How does this math check out

Shifting is completely invalid in math. Deal w/ it

>in your head

>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.

en.wikipedia.org/wiki/Hilbert's_paradox_of_the_Grand_Hotel#Analysis

wolframalpha.com/input/?i=(0.999...)+1

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

1>Fractions>Integers>Decimals的級分>的整數>小數位數

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

this is your mind on StableGenius

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.

Take your pills user

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.

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

Why the homophobia, you faggot?

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

Why the homophobia?

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

>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?

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

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

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

...

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

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????

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

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

nah, calculus insists.

>This is psychosis, not math
I rest my case

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

No.

aynrandlexicon.com/lexicon/infinity.html

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

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

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

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

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.

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.

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

Horrible color choices.

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

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

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.

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.

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

Mfw

The continuum is intuitively true, they said

Kill yourself

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.

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

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.

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.

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

>ITT: Veeky Forums pretends not to understand infinite sums

I don’t like saying this because it’s basically the Veeky Forums 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.

dressing up sigma signs with brassieres - totally normal

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

right.

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

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]

[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]

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

maybe go back to algebra and learn how to combine terms

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.

*[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

no idea why Veeky Forums'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.

this fucking board holy shit.

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

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.

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

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

(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

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

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 Veeky Forums, 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.

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

>calling me bad at using latex
it's Veeky Forums'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

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

it's not divergent, retard
|x|

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...]

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]

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

en.wikipedia.org/wiki/Moving_the_goalposts#Logical_fallacy

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.

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?

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

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

>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

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

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

pictures are almost worthless as proofs

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

mmm-hm well that explains your math grade

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

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

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

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

...

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

Do you guys never get tired?