/sci/ - Science & Math

Yes.

9X=9

wat

[math]
\displaystyle \sum_{n=1}^{\infty}\frac{9}{10^n} = \frac{9}{10} + \frac{9}{100} +\frac{9}{1000} + ... = b = \frac{1}{10}(9 + \frac{9}{10} + \frac{9}{100} +...) = \frac{1}{10}(9+b) = b \\ \frac{1}{10}(9+b) = b \\ \frac{9}{10} = \frac{9}{10}b \\ 1 = b
[/math]

>>9476752
where did you get that 10 times 0.9999... equals 9.999...

>>9476775
9.999.../10 = 0.999...

>>9476752
If you can't do this method with a non-repeating decimal, then the method isn't valid
x = 0.99
10x = 9.90
10x-x = 9.90 - 0.99
9x = 8.91
8.91 / 9 = 0.99
x = 0.99
so its invalid.

describing the amount of 9's in [math]0.\bar{9}[/math] as infinite is not helpful because infinity is not a number and cannot be counted. For any finite amount of 9's in 0.9-, even trillions of 9's, x will always be able to retain it's value. It only appears to work the way it does with infinite 9's because retarded concatenation that can be seen with
X = 0.999
10X = 9.999

instead of
x = 0.999
10x = 9.990
As it would normally work

if shifting the decimal place like that was a valid method, you could just as easily say
[math]x = 0.\bar{9}[/math]

[math]10^{\infty}x = \bar{9}[/math]

which raises the problematic question of whether a number like [math]\bar{9}[/math] is actually greater than any [math]\bar{N}[/math] or any number [math]×10^\infty[/math].

TL;DR, [math]0.\bar{9} \neq 1[/math] and there exists no counterable proof otherwise, only tricks and misunderstandings.

>>9476861
There exists no uncounterable proof otherwise

>>9476861
>hysterical

>>9476861
nein nein nein
nein nein nein
nein nein nein
https://youtu.be/vt50pCNylKc?t=45m

>>9476886
Shifting is completely invalid in math. Deal w/ it

>>9476903
>in your head

>>9476752
>So is 0.9 repeating equivalent to 1?
no. this is just a imperfection of out current counting system
for example, 1/3 in hex notation is 5.

>>9476903
https://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel#Analysis

>>9476752
https://www.wolframalpha.com/input/?i=(0.999...)%2B1

>>9476752
For FUCKS sake people, has NOBODY read the HISTORY of mathematical developments?

1>Fractions>Integers>Decimals<Primes
//
對於亂搞著想的人,已經沒有人讀的數學發展的歷史?

1>的級分>的整數>小數位數<上撇

>>9476908
[math]
\displaystyle
\frac{1}{3} çdot 16^0=5
[/math]

folks, this is the sad, sad view into a sick mind

>>9476908
[math]
\displaystyle
\frac{1}{3}\cdot 16^{0}=5
[/math]

this is your mind on StableGenius

>>9476909
Gayest and/or most retarded thing i've read on wikipedia.

Already proved shifting is meaningless via
x= 0.999...
[math]10^{\infty}x = 999...[/math]
and 999... = 888... = 777... = 666... = 555... = 444... = 333... = 222... = 111... because each value equates to infinity, because infinity as already exists in math is used blatantly incorrectly and paradoxically. Shifting has no value and is not a real operation.

>>9476917
Take your pills anon

>>9477016
You absolute retard. You can't raise 10 to infinity, because infinity is not a fucking number. You can approach it of course, but then all your reasoning falls apart.

Learn the definitions. Learn ZFC. Learn math in general.

>>9477016
>Gayest and/or most retarded thing I've read on wikipedia.

Why the homophobia, you faggot?

>>9477028
it's hopeless, in another thread he insists that 9/10 - 1/2 = 0

>>9477032
Why the homophobia?

>>9476930
sorry, i'm a brainlet. bear with me.
i mean that we can't divide a number 1 by 3, but we can divide a number 6 by 3 for example
it is possible to create such notation where 1 can be divided by 3

>>9477108
>we can't divide a number 1 by 3,
you can't divide a number 1 by 3,

So what is 1/3 in hex?

>>9477123
>you can't divide a number 1 by 3
because OUR number 1 is fractured by 10 pieces

>>9477143
why isn't it fractured by 13 pieces?
because jesus?

>>9477123
>So what is 1/3 in hex?
0.555[...]

>>9476752

>>9477033
No, calculus insists that. Thanks for taking the time graduate middleschool you foreskin fiddling thunderfuck.

>>9477028
i agree, infinity is not a number, but its primary reason for existence in maths along with its primary use is to do anything you want with it for any reason whatsoever, so you can't necessarily prove me wrong for using it as intended.

Like why would an infinite sum exist? How cum dey use da infinity if it doen't a number????

>>9477518
>calculus insists 9/10-1/2=0

you just can't make this up... oh wait, you did

>>9477545
nah, calculus insists.

>>9477583
>This is psychosis, not math
I rest my case

>>9477608
hello psychosis. I'm math. Nice to meet you.

>>9476752
No.

http://aynrandlexicon.com/lexicon/infinity.html

>>9476886
>posts 2:15 hs moovie
still shorter than mollymeme videos but not related

>>9476861
actually goo is this OC?
limits are not understood by computers, they prob dont even exist

>>9476861
>[math]10^\infty x = \bar{9}[/math]
kek

>>9477518
>calculus insists 9/10 - 1/2 = 0
KEK

>>9476752
It seems illogical, but yes, it's true.

Another way to look at it might be that 0.333333333... =1/3.
So what is 0.3333333... X 3?
3/3, 1, 0.999999..., 100%, ln(e); they're all the same number.

>>9478664
Or look at it via infinite sums. If you plotted a graph of value against number of decimal places, you'd get this table;
1:0.9
2:0.99
3;0.999
4:0.9999 etc.
The trend always approaches but never quite reaches 1; in mathematical terms, as number of decimal places tends towards ∞, value tends towards one.

>>9478209
>?t=45m
this was too subtle for you?

>>9477343
Horrible color choices.

>>9476752
[math] \displaystyle
1 = \frac {3}{3} = 3 \cdot \frac {1}{3} = 3 \cdot 0. \bar{3} = 0. \bar{9}
[/math]

>>9476861
No idea how hard you’re memeing but sometimes when people say infinity they’re using shorthand for “as the limit approaches infinity” you pedantic FUCK

>>9477583
What the fuck kind of calculus is this? Where’s the deltas? The dy, the dx? Including an infinite sum doesn’t automatically make something calculus.

>>9478664
This is the absolute best way to think of it. Some dude with a degree is gonna come in here and tell me it’s wrong because it’s not rigorous or whatever; but, if someone is asking you if 0.999... = 1, chances are even slight rigor will make them tune out. Normies know that three thirds make one whole, and one third equals 0.33333...

These people don’t want a real lesson, so just give them something that’ll make them shut up about it.

>>9478774
no way anyone with a degree in math will tell you its wrong

>>9476771
Mfw

>>9476752
The continuum is intuitively true, they said

>>9478743
>>9478758
Kill yourself

>>9478727
Pic related also no. There are an infinite amount of different ways to compose a repeating decimal and they all evaliate differently because their repetition is proveable to accumulate at different rates. Where a complex number or real number is just a number, a number with a repeating decimal is a number with time attached to it, where classical math disregards this time causeath hasn't been reformed and is still trucking along from the innumerable fuckups of brainlets from the annals of history.

>>9478938
>a number with a repeating decimal is a number with time attached to it,
m-muh feelings

>>9478774
Well, I'm a grad student in pure math (analysis to be specific) and I will tell you that you're reasoning is fine. It just boils down to the fact decimal expansions are not unique.

>>9478944
You keep stalking me to different threads and you keep posting >m-muh feelings as if it were supposed to mean something. I get you're too stupid to adapt new maths but that doesn't mean you must be so stupid that you don't realize you appear as a schizophrenic.

>>9478963
applying time to a number is the dumbest thing ever - surprised that you don't imagine them having moustaches and sombreros

>ITT: /sci/ pretends not to understand infinite sums

>>9478963
I don’t like saying this because it’s basically the 4chan equivalent of “I know you are but what am I,” but, dude, you are projecting. Like you are actually literally projecting your insecurity about your made-up math and the possibility that you are experiencing a form of psychosis. Not trying to offend at all here, but getting some form of psychological therapy may be in your best interest.

I know the whole “get help” meme is usually meant as an insult, but I am being 100% sincere.

>>9479167
dressing up sigma signs with brassieres - totally normal

>>9479167
Replying to yourself. Totally normal and not insecure. Totally not projecting.

right.

>>9479302
What exactly do you do in real life that allows you to be like this?

>>9479338
your mother

1/9 = 0.1111...
9*1/9 = 1 = 9*0.1111... = 0.9999...

>no one has posted the geometric proof yet

[math] 0.999...=9/10+9/100+9/1000+... [/math]
[math] 0.999...=9/10(1+1/10+1/100+... [/math]
[math] 0.999...=(1-x)(1+x+x^2+x^3+...x^n) [/math]
[math] 0.999...=1-x+x-x^2+x^2-x^3+x^3-... [/math]
[math] 0.999...=1 [/math]

>>9479796
[math]
x= \frac{1}{10} \\
0. \overline{9}=9x+9x^2+9x^3+9x^4+ \cdots \\
0. \overline{9}=9x \left (1+x+x^2+x^3+ \cdots \right ) \\
0. \overline{9}=(1-x) \left (1+\mathbf{x}+x^2+\mathbf{x^3}+x^4+ \cdots \right ) \\
0. \overline{9}=1-x+ \mathbf{x-x^2}+x^2-x^3+ \mathbf{x^3-x^4}+x^4-x^5+ \cdots \\
0. \overline{9}=1
[/math]

>>9479895
This is some wacky shit indian math isn't it.

maybe go back to algebra and learn how to combine terms

>>9478975
Infinity is not a number.

Applying normal numerical rules to infinity is delusional.

Not only is infinity not a singular number of anything, it is a self-referential shithole range of numbers which satisfies
[math]\infty + x = \infty[/math], meaning infinity is actually
[math]\infty = \big[\infty +1, \infty +2, \infty +3, ..., \infty + \infty, \infty ^{2} +1, \infty ^{2} +2, ... \infty ^{\infty}, ... \big]_{\infty}[/math]

infinity is not a singular largest number. Using the definition of the singular largest number greater than any finite number, it is not infinite at all and is instead a finite (although dynamically variable) limit that satisfies [math]\infty + x = \infty[/math], where because the sum can be no greater than the finite limit of infinity, the result remains the same as if pouring too much water into a glass where there can only be a finite amount of water and the extra simply runs over the lip and is excluded from the total within the glass.
Classical infinity would ironically be finite and therefore paradoxical, so it must instead exist as a set of numbers infinitely larger than all countable numbers, but then cannot be properly used in lieu of any singular number for the supreme inability to reference any singular element within the set since each element in the set references the swtin the example of [math]\stackrel{\infty}{\mathbb{UC}_{1} = \big[ \infty + 1 \big][/math] being: the first element of infinity is (the first element of infinity is (the first element of infinity is (...)+1)+1)+1).
The best way to deal with infinity and infinite repetition is to then instead treat it with abstract time/rate [math]\stackrel{\mathbb{AB}}{\mathbb{TR}}_{\frac{x}{y}}[/math] that may produce a repeating decimal with metadata that could be used to ballpark identify an element or range of elements within the infinite set, such that a number [math]0.\bar{9}_{\frac{9}{10}}[/math] is an indication that the amount of 9's in this number grows/identifies under the rate of [math]\infty \frac{9}{10}[/math] per abstract time unit.

>>9480251

*[math]\stackrel{\infty}{\mathbb{UC}}_{1} = \big[ \infty + 1 \big] [/math] being: the first element of infinity is (the first element of infinity is (the first element of infinity is (...)+1)+1)+1).

**[math]0.\bar{9}_{\frac{9}{10}}[/math] is an indication that the amount of 9's in this number grows at a rate of [math]\infty \frac{9}{10}[/math] per abstract time unit

>>9480260
no idea why /sci/'s LaTeX keeps fucking up the second one.

[math]0.\bar{9}_{\frac{9}{10}}[/math] = pattern of 9's grows at a rate of 9/10ths of infinity per abstract time.

>>9480262
this fucking board holy shit.

>>9480165
3rd grade math, but too tough for a home schooled probably

>>9480260
Fuck latex but to show how the growth rate works, you could subsistute a real number in the definition, for example 1:
If each number were a finitely countable but huge set of all numbers, x + 1 would become x+(the first element of the set of numbers which is (the first element of the set of numbers which is (...))), where of tracking the steps would be the set counting to one, counting to one, counting to one... incrementing the steps by 1 and definining it's rate of growth as smaller than the example of x+5 which is x+(count to the fifth element of (count to the fifth element of (...))) where these equations were to sum, would show for ever step x+1 increments, x+5 increments by 5 steps so x+5 grows at a faster rate in the abstract time world where all work is completable in the same amount of time regardless of work done.

>>9480251
>>9480260
it's pill taking time, foam is coming from your mouth
little shitlatexman

>>9480262
how about some abstract bed time
your brain is boiling over again

>>9480287
(1 - x) (a.1 + b.x + c.x^2 + d.x^3 + e.x^4 +...) =
a(1-x) = (1-x)1 = 1 - (1/10) +
b(1-x) = (1-x)x = (1/10)-(1/100) +
c(1-x) = (1-x)x^2 = (1/100) - (1/1000) +
...
finite ending:
z(1-x) = (1-x)x^n = (1/(x^n)) - (1/(x^(n+1))) = 1 - (1/(x^(n+1))) =/= 1
infinite ending:
no sum manifests from the work (1 - [...]) but can be analytically proven that the result of [...] is half of ([...]+x = 0) where no number divided by 2 = 0, satisfying 1-1+1-1+1-1+... = 1/2 or otherwise having a divergent, unobtainable sum.

aka shitmath

>>9480331
1(1-x) = 1-x
x(1-x) = x-x^2
x^2(1-x) = x^2-x^3
x^3(1-x) = x^3-x^4

is that enough, or do you need crayons and sock puppets for the total retard version

>>9480294
I will never understand how your brainlet insecurity always resorts to calling me bad at using latex when the latex is right there in full working form within the math blocks, yet sci randomly decids to not render it correctly.

Like damn, you are a real bitchnigger.
I dont moderate 4chan, i dont administrate sci, i dont go into the site data and debug their implementation of LaTeX, this isn't reliant on any ability or inability of mine.

I type [math]\infty[/math] and get unformatted garbage or [math]sci decides to treat unblocked text within a block[/math]. This shit doesn't happen on auxillary LaTeX editors.

>>9480344
Heres your fried chicken, nigger. Good work. You've done enough for today, take a break.

>>9480350
>calling me bad at using latex
it's 4chan's computer that's calling your latex bad
try screaming at it
basically you are failing one iq test after another when shitlatex pours out in your posts

>>9480354
Do you need a sigma version too, can't you build it yourself? Or are you out of brassieres?

>>9480331
it's not divergent, retard
|x|<1

>>9480451
1 + [ - 1 + 1 - 1 + 1 - 1 + 1 ... ]
1 + [ - x + x - x^2 + x^2 - x^3 + x^3 ... ]
The partial sums of both series are
1: [1 - 1 = 0] | [1 - 1/10 = 9/10]
2: [0 + 1 = 1] | [9/10 + 1/10 = 1]
3: [1 - 1 = 0] | [1 - 1/100 = 99/100]
4: [0 + 1 = 1] | [99/100 + 1/100 = 1]

if the set "1 + [(-1 + 1) + (-1 + 1) + ...]" = 1/2 where summation approaches {0|1}, then the set "1 + [(-x + x) + (-x^2 + x^2) + ...]" = summation approaching {(1-x^n)|1}, where {a|b} = (a+b)/2, so (2-x^n)/2 = (1 - ((x^n)/2)) where ((1/10)^n) is not zero regardless of how small it is, so the answer, as 1/2 is smaller than 1 in [-1+1-1+1..], is also smaller than 1 in [-x+x...]

>>9480569
crayon mode
[math] \displaystyle
0. \overline{9}=1-x+ \mathbf{x-x^2}+x^2-x^3+ \mathbf{x^3-x^4}+x^4-x^5+ \cdots \\
0. \overline{9}=1-\sum_{n=1}^{\infty}(x^n-x^n)=1

[math]

>>9480569
crayon mode
[math] \displaystyle
0. \overline{9}=1-x+ \mathbf{x-x^2}+x^2-x^3+ \mathbf{x^3-x^4}+x^4-x^5+ \cdots \\
0. \overline{9}=1-\sum_{n=1}^{\infty}(x^n-x^n)=1

[/math]

>>9480569
crayon mode
[math] \displaystyle
0. \overline{9}=1-x+ \mathbf{x-x^2}+x^2-x^3+ \mathbf{x^3-x^4}+x^4-x^5+ \cdots \\
\displaystyle
0. \overline{9}=1-\sum_{n=1}^{\infty}(x^n-x^n)=1

[/math]

>>9480605
If you can solve for xyz, you might understand why you're retarded.

>>9480611
https://en.wikipedia.org/wiki/Moving_the_goalposts#Logical_fallacy

>>9480622
If A and B must meet to create a triangle, X° and Y° must each be 90°-v and Z° must 2v, where v must be a nonzero number regardless of how miniscule it is, thus such an infinitesmal must exist so that [math]0.\overline{9} + x = 1[/math], therefore 0.999... cannot equal 1 without adding a significant number x.
X° and Y° cannot be 90°-0 as A and B would be parallel, never forming the already defined existence of the triangle ABC.

That if A and B were an infinite sum of length, at every test of n there would always be a triangle, regardless of infinitely many tests of n.

>m-muh goalposts
you are so retarded that you can't even entertain simultaneous equivocal concepts without thinking they must be entirely different.
Go back to le reddit.

>>9477532
Maybe it's my low IQ, but I can't think of a way you could be more wrong.

>How cum dey use da infinity if it doen't a number????

Are you mocking yourself?

>>9480651
huffpuf huffpuff huffpuff fatass triangle
REEEEE
0.999... isn't 1 !!!!!!

you make no sense, just hysterical screaming
talk about the details in >>9480605
or shut the fuck up

>>9480672
>but its primary reason for existence in maths along with its primary use is to do anything you want with it for any reason whatsoever

>>9480611
hypotenuse length, [math] n \rightarrow \infty [/math]

a+b or [math] \sqrt{a^{2}+b^{2}} [/math] ?


pictures are almost worthless as proofs

>>9480758
Words are just many, small, simple pictures. :^)

>>9480781
mmm-hm well that explains your math grade

>>9480758
my favorite part about the hypotenuse is how it is an angle.

>>9480569
what a load of crap

the sums in the 1-sequence change radically depending on how you group them

the 1/10^n sequence is immune to change, nothing changes no matter where you put the parentheses

seek help

>>9478708
Thats the point brainlet, it makes it both catchy so people open it, as well as punishing people who make stupid threads like thisone

>>9476752
[SORRY I DO NOT KNOW HOW TO MATHS. PLEASE CONSULT WITH AN ACTUAL FUCKING MATHEMATICIAN]

>>9481580

>>9482059
elegant argument, must say

>>9482059
Elegant argument, must say.
Oh wait, guess that's just your M.O.

Do you guys never get tired?

>>9482126
nein nein nein...

>>9482124
You can't handle an argument. Its easier to deny you everything.

Your brain
does not
even work

>>9482572
neither do your arguments

>>9476752
Yes, .99999etc. = 1, and your math does indeed check out. Also if you know what a Cauchy sequence is and are familiar with the definition of Real numbers as the limit of a Cauchy Sequence off Rationals, then it becomes immediately obvious that .9 repeated = 1.

>>9477016
>t. Math "expert" who hasn't even studied logic, set theory, or topology.

>>9477583
Yo dawg, wuts up with that notation?

Also, the fact that:
(Sigma)(n<Infinity) [1/(2^n)] = (Sigma)(n<infinity) [9/(10^n)]
does not imply that (9/10) = (1/2) or that (9/10) - (1/2) = 0

>>9478938
>>9477583
this guy is obviously trolling, no one can be this retarded
where are the mods

>>9482817
Infinity is not a number. Its not even a singular number. Its a self-referential range of many numbers, classically lacking any finitest approach of ballparking some kind of accuracy within it's set, yet paradoxically treating it with the finitism that no number can be greater than infinity. It has time and rate obviously tied to it, and using infinity without a concept of time or rate, even if its just arbitrary unreal time of units unrelateably smaller than planck time, is disregading an important identity affixed to infinite actions. [math]\frac{1}{2^n} \neq \frac{9}{10^n} [/math] because it can be infinitely testable for every partial sum iteration of n that they are unequal and one is larger than the other. Infinity has carried multiple, paradoxical, self-defeating definitions in classical math and obviously requires reformation to a constant, singular definition that cannot be misused or mistaken. If you got some ideas, throw them down. If you don't, let down your guard and try to learn something.

Do you ever wonder why [math]0.\overline{9}[/math] ought to equal 1 but [math]0.\overline{8}[/math] or any other repeating decimal is just well off enough being itself?

Where do all those 8's go to? Why isn't their controversy about how many 8's there are? Why doesn't [math]0.\overline{8}[/math] need to arbitrarily round up to anything?
Why can there be a true amount of infinite 8's that make it a unique number, but not a true amount of infinite 9's that too make it a unique number?
Asking what a smaller number could exist between 0.999... and 1 is asking what number exists right before infinity. It's a completely irrelevant question, and doesn't aim validate equivocal status between 0.999... and 1, else there would exist a finite countable number J where [math]J + 1 = \infty[/math].

Just stop. Stop it. You're parodying yourselves.

>>9482935
FOR BREIHNLETTES:
>[math]J+n \neq \infty . J \neq \infty, n \neq \infty, n \neq 0[/math]
.
>[math]0.\overline{9}+n \neq 1 . 0.\overline{9} \neq 1, n \neq 0 [/math]

>>9482935
because 0.777... < 0.78
because 0.888... < 0.89
with 0.999... you run out of numbers to separate it from 1
Same happens in any base, in binary 0.111...=1

>>9476769
yea... that's where the math is wrong

>>9476771
This math actually checks out.

>>9477583
>using approximation
>calculus
Hmmm. Hope this is bait.

If there exists no maximal real number equal to infinity, there exists no minimus real number equal to zero.
If there exists no maximal real number that is identifiable to be 1 element less than infinity, there exists no minimus real number that is identifiable to be 1 element greater than zero.

If there is no singular discernable maximal real number that is 1 element less than infinity, there exists no singular discernable maximal real number that is solely less than infinity. Any real number is less than infinity.

If there is no singular discernable minimus real number that is 1 element greater than 0, there exisys no singular discernable minimus real number that is solely greater than 0. Any real number is greater than 0.

No matter how big a number sums, it never equals infinity. No matter how small a decimal can divide into, it never equals 0.

Because there exists no minimus real number equal to zero, nor any boundary for a least significant minimus real number which can be greater than 0, [math]\sum_{n=1}^{\infty} \frac{9}{10^n} \neq 1 [/math]
At no point in the sum will there ever exist a insignificant decimal place, and any real amount of 9's in the repetition will never be an infinite amount of 9's. At every point in the sum, will require addition of a minimal number to sum 1, such that
[math]\sum_{n=1}^{\infty} \frac{9}{10^n} + \big( \rlap{no}{\sum} \frac{1}{10^n} \big) = 1 [/math]

>>9484089
Thus it can be shown
For the sum [math]\sum_{n=1}^{\infty} \frac{3}{10^n}[/math] that at no point in the sum will there ever exist a significant amount of decimal places to unconditionally precisely equate [math]\frac{1}{3}[/math], expressly denoting [math]\frac{1}{3} \neq 0.\overline{3}[/math] because the amount of 3's at most could only ever be a non-infinite maximal real number amount, that if arbitrary infinite work could be completed, [math]\big( \frac{3}{10^n} \big) × 3 [math] would understandably equate to only infinite 9's, because 1/3 is not precisely 0.333...

[math]A: \frac{1}{3} × 3 = \frac{3}{3} = 1[/math]

[math]B: 0.\overline{3} × 3 = 0.\overline{9}[/math]

[math] A \neq B [/math]

>>9484089
Thus it can be shown
For the sum [math]\sum_{n=1}^{\infty} \frac{3}{10^n}[/math] that at no point in the sum will there ever exist a significant amount of decimal places to unconditionally precisely equate [math]\frac{1}{3}[/math], expressly denoting [math]\frac{1}{3} \neq 0.\overline{3}[/math] because the amount of 3's at most could only ever be a non-infinite maximal real number amount, that if arbitrary infinite work could be completed, [math]\big( \frac{3}{10^n} \big) × 3 [math] would understandably equate to only infinite 9's, because 1/3 is not precisely 0.333...

[math]A: \frac{1}{3} × 3 = \frac{3}{3} = 1[/math]

[math]B: 0.\overline{3} × 3 = 0.\overline{9}[/math]

[math] A \neq B [/math]

>>9476752
>.99999cont times 10 = same thing
>checks out
>.999999cont - 99999cont = 9X
>not 0

>>9484089
Thus it can be shown
For the sum [math]\sum_{n=1}^{\infty} \frac{3}{10^n}[/math] that at no point in the sum will there ever exist a significant amount of decimal places to unconditionally precisely equate [math]\frac{1}{3}[/math], expressly denoting [math]\frac{1}{3} \neq 0.\overline{3}[/math] because the amount of 3's at most could only ever be a non-infinite maximal real number amount, that if arbitrary infinite work could be completed, [math]\big( \frac{3}{10^n} \big) × 3 [math] would understandably equate to only infinite 9's, because 1/3 is not precisely 0.333...

• [math]A: \frac{1}{3} × 3 = \frac{3}{3} = 1[/math]

• [math]B: 0.\overline{3} × 3 = 0.\overline{9}[/math]

• [math] A \neq B [/math]

>>9484089
Thus it can be shown
For the sum [math]\sum_{n=1}^{\infty} \frac{3}{10^n}[/math] that at no point in the sum will there ever exist a significant amount of decimal places to unconditionally precisely equate [math]\frac{1}{3}[/math], expressly denoting [math]\frac{1}{3} \neq 0.\overline{3}[/math] because the amount of 3's at most could only ever be a non-infinite maximal real number amount, that if arbitrary infinite work could be completed, [math]\big( \frac{3}{10^n} \big) × 3[/math] would understandably equate to only infinite 9's, because 1/3 is not precisely 0.333...

• [math]A: \frac{1}{3} × 3 = \frac{3}{3} = 1[/math]

• [math]B: 0.\overline{3} × 3 = 0.\overline{9}[/math]

• [math] A \neq B [/math]

>>9484065
What separates 9 from 10

What seperates 99 from 100

What seperates 0.9 from 1.0

What seperates 0.99 from 1.0

What seperates 0.999 from 1.0

What seperates 0.999••• from 1.0

one thing seperates all these, and it's called a significant real number.

>>9484089
0.9 + 0.1 = 1
0.99 + 0.01 = 1
0.999 + 0.001 = 1
0.9999 + 0.0001 = 1
0.99999 + 0.00001 = 1
0.999999 + 0.000001 = 1
0.9999999 + 0.0000001 = 1
0.99999999 + 0.00000001 = 1

0.999••• + 0.000••1 = 1

there is no obtainable infinite amount of 9's, and therefore no unobtainable infinitesmal.

>>9484107
what separates you from latex

>>9484150
what separates you from unproductive ad hominem and giving me a lot of free (you)'s

>>9484153
>so easy to trigger
kek

Keep the replies comin'. More (You)'s for me.

>>9484163
a lot of "You are crazy"

btw what is
[math]\frac{9.999...}{10}[/math]

If you can't even do math i really can't imagine why you'd heckle me or visit /sci/ in the first place. Maybe google or timed out alpha is more your place if you're looking for dumb answers to dumb questions.

>>9484174
aww, he doesn't know the answer to 9.999.../10

I'm not the one who ASKED

>>9484184
I'm not the one who DOESN'T KNOW

You convinced no one by asking.

>>9484189
You convinced no one by not answering.

>>9484196
>he must be retarded cause he can't do my homework for me
>>>/out/

>>9484216
>9.999... isn't the same as 10
>well what's 9.999.../10 then?
>REEEE *runs away*

Homework?
No school asks anything that retarded.

>>9484219
x = x, y = y
x/y = x/y

seems like pretty straightforward common elementary school math actually. If you can't solve it yourself, you are unironically guaranteed dumber than a 5th grader. Considering you have nothing but unsubstantial insults and seem to not really be interested in numbers or maths, you are a generally confused person posting on a board that goes over your head, gets angry at people for problems they did not create, and acts like a child when you're not spoonfed answers to simple arithmethatic methods taught to 9 year old kids. Your dad should have came in your mother's ass instead.

>>9484233
>the lengths he goes to
>to not actually answer
KEK

If there exists no maximal real number equal to infinity, there exists no minimus real number equal to zero.
If there exists no maximal real number that is identifiable to be 1 element less than infinity, there exists no minimus real number that is identifiable to be 1 element greater than zero.

If there is no singular discernable maximal real number that is 1 element less than infinity, there exists no singular discernable maximal real number that is solely less than infinity. Any real number is less than infinity.

If there is no singular discernable minimus real number that is 1 element greater than 0, there exists no singular discernable minimus real number that is solely greater than 0. Any real number is greater than 0.

No matter how big a number sums, it never equals infinity. No matter how small a decimal can divide into, it never equals 0.

Because there exists no minimus real number equal to zero, nor any boundary for a least significant minimus real number which can be greater than 0, [math]\sum_{n=1}^{\infty} \frac{9}{10^n} \neq 1 [/math]
At no point in the sum will there ever exist an insignificant decimal place, and any real amount of 9's in the repetition will never be an infinite amount of 9's. At every point in the sum, will require addition of a minimal number to sum 1, such that
[math]\sum_{n=1}^{\infty} \frac{9}{10^n} + \big( \rlap{no}{\sum} \frac{1}{10^n} \big) = 1 [/math]

>>9484258
uh-huh. so...
9.999.../10 is what then? Is it one?
Less than one? More than one?

>>9484258
>will never be an infinite amount of 9's

But the limit says there's an infinite amount of them. You wrote it yourself.

>>9482907
This is classic word salad. Why are there so many schizos on /sci/?

>>9484404
The limit says there are a neverending amount of 9's. Infinity cannot be reached by incrementing n, so there is no substantial infinite'th step that aims to close up shop and call it a day. It will always be a maximal real number amount that has the capacity to increase or change depending on when a measurement of n is taken. This says that the amount of 9's in [math]0.\overline{9}[/math] is finitely countable for any single measurement, and presents that repeating decimals lose a not-insignificant value of accuracy from their true value because of the decimal system.

This not insignificant value would then help to be accounted for by including work to achieve the number as a metadata paired value.

• [math]\frac{1}{3} = 0.\overline{3}_{\frac{1}{3}}[/math]

• [math]0.\overline{3}_{\frac{1}{3}} × 3 \rightarrow 0.\overline{9}_{\frac{3}{3}} \rightarrow 0.\overline{9}_{1} \rightarrow 0.\overline{9}_{\stackrel{\leftarrow}{1}} = 1[/math]

>>9484258
Why do you keep saying "minimus"? Do you mean minimum?

>>9476752
9X = 9?
What?

0.9e is equal to 0.9e not 1. So no.

>>9484547
'minimum' and 'minimal' can carry a notion of amount or plurality, so i used minimus to define the single least number of smallest real value.

https://en.m.wiktionary.org/wiki/minimus

>>9484570
If anything the issue is with maximal which should probably also be maximus

>>9484545
>Infinity cannot be reached
In math, if they infinity then it is infinity.
Nobody claims to understand how the hell it happened - it just IS.
Whatever it is, it isn't a little diesel engine chugging along in the night, adding 9's to the end one at a time. However it happens, it's a done deal. Now what is left to do, is pondering what effect does it has on the value of the formula.

>>9484545
>Infinity cannot be reached
In math, if they say infinity then it is infinity.
Nobody claims to understand how the hell it happened - it just IS.
Whatever it is, it isn't a little diesel engine chugging along in the night, adding 9's to the end one at a time.
However it happens, it's a done deal. Now what is left to do, is pondering what effect does it have on the value of the formula.

>>9484079
>Is the guy claiming that the infinite sum of the negative integer powers of 2 is approximately equal to 1 and then using 1/2 as shorthand for that sum trolling
gee idk.

>>9482907
end your life maybe?

Mathematician Suicide, Tomorrow's Headline.
//
數學家自殺,明天的頭條。

>>9484980
On the contrary, it is a diesel truck with unlimited feul and an eternal schedule of delivering 9's. There are always more numbers in a repeating decimal.

1/3 is not 0.3
1/3 is not 0.33
1/3 is not 0.333
1/3 is not 0.3333
1/3 is not 0.33333
with each step of an extra 3, we can always more accurately attempt to render 1/3 as a decimal, however there is no significant knowable value of a finite amount of 3's that will ever truly represent 1/3 as an exactly precise decimal. So because 0.3 does not suffice and lacks accuracy, neither does [math]0.\overline{3}[/math] suffice and too lacks accuracy, since the amount of 3's must be a maximal real number amount not too dissimilar from 0.3 having a real number amount of threes, being one. Now this is all just speaking without rounding or presuming a non-arbitrary decimal limit of accuracy as might be required in engineering. 16 decimal places of 16 threes would be practical enough for most real engineering problems, or 32, but generally well below 100. I speak purely in arbitrary precision and work done in arbitrary time; pure maths.
If we can assume no arithmatic steps to increment a real number n to equate infinity or even equate a number that is discernably close to infinity, then infinity can simply not be reached and it is no stretch of the imagination to understand why this should be the defacto case, without need for confusing or counterintuitive mental gymnastics to justify it.
So when we render 1/3 as a decimal, because of our decimal system we can not precisesly and exactly define it as the decimal we're lookimg for, which leads to the repeating pattern. With an ever increasing amount of countable 3's, every test of observing the 3's at a moment is always less accurate than the next observation, but any test must suffice since no test can be the single most accurate as every test will always be less accurate that the next. An unwavering diesel truck with unlimited deliveries to be made.

>>9485282
>infinity can't exist unless i know how it happens
sorry, it just doesn't work that way.

stop using infinity in your formulas - why would you even put it there if you think it doesn't exist

>>9485343
I've defined it's existence. It is larger than any number. This can be classically proveable under already established definitions of infinity.

Don't be retarded. I didn't say it didn't exist, i said it wasn't a number, and sure enough it isn't since there exists no maximal real number that has a knowable difference from infinity, so all maximal real numbers will always be less than infinity.

Imagine a calculation that increments it's value squared with every iteration, having started increments once per millisecond since the beginning of time. It will have not counted, nor will it ever count, a total sum equivalent to infinity. The result at the moment of this post may be astronomically huge, but it would be a finite number, and the moment after you read this post it would have increased significantly once again. I provide you with my observation as of this post, the result of calculation thus far being the maximal real number, but as soon as you've read this post, the true value of the calculation has increased, and until I make another observation we would have no greater maximal real number than what is provided, though we can confidently assume there is already a larger maximal real number than this result even without needing to make the observation; we just wouldn't know it's exact value without making another more recent observation.

Truly though it ought to be some kind of idiocy that you would assume to use anything correctly without knowing how to use it, but that would only be an adoption of the sin of the men who came before you, abusing infinity with no constant working definition often to the effect of multiple simultaneously paradoxical interpretations.

Calling me wrong is not enough. I've shown how infinity is not a number and is greater than all numbers, which aligns with my provided definitions and examples. If it is truly too disagreeable, then provide some proof, some arithmetic and examples that show otherwise.

>>9485476

>>9484276

>>9485495
[math]9.\overline{9} = 9.0 + 0.\big[ \stackrel{\stackrel{this}{max}}{\mathbb{R}} \subset 9's \big] : \frac{9.\overline{9}}{10} = 0 + 0.\big[ \stackrel{\stackrel{that}{max_{+1}}}{\mathbb{R}} \subset 9's \big] \therefore 9.(999) \rightarrow 0.(9999) [/math]

>>9485601
>>9485495
alternatively just move the decimal place over, the number of elements consisting the mantissa and significant integer combined remains the same.

>>9485616
So shifting works....

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

ty and good night

>>9485691
I literally just showed that shifting doesn't work you brainlet.

If you take the classic retarded definition of an infinite amount of relative numbers in a repeating decimal, this would translate such that 0.999... would have x amount of 9's in the number, and 0.999..
× 10 would have x+1 amount of 9's in the number, equivalent to:
9.99 × 10 = 99.99, even though this is clearly wrong and the answer is actually 99.90

shit my man, there are a finite countable number of elements in a repeating decimal. What the fuck did you not understand about that. Its been a major point i've hammered in most of my posts.

>>9485742
just answer the question, is 9.999,,,/10
a)one
b)less than one
c)more than one

a, b, or c?

>>9485742
>classic retarded definition of an infinite
that states that inf+1 = inf
so you can forget the x+1 nonsense

>>9484258
>If there exists no maximal real number equal to infinity, there exists no minimus real number equal to zero.
Do you mean to say that zero is not a real number?

>>9485795
Is there a non-negative number less than 0?

>>9485781
Which exactly why its retarded. Infinity + 1 is nonsense by itself.

>>9485776
Its less than one. Pic is for you, asshole.

>>9485776
you fucking idiot this is elementary school level shit so i'll explain it like you're in elementary schol
if you divide by 10 you move the decimal point once to the left
that means you get 0.999,,,
that's less than 1
you fucking retard

>>9485851
>>9485776
>0.999,,,

>>9485862
ok faggot
0.9 reccuring
happy now cuntface?

>>9485867
very happy
shifting works
ty

>>9485838
>Is there a non-negative number less than 0?
No. Zero is the meet of [math]\mathbb R[/math].

>>9485890
Shifting works only if you assume numbers dont exist and cannot be uniquely identified under finite terms. So it only works if you're a dumb fingersniffing pajeet.

>>9485926
wot

>>9485924
*[math]\mathbb R^+[/math] of course.

>>9485924
Zero isn't a real number. You cannot count zero of a thing, and that isn't say you can't acknowledge there is none left of a thing that once was. Without knowing what the thing is you're meant to count, you can't count that there are zero of said things.

[math]\frac{n}{0}[/math] has no intelligble result either. Zero is not a real number.

>>9485933
>You cannot count zero of a thing
You cannot count [math]\pi[/math] things, but that doesn't make [math]\pi[/math] not a real number.
>Without knowing what the thing is you're meant to count, you can't count that there are zero of said things.
You can count zero of everything that is not there, which is a superset of any "thing" with zero elements present.
>[math]\frac n0[/math] has no intelligble result either.
And [math]\sqrt{-1}\not\in\mathbb R[/math]. How does that discredit it from being a real number?

>>9485942
Jesus are you preparing to run the mile or is there another reason you're stretching so much.

If you analzed pi and defined it in a moment of maximal real number length to it's decimal, you could count to it provided the increments were in [math]\frac{1}{\stackrel{max}{\mathbb{R} \subset \frac{pi}{10}[/math]'ths.

If i presented you a box with 4 balls red green and blue, where there were 1 ball extra of a single color, and i asked how balls of each colored ball in the box exist and you replied 2 red, 1 green, 1 blue, 0 yellow, and you weren't intentionally being a jackass, i might figure there could be something wrong with your brain.

>>9485958
[math]\frac{1}{\stackrel{max}{\mathbb{R}}} \subset \frac{pi}{10}

>>9485961
[math]\frac{1}{\stackrel{max}{\mathbb{R}} \subset \frac{pi}{10}}[/math]

>>9485926
look, if 9.999...
turned into 0.999...
then shifting works, you can tap dance around it till kingdom come if you want, but claiming black is white is just nuts and convinces no one

>>9485926
>>9485926
look, if 9.999...
turned into 0.999...
then shifting works, you can tap dance around it 'til kingdom come if you want, but claiming black is white is just nuts and convinces no one

>>9485958
>>9485964
>[eqn]\frac1{\stackrel{\max}{\mathbb R}\subset \frac\pi{10}}[/eqn]
Okay, you've lost me there. What does [math]\stackrel{\max}{\mathbb R}[/math] represent? Also, how can it be a subset of [math]\frac\pi{10}[/math]? Are you using Dedekind cuts? Lastly, how can you take the reciprocal of a set?
>If i presented you a box with 4 balls red green and blue, where there were 1 ball extra of a single color, and i asked how balls of each colored ball in the box exist
2 red, 1 green, 1 blue, and no others.

>>9485975
It turned from 9.a-hundred-9's to 0.a-hundred-and-one-9's, and you are being a dumb nigger.

See this number?
A: 0.9999

What is A × 10,000?

A×10,000 = 9,999

There were four 9's before and four 9's after.

Heres your classically mentally challenged repeating number:
B: 0.9999...
What is B × 10,000, to four decimal places?
B×10,000 = 9,999.9999...

There were four 9's before, but eight 9's after! Ain't that just fuckin retarded! This classical repeating number has no specific identity and it just lets retards like yourself molest it and groom it without guidance to prove a nonexistant point no one ever gave a shit about, cause you're too dumb to rationalize infinity but not dumb enough to simply not use it or not bitch about dumb shit like how you should be able to invent extra 9's out of thin air and redefine variables mid-equation.

>>9485980
MaxR is a maximal real number.

MaxR (of) pi/10 is the maximal real number of finitely countable digits of pi yet discovered, reduced by a tenth so the entire number fits under the decimal 0.314159,usw.

Whether thats a gorillion digits or whatever is irrelevant, there are a finite countable amount defining pi's accuracy under the decimal system, which is a value that is never quite the true exact precise value of PI else therr would be a true finite real number of digits to pi less than a maximal amount, and all this under 1 is denoting the fractional smallest singular incremental amount so you could start counting and, in arbitrary time, complete a whole gorrillion/gorillion fractional count equal to a whole, thereby having counted based in pi.

It entertains your challenge unless you werent being a nigger there too hoping to make some quip about how you'd count 3 whole intergers but not the remainder as an integer.

>>9486007
>See this number?
>A: 0.9999
I immediately see it isn't a recurring decimal,
so the rest is meaningless

>>9486030
>pi
>finite
choose one

>>9486048
6/10 shitposter thanks for bumping the thread though.

>>9486007
>classical repeating number has no specific identity

math and identity politics don't mix well

>>9486052
I choose both as they've been chosen as such since antiquity you mouth breather.

>>9486058
"Being an irrational number, π cannot be expressed exactly as a common fraction (equivalently, its decimal representation never ends and never settles into a permanent repeating pattern)."

>>9486052
What infinity is
>unending

What you think infinity is
>the biggest possible real number

The thing that is actually what you think infinity is
>maximal real finite number

>>9486061
If you're new to the thread you can find reformed definition and usage of infinity if you look back to at most 40 posts, probably.

>>9486030
>[math]\stackrel\max{\mathbb R}[/math] is a maximal real number.
Define "maximal," because the definition I use clearly doesn't apply here.
>[math]\stackrel\max{\mathbb R}[/math] (of) [math]\frac\pi{10}[/math] is the maximal real number of finitely countable digits of [math]\frac\pi{10}[/math] yet discovered
"Yet discovered" by whom? A general formula for the [math]n[/math]th (hexadecimal) digit of [math]\pi[/math] exists.
>Whether thats a gorillion digits or whatever is irrelevant, there are a finite countable amount defining pi's accuracy under the decimal system
The "decimal system" is a positional notation that is finite in writing only. It has no built-in notion of "accuracy." Nothing stops you from asking yourself what the [math]n[/math]th digit of [math]\pi\[/math] in the decimal system is.
>which is a value that is never quite the true exact precise value of PI else therr would be a true finite real number of digits to pi less than a maximal amount,
But then it's not [math]\pi[/math], is it? I said "counting [math]\pi[/math] things", not "almost [math]\pi[/math] things". You could count to any good approximation of 0, but by your own logic it still isn't real.

>>9476752
0.9... = 1 because we say it does.

Literally. It's true as a result of the way we define our number system.

>>9486007
>invent extra 9's out of thin air
if there are infinite 9's in 0.999... then yes, you can take any finite amount from them and it won't make a dent
inf - n = inf

>>9486072
>>9486091

>>9486064
>>9486064
>>9486064
>>9486064
.

>>9486104
I'm as American as you are, seeing as you seem to be a German speaker.

"Infinity" does not have a specific definition, because it is used in different contexts in different ways, much like many other mathematical terms. It is one of the topological ends of [math]\mathbb R[/math] when doing real analysis, for example. When enumerating the digits of a number, saying that the expansion is "infinite" means [math]\omega[/math] digits are required.

>>9484258
This is concise and well written, thanks.

>>9486121
>>9484258
samefag

>>9486119
Nah, infinity has been abused and misused more than you realize.
Half of calculus wouldn't even exist if not the misuse of retardation that is "infinite sums". Infinity has been so cucked that aleph number can be used to mean what infinity was actually always supposed to mean.

There isn't any way to count to infinity even in arbitrary time, you'll only ever count a larger and larger maximal real number since infinity has no specific relation with any number beyond it simy being bigger than all real numbers, so as long as you have a real number and you're incrementing it, infinity is never reached much less approached, and instead has no numerical value because no real number equals infinity. In any case of which you should be able to identify many where infinity is treated as a maximal integer that exists on the numberline, paradoxically, despite no steps performable to reach it.

>>9486147
>arbitrary time,
adding time to numbers is just retarded
math isn't physics

>>9486155
By arbitrary time i mean time units that are relatively valueless, only existing for the meta ideology of observing unique events, such that counting to a trillion in increments of 1 might be instantly possible in arbitrary time rather than making a computer run overnight to do it or, less intelligently, attempting to verbally count to a trillion which may take a lifetime. The difference between just instantly invoking the number 1 trillion and somehow summing it incrementally in arbitrary time would be the one with time would have a recordable number of events and partial sums that identify the number at each step of its progression, like a set of a trillion elements 1 to 1,000,000,000,000

its arbitrary, unreal time though so you dont need to get autistic about it. The point is with an unending number, not even arbitrary time would be sufficient enough to allow the increments to reach infinity since there exists no arithmetic of real numbers that could be performed at any significant increment which could sum infinity, so it never does.

>>9486175
sounds like aleph-1

>>9486175
sounds like aleph-zero

>>9486184
except aleph-zero has no limit, it's countable but that's it

>>9486184
Like i said, infinity had been misused and abused to the point its obvious apparent identity of being larger than any real number, right there since its earliest usage, has been cucked from it and shoved onto aleph, though other values of aleph are retarded.

All in all, higher math is a fuckin retarded inconsistent smorgasbord of counter intuitive bullshit and needs a reformation. Wir sagen auf wiedersehen von die ß, anything can be reformed.

>>9486147
The "infinite" in infinite sums is but a notational trick. Their definition makes it clear, so why do you think infinite sums a retarded concept?

anyway with the MaxR shit, this defines a maximum number discovered per arbitrary (or real) time. For example in [math]\sum_{n=1}^{\infty} 2, at n=1, the Maximal Real Number for this work is just 2, amd easily countable and easily defineable. At n=2, the MaxR becomes 4. If we decided to use this value of 4 for some other math, we would be referencing the maximal real number of the work from that sum that existed at some point. So lets imagine this just increments by 2 in some ballpark computer time of 1 increment per millisecond, and that we will leave this to increment indefinitely unendingly on this computer that tuns of solar power and dam generated electricity so it'll basically never stop incrementing. This unending incrementing is easily analogous to the incrementing of the number of repeating numbers in a repeating decimal. We can always check our 2sum counter and see where it's at, like maybe now its at 450,000 so 450,000 becomes our most recent result and the maximal real number for this local work. But say we fuckin get visited by a spacewizard who throws us into a time warp like samurai jack and we end up in far in a dystopian alternate future where society had broken down and people stopped countings years and days at some point so we dont even know how far we've come, but our little computer is still incrementing cause the sun still shines. We check the computer then and it gives us some gigantic number with thousands of digits that no one really wants to read, but its definitely a number and it definitely has an end to the thousands of digits so it's definitely finite, and this number then becomes the maximal real number for the work.

[math]\stackrel{max}{\mathbb{R}} [/math] is a dynamically increasing but finitely countable variable at every unique measurement of it relative to it's work, that is constantly overwritten in examples of repeating decimals or infinite sums, and exists in a way such that the only "number" greater than a MaxR is infinity.

anyway with the MaxR shit, this defines a maximum number discovered per arbitrary (or real) time. For example in [math]\sum_{n=1}^{\infty} 2[/math] at n=1, the Maximal Real Number for this work is just 2, amd easily countable and easily defineable. At n=2, the MaxR becomes 4. If we decided to use this value of 4 for some other math, we would be referencing the maximal real number of the work from that sum that existed at some point. So lets imagine this just increments by 2 in some ballpark computer time of 1 increment per millisecond, and that we will leave this to increment indefinitely unendingly on this computer that tuns of solar power and dam generated electricity so it'll basically never stop incrementing. This unending incrementing is easily analogous to the incrementing of the number of repeating numbers in a repeating decimal. We can always check our 2sum counter and see where it's at, like maybe now its at 450,000 so 450,000 becomes our most recent result and the maximal real number for this local work. But say we fuckin get visited by a spacewizard who throws us into a time warp like samurai jack and we end up in far in a dystopian alternate future where society had broken down and people stopped countings years and days at some point so we dont even know how far we've come, but our little computer is still incrementing cause the sun still shines. We check the computer then and it gives us some gigantic number with thousands of digits that no one really wants to read, but its definitely a number and it definitely has an end to the thousands of digits so it's definitely finite, and this number then becomes the maximal real number for the work.

[math]\stackrel{max}{\mathbb{R}} [/math] is a dynamically increasing but finitely countable variable at every unique measurement of it relative to it's work, that is constantly overwritten in examples of repeating decimals or infinite sums, and exists in a way such that the only "number" greater than MaxR is infty

>>9486254
Didnt mean that last part. There is always a greater real finite number than a maximal real number, and infinity doesnt deserve to be called a number even with air quotes

>>9486272
Questions: Who taught you this? Or did you come up with it yourself? If you did, why? How is math that’s so wildly different from what is used in academia helpful to you?

>>9486979
It was passed down to me from the topological dimension during a heteronomic-visual revelation by a talking pigeon.

>>9486988
Please, elaborate.

>>9486979
I figured it out logically, unrestricted by any retarded assumption that humans had ever yet accomplished anything of real value. It goes like this, i smashed your tower so well the first time that you'll never figure to try it again without divine intervention, and i'm really looking for something else to smash.

>>9487045
Clever girl

>>9484072
Fuckoff BRAINLETTTTTTT.
X =0.9999999999999
10x = 9.9999999999999999
Line up the columns retard
9x = 9
Divide nine
X = 9/9
X = 1
How could this be simpler for you
>QED

>>9487045
What has it done that the rest of mathematics hasn’t?

>>9486254
But I already know that given some natural number, there will always be a moment at which it becomes less than your sum. What's the point?

>>9487187
sigmas with brassieres
I call them sig-mamas

>>9487259

>>9476771
ONLY GOOD POST. This board is literally shit.

>>9487292

>>9479895 is good too

>>9487145
How many 9's are in 0.999...?
How many 9's are in 999.999...?

>>9487648
Infinity

>>9487653
Ahuh... and which number is infinity, exactly?

>>9487187
I'm not sure your question actually makes sense. What has a working definition of infinity done that the rest of math hasn't?


....
What has the rest of math ever done?
The penultimate application of math was making a calculator that can do math real fast and it's called it a computer.

>>9487259
>ahuhuh guys look [math]\infty[/math] looks like boobs!

>>9485015
then call me

How is it that we have a fucking thread about infinities every other day and yet none of them are ever insightful discussions about the topic? Its either:
>BRO SHIFTING THE DECIMAL IS FICTIONAL
or
>MUH ABSTRACTIONS

How is it that we have a fucking thread about _______ every other day and yet none of them are ever insightful discussions about the topic? Its either:
>CORRECT ANSWERS
or
>INCORRECT ANSWERS

>>9487655
[math]\omega[/math]

>>9488903
Is infinity even or odd?
If infinity were a number, it ought to be even or odd!

Is infinity a prime? Is it complex or an integer?

Is infinity divisable into a smaller number? All real numbers are divisable!

Hmm...

>>9487648
>>9487653
>infinite 9s after a decimal ought to equal 1, they say
>0.9••• exists
>9.9••• (0.9••• × 10) exists
>99.9••• (0.9••• × 10^2) exists
>999.9••• (0.9••• × 10^3) exists
>9999.9••• (0.9••• × 10^4) exists
>0.9••• × 10^100 exists
>0.9••• × 10^1000000 exists
>0.9••• × 10^(the biggest number) exists
>0.9••• × 10^∞ doesn^t exist
>infinite 9's after the decimal is ok, but infinite 9's in front of the decimal is not ok

>>9489783
>but infinite 9's in front of the decimal is not ok
....999,999,999 = -1
....999,999,999.999,999,999.... = 0

literally infinity's complement

>>9487669
Have you taken any university-level math courses yet?

>>9489764
[math]\omega[/math] is the first nonzero limit ordinal, so please do not confuse it with real or complex numbers. It is the set of natural numbers.

Seeing as [math]\omega=2\omega[/math] and [math]\omega=2\omega+1[/math], one could say that [math]\omega[/math] is both even and odd; but again, that is a property of naturals, not of transfinite ordinals.

With a similar argument one could say that [math]\omega[/math] is both prime and divisible by any natural (bar zero, if you consider it a natural); again, divisibility is a relation on naturals that cannot be easily extended to ordinals.

You seem to confuse multiple kinds of numbers (perhaps voluntarily); I'm merely talking about naturals, yet you seem to bring up properties of all kinds: oddness, evenness, primality etc. make no sense in the domain of the reals; at the same time, naturals are only sometimes divisible (which is shaky anyway: are we talking about partitioning? About division?).

>>9489882
Real numbers are always divisible.
You are very dumb. your baby omega symbol has no hard and good definition so I don't know what you are even beginning to try to invoke by writing it.

There exists no real element greater than or equal to infinity, and no real element that can be said to be exactly n elements less than infinity. The distance from 1 to infinity is comparable to the distance from an number with an infinite amount of digits to infinity.

Infinity is not a number, nore a finite limit. It has no identity of even or odd or primality or normality or complexity. It does not exist to be invoked in lieu of a number like a letter variable would, any attempts of invoking it in a limit should be well understood that it is defining unending work, and in order to concatinate unending work is to necessarily express an answer in no real number solution, so a sum 9/10^n must only equal 0.999•••, a repeating unending number for repeating unending work.

>>9490177
>Real numbers are always divisible.
Sure, but we're talking about the amount of digits a number has, not a real number. In this regard, a number like [math]\pi[/math] would require [math]\omega[/math] digits.
>You are very dumb. your baby omega symbol has no hard and good definition so I don't know what you are even beginning to try to invoke by writing it.
It is not my invention. The "baby omega symbol" is the first limit ordinal.
Cardinals are a formalization of the "size" (cardinality) of a set, while ordinals are a formalization of the "ordering" of a set with a certain cardinality.
[math]\aleph_0[/math], if you want to be pedantic, is the cardinality of the sequence of digits of [math]\pi[/math], whereas [math]\omega[/math] is the ordering upon it.
>There exists no real element greater than or equal to infinity, and no real element that can be said to be exactly n elements less than infinity.
Correct.
>The distance from 1 to infinity is comparable to the distance from an number with an infinite amount of digits to infinity.
Well, "infinite amount of digits" is iffy. Most reals require infinitely many decimal digits to be described correctly. Fundamentally this is correct, however.
>Infinity is not a number,
That depends on what you mean by "infinity" (infinite number of elements? one of the ends of [math]\mathbb R[/math]? etc.) and by "number" (naturals? reals? cardinals? etc.).
>nore a finite limit.
A bit tautological, but okay.
>It has no identity of even or odd or primality or normality or complexity.
Again, "infinity" is not a monolithic concept.
Oddness, evenness, or primality are properties of naturals, which any definition of "infinity" is not.
Normality is undefined, because "normal" is not a definition.
Complexity (which I assume to be "being a complex number") makes sense when discussing directions in [math]\mathbb C[/math], for one.

(cont.)

>>9490318
>>9490177
>It does not exist to be invoked in lieu of a number like a letter variable would
Again, that depends on context. In real analysis, that is simply shorthand, but when talking about cardinality, [math]\aleph_0[/math] is not at all a problem.
>any attempts of invoking it in a limit should be well understood that it is defining unending work
No. Have you ever seen the definition of limit, be it discrete or continuous? There is no mention, nor any expectation of "unending work." No argument is made about something "at infinity."
>and in order to concatinate unending work is to necessarily express an answer in no real number solution
Again with the "unending work," and you seem to add your opinion ("necessarily express an answer in no real number solution") as a fact.
>a sum 9/10^n must only equal 0.999•••, a repeating unending number for repeating unending work.
Which would be almost agreeable if not for the pesky fact that no "unending work" was ever required.

>>9490353
Infinity is unending. It is required to acknowledge that. I'm trying to help break the mold of broken classical maths here, and acknowledge infinity under a stable constant singular set of definitions that don't or shouldn't arbitrarily change "depending on the maths" involved, often changing to the effect of a paradoxical definition existing "here" versus a different definition "there".

So far, >>9484258 this gets right to the point of things in cooperating some basic understandings of infinity to encourage a singular understanding of it.

If no arithmetic on real numbers can produce a number that directly equals or is even close to infinity, then infinity cannot be a "limit". Contrary to what you seem to believe, the very word "limit" itself explicitly invokes an end to/of some substantial reference, so setting a limit to infinity is just a different way of saying unlimited, since no amount of real work may increment to the limit's end, being infinity. If no real number may reach infinity and there exists maximal real numbers greater than other numbers, then there also exists no real number that could reach zero, where minimal real numbers could always be defined by [math]\stackrel{min}{\mathbb{R}} = \frac{1}{\stackrel{max}{\mathbb{R}}}[/math]
So if it is understood as it has been shown, a number [math]0.\overline{9}[/math] would have a maximal real finite number amount of 9's in it's repetition for any specific invocation of the number, and therefore exist a not-insignificant minimal real number [math]\frac{1}{\stackrel{max}{\mathbb{R}} \subset 9's \in 0.\overline{9}}[/math] which would be required to add to 0.999... to properly sum 1.

>>9491227
Or rather i think that should be [math]\frac{1}{10^{/stackrel{max}{\mathbb{R}} \subset 9's \in 0.\overline{9}}}[/math]

>>9491227
>>9491298
Or rather i think that should be [math]\frac{1}{10^{\stackrel{max}{\mathbb{R}} \subset 9's \in 0.\overline{9}}}[/math]

>>9491227
This also gets rid of the counterintuitive and disingenuous act of decimal shifting on repeating decimals, which has been a retarded unmathematical way of arbitrarily redefining variables mid-equation for mindnumbingly dumb algebraic proofs like
>x=0.999...
>10x = 9.999...
>10x - x = 9
>9x=9; x=1
which otherwise state it's okay for there to be a "true infinite" amount of 9's.after the decimal, but bringing x up to the power of to the same true infinite value would be verboten without arbitrarily claiming the result isn't real or is just infinity.

>>9491227
So what value must be added to [math]0.\overline{3}[/math] to make it truly sum [math]\frac{1}{3}[/math]?

>>9491529
Obviously its 1/3rd the value of the 0.999 example but that might end up seeming redundant or recursive, which is why a repeating decimal should carry it's identity combined like [math]0.\overline{3}_{\frac{1}{3}}[/math]

>>9491460
>mfw -1/12 bullshit can no longer be proven true cause it requires shifting on infinite sets
And the world lost nothing of value

>>9491460
x = 0.333...
10x = 3.333...
10x - x = 3
9x = 3
3x = 1
x = 1/3 = 0.333...
x*3 = 0.999...

3x= 0.999...
30x = 9.999...
30x - 3x = 9
27x = 9
3x = 1
x = 1/3 = 0.333...

As neat it'd be if this actually worked, it relies on redefining a variable mid equation
>3x = 1
>3x = 0.999...
and it relies on the assumption that there exists no finite unique measurement of a repeating decimal thereby allowing 10x to have one more total 3 in it's number 3.333... than 0.333... had access to, where this allowance relies on the idea that a true infinite amount exists and supplanting the idea that there exists numbers infinity+n , when there actually exists no real arithmetic to result infinity in the first place. These Paradoxical, willy-nilly, flip-floppy definitions are the abuse and misuse of infinity. Shifting is invalid.

>>9491227
It being your main pique, I have asked you repeatedly to point out at which point of the mathematical definition of limit (as regards analysis, of course) there is any mention of "unending work"; since your argument, from what little substance you put out in that regard, seems to amount to sole philosophy and opinion, and I cannot tell whether or not it is also based on a misconception of "limit" no different to what one would first think when hearing of "utility" in game theory, I must require that you address it before continuing.
Furthermore, you must admit that muddying the waters by arbitrarily switching between naturals, reals, and "numbers" as a generic concept is disingenuous; there is no one "true" definition of number, as you will know.

>>9491460
>>9492719
If there were [math]\aleph_0[/math] digits (threes or nines, as it may be) before, after "shifting" there are exactly [math]k[/math] more; namely,
[math]\aleph_0+k=\aleph_0[/math] for any [math]k\in\mathbb N[/math]. It is pretty easy to shift by [math]\aleph_0[/math], but it's probably not what you'd expect: [math]10^{\aleph_0}\cdot1=\mathfrak c[/math] (or [math]\aleph_1[/math], if the CH is part of your axioms) which doesn't help much, does it?

So to identify how a repeating decimal operates and to better define infinity outright, we have [math]\stackrel{max}{\mathbb{R}}, \stackrel{min}{\mathbb{R}}, [/math] of Maximal Real Number and Minimus Real Number and now lastly, [math]\stackrel{max}{\mathbb{U}} [/math] being the Maximus Number, which is how best to describe the amount or size of the ever-most-current and ongoing result of infinite repetition. The maximus number has similarities to classical infinity used as a number, being there is no way to equate it or count to it, yet it is the basis for every maximal real finite number which can be equated and counted regardless of astronomical size. If we were to try to count the number of 9's in 0.999... as if the 9's were a healthy river with a consistent stream, the maximus number would represent fish in the river. When we go to make a measurement, what we are doing is aiming for the maximus - but every time we try to grab it, the fish slips out of our hands and leaves us only with the memory of having touched it along with a few scales, and these memory and scales represent a maximal real number which is a past event or a trail of the maximus number. We cant count the scales on the fish, but we can count the scales in our hand and assume the fish has plenty more. In this way, we can assume arbitrary accuracy for defining the amount of repetitions that exist in the concept of a repeating decimal being a maximus number which is less than infinity but still greater than all other numbers that have been recorded and observed in the set of reals. The amount of 9's in the freeform arbitrary idea of 0.999... is the maximus amount and like infinity, not a real number, but the amount of 9's in an invocation of the number 0.999... to use in arithmetic must be maximal real number amount representing that the fish has still not been caught but we still have the memory of having tried as well as a handful of real countable scales; maximal number is real @ MaxR

>>9492719
>relies on redefining a variable

no such "problem" at >>9478727

>>9493604
oh [math] \stackrel{fuk}{\mathbb{U}} [/math] take your pills already and hit the sack

delirious never ending insane babbling day after day

>>9492719
>Shifting is invalid.

>>9485979

1=1
1=1/3 +1/3 +1/3
1/3= 0,33333333...
1= 3X0,33333333...
1=0,9999999999

>>9492719
>Shifting is invalid.

>>9485776
>>9485867
>>9485979

>>9493604
If we can define a repeating decimal or any infinite set or sum by a singular maximus value and many approximate values, it should then be easy to manipulate them with maths designed to accomodate them.

For example, if we make a measurement x=0.999..., we have encapsulated a finite maximal real value representation of that repeating decimal, and we can say x.mr= the maximal real number of 9's in this number so that 10x = 9.999... and 10x.mr = x.mr, such that 10x now lacks a rightmost significant 9 as any similiar finite number would
9.99 × 10 = 99.9_

Another measure of our 0.9- stream could allow us the number y=0.999..., but how would it be apparent that y is greater than x if there is no such thing as an insignificant decimal place? How could y-x= a non-zero, positive real number? What more accurate way could we define x and y so they carry their order in the real number set when the results so far have only been honorarily finite?
Well:
[math]\big( x= 0.\overline{9}_{s1}\big) , \big( y= 0.\overline{9}_{s2} \big) \par y-x = 0.\overline{0}_{s2-s1} [/math] would work for arbitrary numbers continued, but since these are finite values it out to be knowable of real finite answers, and for that we need redefinition of repeating decimals. We could instead say
[math]x = 0.\overline{9}_{\frac{1}{2}} \par y= 0.\overline{9}_{\frac{2}{3}} \ par y-x = 0.\overline_{0}_{\frac{1}{6}} [/math] and probably settle there cause any more accurate result would require knowing more parameters about the variables, such as whether we were crafting them from infinite sums where we have access to it's series of work, or if we are arbitrarily invoking random references. Back to the river example, we could release fish into the river knowing when their lives began as farm-raised, but for any fish we didn't release could it really be possible to define when they began their lives? Taking different x & y measurements of the same repeating series at different moments requires more.

>>9494033
Except for the part where you equated 1 to 0.999, sure - if we disregard the part where you redefined a value, then you haven't redefined a value!

>>9494306
yes, I'll pull more and more weird home-made notation out of my ass, that'll prove it

and of course fucked up latex, just to prove I can't figure out a fucking mark up code
in spite of being a genius that proves all math wrong

>>9494358
four equal signs, which one fails?
#1 #2 #3 or #4 ?

>>9494358
four equal signs, which one fails?
#1 #2 #3 or #4 ?

>>9478727

>>9494110
you could say his efforts are... unending

[math]\color{red}{\textbf{(USER WAS BANNED FOR THIS POST)}}[/math]

>>9494432
How are MH room IDs constructed?

>>9494361
I googled a latex paragraph seperation and got \par, sci doesnt support it though. There is a very low probablity sci's latex has been updated recently.
>>9494411
It fails by lacking identification for the repeating decimal while performing arithmetic. You oblately assume 0.999 = 1 because 0.333 = 0.999, but there are innumerable ways to craft the number 0.999 so you need to identify how you did it using 1/3, and that is properly written as [math]0.\overline{3}_{\frac{1}{3}} × 3 = 0.\overline{9}_{\frac{3}{3}}[/math] where that single whole 3/3 part evaluates as a whole which is injected/added to 0.999 (
[math]0.\overline{9}_{\stackrel{\leftarrow}{1}}[/math] in an arithmatic way described at the bottom of this post >>9484258, also writeable as [math]0.\overline{9}_{1} = 0.\overline{9} + \big[ \frac{1}{10^{\stackrel{max}{\mathbb{R}} \subset 9's \in 0.\overline{9}}} \big] = 1 [/math] , which unlike your method, retains relative values for each component of the equation while showing with arithmetic how a repeating 9 number can equal 1 without simply assuming all repeating 9 numbers are identical nor that they should equate to 1 arbitrarily without proof of work when it can be analytically proven there is a smallest, not-insignificant value that can be added to a repeating 9 number to equal one, and disregarding that value should assume 0.999 is its own number.

>>9494468
12 digits of base 62

its like 3 sextillion or something. Stupidly large number produced for the fact capcom is really lazy and dumb and couldnt figure an intelligent way to keep track of multiplayer rooms by assigning and revoking unique ID's so they just left it to a random although incredibly improbable chance that two identical ID's would be generated ever let alone simultaneously. It has more possible room ID's than possible youtube video URL ID's, even despite youtube urls being relatively permanent while MH rooms exist for a couple days at most.

>>9494578
#1 #2 #3 or #4 ?

>>9494578
>You oblately assume 0.999 = 1
no I don't, read from left to right

>>9494638
>implying x=y and y=x don't say the same thing
>the e in pemdas stands for equivalence

>>9494672
>>9494624

>>9494361
All notation is homemade. Notation is a social construct.

>>9494823
Guess it doesn't work without a society then.

>>9494846
Leave it to a mathlet cuck to do nothing but bandwagon. Coward!

>>9494578
What is [math]0.\overline{1}_{\frac{1}{3}} × 3 = 0.\overline{3}_{1} = ? [/math]

>>9495291
[math]0.\overline{3}4[/math] which is the repition of 3's and the last element of the number being +1

>>9495232
At least my wagon has a place where I can look up what some specific notation means.

>>9476769
x = 1

>>9476752

Yes. I don't get why is this so hard to get... Just two ways of name the same thing.

>>9477343
None of those are proofs. They all assume the real numbers form a field which requires you to prove the decimal number construction satisfy the axioms which requires you to DEFINE 1=0.999... and modulo it out into equivalence classes of decimals.

>>9484258
>If B.C.E. years are unable to start then A.D.E. years are unable to begin.
>B.C.E. years are unable to start.
>Thus, A.D.E. years are unable to begin.
>If A.D.E. is endless in year then the years in A.D.E. don’t cease.
>A.D.E. is endless in year.

>Therefore, the years in A.D.E. don’t cease.

>>9479895
>x = 1/10
>1-x = 9x
kek

>>9496126
?????

>>9496000
Doesn't matter. Normies and brainlets don't care about rigour. The three-glasses explanation will convince almost anyone because 1/3 = 0.33333... is something that's hammered into their brains from elementary school onward.

>>9496614
>elementary school
k
https://www.wolframalpha.com/input/?i=(0.333...)+-+1%2F3

>>9496140
classic chucklefuck

>>9496679
What's your point?

>>9496730
Wolframalpha is more rigorous than an anonymous shitposter.
Seriously, you couldn't figure that out? Figures.

>>9496000
Unbelievable: the reals are a field, as long as they are defined the way they are!
If you change the definition you also change the object of discourse.

>>9496775
1/3 - 0.3 is not rigorous. They have a canned answer for 1/3.

If 1/3 - 0.333* were 0, it would imply that 1/3 is not a rigorous value or that 0.333* has a sufficient amount of infinite 3's to satisfy equality. Since there is no such thing as a sufficient amount of infinity because infinity is not a finite number, it can only mean that wolfram is shit.
Take your timed out alpha stuff and gittout.

>>9497274
g8 shitposting

>>9496140
>>9496686
I don't get it
1 - 1/10 = 9/10
9x = 9 * 1/10 = 9/10

>>9497302
no mystery,
>>9496140 is a retard

>>9497295
How many 3s are in 0.3 repeating?

>>9497339
9

>>9497339
3

>>9497339
1

>>9497339
0.3

>>9497339
sig-mama

>>9497339
no more than [math] \stackrel{etard}{\mathbb{R}} [/math]

>>9497357
Mother of all sigmas. If only sigmas could be half as useful.

>>9497362
The only infinite amount that will ever matter for you is the eternity of hell.

>>9497366
they're good for a threesom

>>9497362
>>9497369
Just remember, it's unending

>>9497371
Take your nasty incest shit to /d/ or something nigger.

>>9476752
No.

Remember, the overline on a repeating number doesn't mean infinite. That's stupid. We already have a symbol to invoke infinity.

The overline just acknowledges that a pattern is present.

>>9476775
x=.999999999
10x-x=9x
10*.999999 = 9.9999999
9.999999999 - .999999999 = 9
9*.9999999 = 8.99999999

9=8.99999999
so 9 = 8 + .9999999
so .999999999 = 1

>>9497386
bing-bong-bing-bing-bing-bong

>>9497394
Wud b neat if tru

>ITT people believe infinity+1 exists

>>9497339
[math]\aleph_0[/math]

>>9497556
you see, hilbert was gay
(>>9477016)

>>9497673
Imagine a hotel with infinite rooms, and that there also existed infinite people who wanted to visit this hotel....

How many people exist?
Not all people wish to visit the hotel, but all people who have visted the hotel are infinite.

>>9497888

>>9497904
> [math]\infty < \infty[/math]
Really gave me a big think.

Thanfsk alot mr. hilbert.

>>9497274
What do you mean by "rigorous value"?

>>9498388
It means its obviously not infinite since infinity < infinity

nigger mods, delet this bait threads automatically!!!!!!
we have 5 each day

also 1/3= 0,^3
3/3 = 0,^9
3/3 = 1
1=0,^9

>>9500288
>[math]\frac{1}{3} = 0^3[/math]

>1 = 0.999...
only if you don't know how to do long division

>people think infinite decimals actually makes sense
"no"

>>9476771
hi mathologer

>>9476861
Dude, you are a legit retard and should just kys before you embarrass yourself or your institution any further. I would literally fucking strangle you in the hallway for your insolent retardation, if I recognized you as one of my own students.

Find a flaw with this proof >>9476771
Pro-tip: you can't.

>>9500319
you shouldve deduced that he meant 0.3333 not 0^3 you brainlet

>>9501202
>mathologer
9/10
>that fucking guy in the background always making jokes
6/10
>shilling your diversity kid
0/10

too bad I use geometric means to rate youtubers

>>9501219
>you should have deduced he meant .3 repeating and not 0^3 even though he wrote 0^3
sorry for the rude awakening but that is absolutely not how anything will ever work.