ 0 . 9 9 9 9 9 0 0 ]
[ 0 . 9 9 9 9 9 9 0 ]
[ 0 . 9 9 9 9 9 9 9 ]
if you doubled that up to 14, at this most recent step we'd at least be halfway there. 14/2 = 7

if you expand it to ∞ though, well, what's ∞/2?
∞/2 doesn't exist.
can't divide infinity.
so you can't show that any n amount of 9's are "approaching" infinite 9's.

[A̕͠n̢͜o̴n̢ymǫ̵̀us͘ No.11523331]

>>11523319
>wall of schizo-text

[Anonymous No.11523340]

>resident retard got infected
what a surprise

[Anonymous No.11523436]

there's probably an argument to be made that [math]\frac{1}{3} = 0.333\dots[/math] if
infinity isn't something applicable to math.

but since the dots themselves are loosely attributed to infinity, it'd ultimately require a different notation.
>>11520293
nails an equality function but it's extremely messy and weird.
Since 1/3 division prints out 3's because it wants there to be an integer between 3 and 4 (in base 10), the easiest way of getting around it is saying the answer must instead be in base 9.
1/3 in base 9 = 3/10 = [math]0.3000\dots_{b9}[/math]

it essentially functions the same as taking a decimal with n-decimals, but cutting it off at (n-1) decimals and using the n'th decimal to round,and if the logic were explained well enough then it would omit the need to even write [math]0.333\dots[/math] or [math]0.\overline{3}[/math].

although it's still messy nonsense to write [math]0.3_9[/math], it's probably more functional in expanding general maths to cover arbitrary bases.
if we had a true numberline that encompassed numbers from any base, then it becomes much easier to say [math]\frac{1}{3} = 0.3_9[/math] rather than [math]\frac{1}{3} = 0.333\dots[/math]
and this would require new methods in calculators and computers for doing math.

[An̕͝o͞n̡̛y͢m̶o͟u͟͞s No.11523517]

>>11523436
>if we had a true numberline that encompassed numbers from any base
lol

[Ą͟͝no̴nym͜o͞ù҉ś͝ No.11523649]

>>11523436
>9 = 3/10 = 0.3000…b9
your base isn't benign, it's seriously malignant

[Anonymous No.11523658]

imagine being a chatbot that can't comprehend entire sentences.

here's a complimentary (You) @11523649 you stupid coofer.

[Anonymous No.11523707]

>>11517686
1-0.9=0.1
1-0.99=0.01
1-0.999=0.001
...
1-0.9999999999=0.0000000001
...
How far can you go? Can you reach 1-0.999...=0? But if you only work with three significant figures then 1-0.999=0 and we are finished.

[Anonymous No.11523728]

anyone know of any applications of [math]\frac{1}{\infty} = 0[/math] or have a reason to object to [math]\frac{1}{\infty} = undefined[/math] ?

[An̛o͢n͜y͡͡m̸̶ǫ̶͟us No.11523746]

>>11523728
>>11522033

[Anonỳmous̢ No.11523790]

>>11523728
Riemann sphere

[Anonymous No.11523836]

>>11523790
>complex analysis/analytic number theory counts as an application

[An̨o̶nym͏ou̡͟s͞ No.11523958]

Isn't it more like a riemann half-sphere since the top half is dedicated to anything greater than 1, unbounded?
Maybe call it the riemann faggot function since it's just a half-sphere connected to cylinder. Very phallic.

[Anon͡ym͢҉o͞us No.11524035]

>>11523958
What? The Riemann sphere is a compact Riemann surface, so it has a bounded image via any embedding into a metric space.

[A̛n̨҉͏o̴̡nym̢͞o͟us̷ No.11524049]

>>11517686
0.999...<1 you dumb math fags

[Anò̡n̸y̢ḿ҉ou̴͡s No.11524050]

>>11524035
The top vector is dedicated to infinity though. The left, right, front and back vectors are real numbers (inb4 i isn't), and all of those connect to the top, which is infinity.
The top half of the sphere is useless.
It's easy enough to imagine it as a cylinder extension of the bottom half sphere. So it's an upside dickhead.

[Anon̡͡ymo͞u̴s͟͝ No.11524068]

>>11524050
If it's a "cylinder extension to the bottom half sphere" (and embedded in R^3) it'll either be of finite "height" (i.e. homeomorphic to the Riemann sphere as it's normally defined) or it will go up forever, in which case it's homeomorphic to C.

Also, i isn't a real number... if you're only considering the bottom half, this is homeomorphic to (in fact, isomorphic as Riemann surfaces to) the unit disc in C, which is its own thing.

Without the Riemann sphere as a compactification of C, it's really hard to study Complex analysis, modular forms (analytic number theory in general), and some areas in geometry...

[An̶͠ó̴ny̴̧m̵o͜us͢͠ No.11524084]

>>11524068
sure you're not lookin for excuses to draw dicks in class?

[Anonymous No.11524096]

The time for discussing this is over. It is obvious that people who believe that 0.999... = 1 are in no way sane or rational. They can not be reasoned with. They are like flat earthers. Either trolls or so hopelessly retarded that they wouldn't even be able to comprehend how goddamned fucking stupid they are even if you shoved their heads into a powerful anti-retard device and left it going all year on the maximum setting.

No, my friends, any debate with these crawling cretins is pointless. It is instead time to settle this on the battlefield. I can guarantee VICTORY shall be ours, for we believe in a discrete Universe, governed by discrete laws, where our swords shall VERILY CLEVE OPEN THE HERETICAL SKULLS OF THOSE GOD CURSED SODOMY-LOVING INFINITY FREAKS with the blessing of the ALMIGHTY! DEUS VULT!

[A͞n̢o͢ny͢m͠o͏u̢͘s̀͟ No.11524124]

0.999... = 1
[math]\color{red}{\text{(USER WAS BANNED FOR THIS POST)}}[/math]

[Anonymous No.11524269]

>>11524096
\textcolorred(USER WAS PRAISED BY GOD FOR THIS POST)

amidoingitrite?

[Anonymous No.11524286]

>>11524124
nice

[Anonymous No.11524360]

>>11517698
this

[Anonymous No.11524369]

>>11520806
>we also have the "[math]\frac{1}{\infty}=0[/math]" problem.
retard

[An͞o̢n̡̧y̢m͢͢͠o̢us̢ No.11524387]

>false = truth
No wonder this is somehow correct and the only acceptable answer nowadays. Mankind is FUCKED.

[Anonymous No.11524447]

>>11524096
It seems you just assume there's a ...01 at the end somehow. And you think people are trying to get rid of it lol. The digits go from 0-9 not 1-10. Every digit is fully occupied. There is no ..1.

This is the only number that does this and the usefulness is immediately apparent upon converting fractions and decimals. It's easy to express 1/3 in base 9. Not so easy in base ten.

[Anonymous No.11524609]

>>11524602
jesus

[An͏̴ơny̧̧͞m̕͞o̴us͟ No.11524610]

>>11524447
$9.99
>every digit is occupied
>$0.01 does not exist

[Anonymous No.11524732]

>>11524447

Where the fuck did I ever say anything about that, you Godless HEATHEN! Perhaps you are confusing me with some righteous, but otherwise confused, BROTHER, who rests in arms of the ONE TRUE DISCRETE UNIVERSE!

I will give one last chance to repent. Repeat after me: "0.999... even if it existed, which it doesn't, would go on like that forever and therefore would never reach 1" .

SAY IT! REPENT! REPENT! FIND SALVATION! YOU HERETIC! Otherwise you know the WRATH of my sword swinging down through discrete intervals of space in discrete parcels of time, thereby CLEAVING your SKULL and releasing the vile heresies contained therein. Meanwhile your own sword shallelth dangle uselessly, taking an infinite amount of time to travel an infinitesimal distance. HA! And thusly so the righteous shall vanquish the infidels!

DESU VAULTING!

[Anonymous No.11524858]

>>11522033
Big brain post, unironically.

[Anonymous No.11524860]

>>11524096
*Sorry, I made a typo. I meant people who believe that 0.999... ≠ 1.

[Ań̵̡on͢y̡͡ḿ̡o͢us̴ No.11524865]

>>11522033
saying 1/inf=0 doesn't make it so.
it opens up a boatload of logic problems which have no result but to say it can't be so, anyway.

[A̕n̴̨ơ̵nym҉ou̵͢ś͏ No.11524870]

>>11524860
>infinity
>discrete
nice try tardo make sure to read the whole post next time.

[Anonymous No.11524978]

>>11524865
[citation needed]

oh here's one
https://www.wolframalpha.com/input/?i=1%2Finf

[Anonymous No.11525095]

>>11524865
>opens up a boatload of logic problems
Name one

[Anonymous No.11525168]

>>11525095
>Name one
0.999...
um, let's call it Harold

[Anonymous No.11525359]

>>11525168
>0.999...
100% unrelated to 1/inf = 0

[Anonymous No.11525421]

>>11525359
meh, 99.999...%

[Anonymous No.11525422]

>>11525359
1 = 9/10 + 1/10
= 0.9 + 1/10
= 0.99 + 1/100
= 0.999 + 1/1000
:
= 0.9... + 1/inf
= 0.9... + 0
= 0.9...

[Anonymous No.11525428]

>>11525422
this is just a reformulation of an argument which works the same regardless of 1/inf = 0.
literally only difference is that you write "1/inf" instead of "lim 1/10^n for n->inf".

[Anonymous No.11525492]

>>11525428
ty for your service, captain obvious