/sci/ - Science & Math

an infinite number of nines with an 8 at the end
>infinite
>at the end

Fuck off with this shit already.

>>11947555
>an infinite number of nines with an 8 in the end
That's not a number. That's not even a valid concept. You can't have an infinite number of 9s and still call it a finite number. How is it hard to understand the ... at the end?

>>11947555
>a not ending series of 9s with an 8 in the end
>not ending series
>8 in the end

are you a brainlet?

>>11947559
>>infinite
>>at the end

You know, at the same point where you carry the one and it turns magically into 1.000...

>>11947555
trips of truth, if 0.999... = 1 than 0.999....8 = 0.999.... which is back to 1. therefore 0.00...1 = 1

Decimals are a terrible expression of numerical quantity.

>>11947696
0.999...9 ≠ 1
0.999...8 ≠ 1
neither of those decimals = 1

>>11947711
I'm beginning to understand why That archon fellow started talking about the neighbourhood infinity.

Convergence to infinity does not give permission t o use the equality operator.

at no point will any sum of 9's every cross unity and make 1. By disproving me you disprove 0.999... = 1

convergence to infinity is not equality

>>11947739
>at no point will any sum of 9's every cross unity and make 1.
any FINITE sum. 0.999... is not a finite sum of 9's.

>>11947623
>You know, at the same point where you carry the one and it turns magically into 1.000...
you never carry a fucking 1 in .999...
1 - .999... = .000...
there is never a point where that subtraction has a digit besides 0

>>11947739
1 - 0.999...9 = 0.000...1
1 - 0.999...8 = 0.000...2
1 - 0.999... = 0.000...

>>11947757
Its just a rule that gets closer and closer, if we're assuming continuous numbers, like no lower bound of quantization, like a plank length, I'm satisfied with saying it my as well be 1, ~=, but ==, or === no way

>>11947788
see>>11947775
> 1 - 0.999... = 0.000...

>>11947775
> 1 - 0.999... = 0.000...

I'm satisfied with this statement if were using '...' on one side let us use it on the other, now our logic is at least self contained over the equality operator

>>11947792
lol, just as i was writing on it

>>11947788
>Its just a rule that gets closer and closer,
it's not
>if we're assuming continuous numbers,
what are "continuous numbers" ?

>>11947807
mathematical abstraction created by mathematicans who never had to engineer anything in their lives.

they are the most popular metaphysical numbers

>>11947807
I'd like to know more on how infinity is more than this rule however, what intuition motivates your choice of text?

>>11947794
i like it because it reads colloquially as “no difference between 1 and 0.999...”

>>11947826
0.999... is not "a rule that gets closer and closer". the sequence (0.9, 0.99, 0.999, ...) is a rule that gets closer and closer. 0.999... is not this rule, it's what this rule gets closer and closer to.

>>11947832
I suppose its worth digging deeper on if 0 = 0.00... is this a true zero?

>>11947840
only in the same sense, that there’s no difference between 0 and 0.000...

>>11947837
yeah makes sence, going old school 0 - 0.00.. = 0
generalized form is the word? i forget

>>11947837
hmm interesting, to me this sounds like the cart was placed before the horse however. If this is true, than 0.999... = 1 isn't an invoked expression, but an Identity. 0.999... ≡ 1

When will brainlets learn? People smarter than you already solved this issue centuries ago, you can literally pick a book right now and get an explanation, yet you refuse to use your fucking brain and spout nonsensical bullshit at your superiors as if you were capable of holding a proper debate on the subject. If you're a layman YOUR OPINION DOES NOT FUCKING MATTER.

My man Euler is turning in his grave.

>>11947857
>isn't an invoked expression, but an Identity.
we don't speak cs here, only math.
[math]0.999\dots = \lim_{n \to \infty}\sum_{k=1}^n \frac{9}{10^k} = \lim_{n \to \infty}(1 - \frac{1}{10^n} )= 1[/math].

>>11947857
correct it’s an identity so ≡ or colloquially =

>>11947857
Please, if you think it's only defined as 1, define 0.999... in a way that's consistent with how it's written and yet isn't equal to one. (You can't because it's a fact, not a definition)

>>11947857
>than 0.999... = 1 isn't an invoked expression, but an Identity.
the fuck is an "invoked expression"

>>11947867
makes scene, I knew it changed my perspective, but you just revealed to me to just how much cs has subconsciously changed my intuitions of mathematics. using limit operators i'm satisfied

>>11947873
Cool beans, i remember some math textbooks defining this colloquialism. I've been fighting compilers so long that i forget that language can be loose like this

>>11947880
they said no cs here, but my definition rests on an intuition purely on how we physically generate this state in nature. 0.999... for me, is an infinite energy expression.
function appendNine(init) {
return appendNine(Number(String(init) + '9')))
}
console.log(appendNine('0.9'))

>>11947892
The context I'm using here is heavily reflected in Buckminster Fullers philosophy. I do not seek to challenge the theoretical nature that 0.999... = 1, but to challenge this expression to materialize in nature.

http://www.arvindguptatoys.com/arvindgupta/synergy-fuller.pdf

on the irrationality of Pi.

Of practical concern is whether or not i can stick the math in a computer like 1.1 + 0.1 === 1.2 not returning true

>>11947555
0.9999...8 is an arbitrary string of digits with no meaning. you cant just say that an infinite decimal has a specific digit on the end

>>11947920
don't overthink it
1 - 0.999... = 0
π - 3.141... = 0
there's no difference

>>11947807
>what are "continuous numbers" ?
bitch has never heard of Topological Completeness, what a fucking retard
>>11947904
you should stop relying on computers, the computable numbers are only a miniscule subset of the reals

>>11948119
>don't overthink it
crap too late
pi - 3.14.... = 0 actually has something quite profound to say on this debate. back to >>11947945
this concern, and the idea that we cant just place 8 at the end. What is 3.14.... implying but a functional expression of ...?

As such it wouldn't be difficult to construct a functional express so that 0.99999...1 exists?

otherwise its hard to do pi - 3.14.... = 0 because this means 3.144444444 not increasing precision


>>11948141
I like this, I'm considering going full geometry at this point, probably worth it, it is my area of least knowledge. I should also look to analogue computation to round it off.

got any other idea's?

>>11948235
>cant just place 8 at the end
see>>11947775

>>11948242
how do you feel than about pi - 3.14... = 0? we keep placing different numbers at the end

>>11948246
i wrote that, too. there’s no difference

>>11947555
Ok explain this
x = 0.999999...
10x = 9.99999...
9x = 9
x = 1
0.9999... = x = 1
0.9999... = 1
Where is the mistake?

>>11948251
Im satisfied in theory, but again, if i drive that expression through a compiler it would and never could pop out a zero.

I'm writing in circles now, thank you for your feedback, i appreciate it greatly

>>11948272
>if i drive that expression through a compiler it would and never could pop out a zero.
why not? how does your compiler differentiate the pi ratio from an approximation of the pi ratio?

>>11948242
>>cant just place 8 at the end
>see>>11947775
.999...8 is a finite, unspecified amount of 9s followed by an 8
>>11948272
>Im satisfied in theory, but again, if i drive that expression through a compiler it would and never could pop out a zero.
stop mentioning computers, they have nothing to do with this

>>11948296
>.999...8 is a finite, unspecified amount of 9s followed by an 8
correct

>>11948284
computation time, it will never reach the end. it will compute the next digit of pi, or what ever irrational, than the next, than the next, it will never reach an end. Heat death will come to the universe before the computation is complete. We humans are defining a model of infinity, making an identity, not an equality.

I see it as a cope out by the mathematicians actually, its probably the most social science thing they seem to do. Oh yeah, infinity, we'll get there eventually... only in your heads academia!

>>11948296
>stop mentioning computers
Its the crux of my arguement, you guys are copeing with infinity behind the incomprehensibility of large numbers.

Infinity is not physical, it is purely metaphysical

>>11948284
>how does your compiler differentiate the pi ratio from an approximation of the pi ratio?
one should be able to construct an expression of pi consisting of whole numbers than can execute to arbitrary precision. Pi would be a function

>>11948355
>computation time, it will never reach the end
the end of what? the difference will always be zero

>>11948358
how do you calculate the difference between an arbitrarily precise function and the decimal representation of an arbitrarily precise function?

>>11948367
you'll want two function generators of Pi(n) and one for Pi(n+1) and compare a decimal back for sake of proof. But you bring me to another good point about how these maths are an identity, not an equality. We are defining the decimal representation of infinity as what we mean by ramanujan and other great infinity thinkers. by no means does 0.9999999.. become 1 in any physical sence, but we define it to be that way for elegance and simplicity of expression. There is no debate here but on grammar

>>11948385
>compare a decimal back
it’s the same no matter how long your compiler runs. the difference is always zero.
>0.9999999.. become 1
there’s no difference, the difference is always and forever zero

>>11948359
The end of the universe. computers have to go number by number in a way, when computing an irrational number the best we can do is send a computer on a journey to obtain ever closer definitions of it, there will always be another digit after the last that requires electrons running through a circuit.

>>11948397
I was refering to the expression pi - 3.14... = 0

but to it would approach zero and never get there, even at the end of the universe it wouldn't be complete in the proof

>>11948385
There is no other reasonable way to define it. What does "0.999..." represent? A number whose decimal representation is an unending string of 9s, which is the same as the limit of the sum you've seen posted. That limit is equal to one. None of those things are artificial constructs or cleverly-chosen definitions, they're just the natural and only reasonable mathematical interpretation of "0.999..."

>>11948406
no, it would always be zero. pi - 3.14... can never not be zero. describe an example where you or a computer calculates a nonzero value for the difference

>>11948355
>We humans are defining a model of infinity, making an identity, not an equality.
>I see it as a cope out by the mathematicians actually, its probably the most social science thing they seem to do. Oh yeah, infinity, we'll get there eventually... only in your heads academia!
fuck are you smoking
do you even know the definition of an infinite series
it doesnt have anything to do with infinity, it just says that given any error epsilon, i can find an index so that past that point, the finite sum up to there and the actual value is less than epsilon

>>11948399
closer definitions of what? the difference is always zero

>>11948418
>Thinking CS-tards understand the epsilon-delta construction of the limit

>>11948426
erectile-dysfunction construction doesn’t matter. the only thing that matters is that you can never calculate a difference between the pi ratio and your calculation of the pi ratio.

>>11947555
0.9...x =0.9...=1

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

>>11947711
>>11948475

The problem is .999... does not exist in reality because there is no infinite in our reality (except God). For example, you cannot take an inch and half it, then continue to halve the products infinitely. There is a smallest measure of distance that will be reached where you’re able to halve it.

>>11948312
nah '...' aka ellipsis means infinite amount

>>11948456
yes you calculate the difference of itself by itself + one more decimal place. You will never reach a true 0 difference, otherwise the number wouldn't be irrational.

>>11948418
Buckminster Fuller buddy, synergetics is quadruple grade bud.

Yeah, thats why i didn't argue with the geometric series test within >>11947867 I am satisfied with the theory and definitions you all present. But y'all need to start talking to engineers again mathleets, your numbers have no bearing in reality.

Imagine, a physist asking you to charge the battery so that it contains 1 joule of energy, comes back 0.999... you think that circuit would run? how did you manage to get an irrational value of charge inside that battery

>>11948485
no

>>11948481
math isn't reality, there is a reason this board is called "/sci/ - Science & Math"

>>11948486
>you calculate the difference of itself by itself + one more decimal place.
that just means you calculated one more decimal. the difference is still zero no matter how many decimals you calculate.

>>11948487
read a book

>>11948495
3 - 3.1 = -0.1
3.1 - 3.14 = -0.03
....

go one anon how it always equals zero, let me know when you get there

>>11948497
no u

>>11948501
https://en.wikipedia.org/wiki/Ellipsis#In_mathematical_notation

>>11948500
>3.1 - 3.14 = -0.03
this is further evidence that youre bad at math

>>11948508
figured it was probably wrong, but i didn't bother to check

>>11948500
that’s like saying 1+1+1 isn’t 3 because 1+1 is 2. you’re calculating another decimal place on one side but pretending you didn’t calculate it on the other.

>>11948505
i didn’t see 0.999...8 in your wikipedia article, can you screenshot it for me

>>11948522
spoonfeeding retards is your mom's job

>>11948513
Its a thought test in the evocation of the maths.

1.2 - 1.2 =

1.2 - 1.20 = 0
1.20 - 1.200 = 0

we can see, that for a rational number, there will come a precision (decimal place) where taking the difference of the precision + 1 is zero.

>>11947559
2/3 = .666...7

>>11948524
we're trying to find this point of an irrational number at infinity, theoretically sound as an identity yes, but not a physical expression of math

>>11948527
>this is what cs does to your brain

>>11948524
>we can see, that for a rational number, there will come a precision (decimal place) where taking the difference of the precision + 1 is zero.
this is not true, 1/3 and 1/7 and so on would like to disagree

>>11947555
.9 < 1
.99 < 1
.999 < 1
.999... < 1

>>11948523
i know but how did you sneak a computer into her office, timmy? you should be eating not typing

>>11948531
Plug it into a calculator

>>11948524
>for a rational number
ok now show us 1/3 - 1/3

>>11948532
for (1/3)
0.3 - 0.33 = -0.03
0.33 - 0.333 = -0.003

for (1/7)
0.14285714285 - 0.142857142850 = 0

>>11948533
1 < 100
1 + 1 < 100
1 + 1 + 1 < 100
1 + 1 + 1 +... < 100

>>11948533
>let's pretend finite is infinite
hurr durr

>>11948541
>>11948544
Low iq posts
Point is every number after .9 will be smaller than .9 and .9 < 1

>>11948533
>he doesnt know strict inequalities become possible equalities after a limit
lern topology

>>11948548
Elaborate

>>11948540
ah i fudge up interpreting google, 1/7 is irrational repeating those digits, you'll get a a similar thing

>>11948524
even allowing for arbitrarily large bases with arbitrarily long cipher dictionaries, it doesn’t change the fact that you can never calculate a difference between pi and your calculation of pi.

>>11948547
.9 < .9665
.96 < .9665
.966 < .9665
.9666... < .9665?

Point is .9 < .9665 and every number after .9 < .9665

>>11948563
calculate the difference of pi at precision n and pi at precision n+1 if these values are 0 you have your convergence and your equality operator, but if it doesn't deconstruct to unity before infinite it is not an equality it is an identity

>>11948547
>Low iq posts
>Point is every number after .9 will be smaller than .9 and .9 < 1
you really shitting on people for low iq and then drop that shit?

>>11948552
so if you take the set of all numbers less than 1, (-inf, 1), this is called an open set, and it does not contain 1
however, if we take the CLOSURE of this set, we get (-inf, 1] now including 1
This is because the closure contains all the limit points of the original set, so this means 1 is a limit of all the numbers less than it.
we could do the same thing with (0,1)
there is a limit to 0 within this set, we can just take the numbers 1/2 and then 1/3, 1/4, 1/5, ...
all these numbers are positive but they limit to 0, something nonpositive.
A limit point has a proper definition that i wont get into

>>11948568
>but if it doesn't deconstruct to unity before infinite it is not an equality it is an identity
youre just making shit up, go fuck off

>>11948547
negative iq post

>>11948568
what pi are you referring to? how is that pi different from your calculation of pi, and what’s the difference?

>>11948567
>.9666... < .9665?
What the fuck are you trying to say you retard?

>>11948570
>if we take the CLOSURE of this set, we get (-inf, 1] now including 1
it doesn't contain anything less than 1 no does it?
>A limit point has a proper definition that i wont get into
pic related

I swear there have to be Jew shills being these posts at this point

3 < π
3.1 < π
3.14 < π
3.141 < π
3.1415 < π
3.14159 < π
3.141592 < π
this continues endlessly
π < π

>>11947555
.999.. > 1 prove me wrong

>>11948582
That analogy doesn't work with .999.. because 1 is already larger than the first digit which is .9

>>11948583
.9...-1=0

>>11948570
probably a valid critique, as the infinite has no physical analogue, that part is made up, this is the essence of identity, a stake in the ground by which the maths is developed. Its hardly a poor stake either, just as time wheathered the science into dogma, I think the mathematicians are overextending thinking 0.9999... equals 1, like a property of nature, instead of what it is, a definition they made up to create eloquent maths

>>11948586
>moving goal posts
1/9 = 0.111...
+
8/9 = 0.888...
=
9/9 = 0.999...

>>11948593
Plug 2/3 in your calculator

>>11948589
Bruh, nobody's making up anything. The only definition needed is that .999... is defined as limit of the sum i.e. (0.9 + 0.09 + 0.009...). This is the standard and intuitive definition. Everything past that is a legitimate equality.

>>11948597
too tired, plugged your mom all night

>>11948578
I can see why thats confusing, my bad.

consider the stepwise computation with the effort to prove that irrational pi - irrational pi = 0. Now the mathematicians, who don't really do science, see two apples and are keen to cross it out and never step foot again, but to a scientist we must test with physical experiment.

To invoke pi computationally we must stuff more and more precision into the array i'll call test_pi_n, we'll start by pushing 3 into the array.

Next we'll define a second array called test_pi_n_1 and push 3.1 to start.

The test we assert if test_pi_n - test_pi_n_1 = 0

if false
test_pi_n = test_pi_n_1
test_pi_n1.push('4')

test again. Now inject epic quantities of energy and computational power, and wait for the computer to return true

>>11948604
funny

>>11948606
How would this "scientific test" of yours respond to testing the equality of the following numbers:
0.1001
0.1002

>>11948598
Making up isn't a bad thing, its creativity, but thats what infinity is, now one has punched an infinite amount of 9s into a calculator to see if it will return 1 some day. But as a mathematician its usefully to make up the identity 0.99...=1 I don't see calculus even working without this

>>11948612
>scientific test
>math
retard

>>11948612
two scalars bounded by the same functional expression is an explicit requirement.

0.1001 - 0.1001 = 0
0.1002 - 0.10020 = 0

you could try extending it like that though, i'm not sure what youll find though

>>11948606
you haven’t described any calculations, just the initial values 3 and 3.1, which would return no difference between pi and 3.1

>>11948614
>one has punched an infinite amount of 9s into a calculator
inf isn't a number

>>11948606
What conclusion am i supposed to draw if I run this test on 1/3? that 1/3 != 1/3 in the real world?

>>11948579
>it doesn't contain anything less than 1 no does it?
what?
>>A limit point has a proper definition that i wont get into
>pic related
no, a limit and a limit point are separate. a limit is from baby calculus, a limit point is from big boy topology
>>11948597
plug 10^10^10^3000 into your calculator, fuck did i just disprove big numbers??
>>11948614
nothing you say makes sense
>now one has punched an infinite amount of 9s into a calculator to see if it will return 1 some day.
this has absolutely nothing to do with what we're talking about
>>11948617
the original post did indeed reference science, and using computers is literally within the realm of science, not mathematics
your at is misaimed

>>11948621
so why in the hell are we using ... in the mathematics, isn't this supposed to represent a whole swath of numbers including the horizontal 8?

>>11947555
[math]0.98 = 1-\frac{2}{10^{2}}[/math]
[math]0.998 = 1-\frac{2}{10^{3}}[/math]
[math]0.\left \{ \left. 9 \times n \right \} \right.8 = 1-\frac{2}{10^{n}}[/math]
[math]\lim_{n\rightarrow \infty }\left ( 1-\frac{2}{10^{n}} \right )=1[/math]
[math]\lim_{n\rightarrow \infty }\left ( 0.\left \{ \left. 9 \times n \right \} \right.8 \right )= 1 [/math]

Now fuck off.

>>11948624
1/3 is functional expression of two scalar quantities, a computer chomps this bitwise, it becomes decimals in the machine

>>11948632
>1/3 is functional expression of two scalar quantities
no its a fucking number
stop adding useless terminology, it makes you look like a schizo you fucking schizo

S A G E
A
G
E

>>11948621
"Infinity isn't a number" means that you can't do basic arithmetic with it.
Infinity does however refer to a precise amount. So the expression "An infinite number of..." is well defined.

>>11948633

x/y => function
1 scalar one
3 scalar two

Its called grammatical concentration, the practicle allows me to tread a denser idea space
you'd need an ideal analogue computer to process 1/3 , and it will have noise.

Logic gates are the window of evocation of the physical world, much more constrained i dare say

>>11948630
ok retard

>>11948630
pic>>11948579

>>11948638

>>11948618
The point is that all your "scientific experiment" needs to be tricked is for two adjacent digits of pi to be zeroes. (I guarantee this occurs at least once):

pi_n = 3.14{digits}0
pi_n+1 = 3.14{digits}00

pi_n = pi_n+1 is true

But please continue to tell me how this test is more legitimate than a mathematical proof.

>>11948644
nice! so true! thanks anon, there would have to be if 0 take n+2 if 0 take n+3, i wonder if this has implications for the theroy

>>11948636
>can't do basic arithmetic
it's more limited, but some are still ok
inf-inf undefined
1^inf undefined
inf/inf undefined
0*inf undefined
but some are ok
inf+inf=inf
1/inf=0

>>11948634
9.999...- x = / = 9.999..
pic related

>>11948653
this is the dumbest post in the entire thread

>>11948642
What about it? Any mathematician would accept what I wrote as a proof that 0.99...98 = 1. What's wrong with my use of a limit?

>>11948656
Look at the image of that post

>>11948634
infinities come in different sizes
pic rel

>>11948658
I have looked at the image in that post. It defines a limit. I used a limit within that definition. What's the problem?

>>11948658
fugg

>>11948664
Did you see the word "Approximated"? That's essentially what a limit is.

>>11948670
the individual elements in a limit are approximations, the final limit is not you bumbling retard
>>11948658
>infinities come in different sizes
this has literally nothing to do with .999...

>>11948582
how did you calculate this, and what’s the difference between the pi ratio and your best calculation of the pi ratio?

>>11948670
Alright, I'll prove it in a different way since you don't understand limits.

If two real numbers are distinct then it's possible to construct a rational number between them:
https://math.stackexchange.com/questions/421580/is-there-a-rational-number-between-any-two-irrationals

It's trivial to prove that if p/q < 1, then p/q < 0.99...98. Therefore the two numbers are not distinct.

>>11948606
also bumping you again since we were having a nice chat, you haven’t described any calculations, just two initial values

>>11948701
oh cool, thanks, lots of light on my rhetoric I had trouble organizing it.

>>11948500 i got started here for an anon just to get started, and i'll bump this guy >>11948582 because its seems to me like a similar take on what i'm describing, though this way starts with an irrational perfectly defined pi, nature doesn't seem to give us this out of the box, no import pi from pi, we have to write that in ourselves.

>>11948644
provided a very valid critique of the method, the test will fail once repeating 0's hit logic, a solution would be to than compare n+2 to i suppose n+ infinity - 1 or how a mathematician would express that. It kills intermediate inference, like just taking the first few values and making a guess at what the computer will output, since the number could be like 0.500000000 <endless chasm of zeros> 1...

>>11947863
You would be saying the earth is flat in the 1500s

>>11948634
>X HAS 2 DIFFERENT VALUES THAT MEAN IT SAME
no, you just made a mistake
this is the same as proving that 1 = 2

>>11948803
then where's the mistake

>>11948792
Bet you'd be fisting cows in the field in 1500.

>>11947863
>When will brainlets learn?
>everything is water
>When will brainlets learn?
>there are 4 elements
>When will brainlets learn?
>bloodletting cures disease
*yawns*
NEXT

>>11948693
So are you saying that .99...8 & .99..9 are the same since there's nothing between them?

>>11948885
>>11948475

>>11948911
pic>>11948579

>>11948915
that has nothing to do with what he said

>>11948885
I'm saying that 0.99...9 = 1 because there's no rational number between them. By the same logic, 0.99...8 = 1. Therefore, by transitivity of equality, 0.99...9 = 0.99...8

>>11948693
>>11948928
there's a .00...1 if you subtract them
1 - .99...9 = .00..1

Did you just link something without reading what they were saying?

>>11948943
0.00...1 isn't a rational number. It can't be represented as the quotient of two integers. If you can find two integers p and q such that 0.99...9 < p/q < 1 you'll get a fields medal.

>>11948958
But that's fucking retarded what's stopping me from counting down
>.999..9
>.999..8
>.999..0
>0

and stating that 0 = 1?

>>11948970
The infinite 9's are stopping you. If you count back a finite number, you'll still have infinitely many 9's left, and therefore the same number. That's how infinity works.

>>11948536
Low quality bait but I'll bite. Ti84's implementation of floating point doesn't support infinity, so all floats are simply truncated and that results in a loss of precision

>>11948977
Infinity comes in different sises though >>11948666

Which is why this meme >>11948634 is bullshit

>>11948986
And your point is...? All infinities are bigger than any natural number. If you count backwards from any of them in natural numbers you end up with the same quantity.

See >>11948958, find that p/q. If you're right then it's trivial to find.

>>11948986
different infinity sizes have nothing to do with this
every infinity mentioned in this thread is countable, stop bringing this up, its unrelated
>>11948970
>But that's fucking retarded
no, you are
if its rational then give us the fucking ratio that makes it

I love to see the stubborness around here. Most of you claim to disprove it when you don't even have the rigorosity to.

>0.999...8 (an infinite number of nines with an 8 in the end)

every day all day

>>11944809

>>11949465
You think you're being smart, but it's actually very easy to express:

1-2*10^(-x), x->inf

(You) are retarded.

>>11949645
>1-2*10^(-x), x->inf
[math]\lim_{x \to \infty}(1-2\cdot10^{-x} )= 1[/math]

>>11949649
That's the limit (i.e. the first value the sum is NOT).
You first years need to learn the difference between a sequence of values and the limit of that sequence.

The limit of f(x) does not feature in the set of all values populated by f(x), where f(x)=1-2*10^(-x), x->inf.


To make things easier for you, the limit of a divergent sequence, let's say f(x)=x, x->inf, is INFINITY. Yet at no point does f(x) equal infinity.

>>11949660
>implying 0.999... is not a limit

>>11949645
the limit of that is not an infinite series of 9s followed by an eight, its 1
by the same logic 1/10^n goes to an infinite series of 0s followed by a 1
but an infinite series of 0s followed by anything is just 0, its not an infinitesimal
x = .000...1 so 10x = .000...10, which is still just an infinite number of zeros followed by a 1
so x = 10x and x=0
1/10^n does not return an infinitesimal, it just returns 0

infinitessimals are an ALGEBRAIC concept, limits are a GEOMETRIC concept
they are totally fucking unrelated
limits never give you something even related to an infinitesimal

>>11949660
none of the sentences in this post relate to anything
it doesnt matter that the limit isnt in the set of finite approximations
thats a stupid thing to point out

(You) are retarded.

>>11949861
At what point is f(x)/g(x), x->inf no longer 2/3?

f(x): 2*10^(-x)
g(x): 3*10^(-x)

The limit of each function is zero, but neither function has zero in its domain.

>>11950227
>The limit of each function is zero, but neither function has zero in its domain.
yes, and?

>>11949861
>the limit of that is not an infinite series of 9s followed by an eight, its 1
>by the same logic 1/10^n goes to an infinite series of 0s followed by a 1
>but an infinite series of 0s followed by anything is just 0, its not an infinitesimal
Congrats you finally got it. The only possible point of confusion now is why 0.0....1 is equal to lim 1/(10^n). Despite your protests, it is true. It's funny that you try to make the distinction between infinitesimals and limits when infinitesimals only exist in the context of limits.

>>11947555
we must secure the existence of our nines and a future for ones children

>>11950246

Great, so we now know this (>>11949465) comment's mockery was misplaced. Thank you for your concession.

>>11950249
>Congrats you finally got it. The only possible point of confusion now is why 0.0....1 is equal to lim 1/(10^n). Despite your protests, it is true. It's funny that you try to make the distinction between infinitesimals and limits when infinitesimals only exist in the context of limits.
you didnt understand anything in my post then
the limit of 1/10^n is 0
the "infinitesimal" .000...1 is also equal to the limit, which means its 0
so its not an infinitesimal, its just 0

>It's funny that you try to make the distinction between infinitesimals and limits when infinitesimals only exist in the context of limits.
you literally dont understand infinitesimals, infinitesimals are not a geometric concept like limits
infinitesimals are an algebraic concept, thats why you never ever get an infinitesimal from a limit
you only get "fake" ones like .000...1, which is not an infinitesimal, its 0

an infinitesimal is a number d so that d^2 = 0 but d =/= 0
the .000...1 does not satisfy this

>>11950262
>Great, so we now know this (>>11949465) comment's mockery was misplaced.
no its not
you cant have an infinite number of things with something at the end
which is why .000...1 is just equal to 0
>Thank you for your concession.
i didnt concede anything though?

>>11950273
>you cant have an infinite number of things with something at the end
Yes you can.

>which is why .000...1 is just equal to 0

No, 0.0....0001 does not equal zero. Its limit does, however.

>>11950273
Let me summarize
>0.0....1 is a "fake infinitesimal"
incorrect, but we'll let it slide for now
>0.0....1 is just equal to the limit which is equal to zero
correct
Now working from that,
Will you agree that
.999... = 1 - 0.0...1?
If so, based on your agreement that:
0.0...1 = 0,
We can write:
.999... = 1 - 0
.999... = 1

>>11950279
>>you cant have an infinite number of things with something at the end
>Yes you can.
no you cannot, infinite means, without end
>No, 0.0....0001 does not equal zero. Its limit does, however.
youre a fucking retard
a number does not have a limit
it is fixed

>>11950298
>>0.0....1 is a "fake infinitesimal"
>incorrect, but we'll let it slide for now
it is not an infinitesimal, it just equals 0
.999... = 1
and since 1 = 1 - 0 we have .999... = 1 - 0

>>11950313
0.00...0001 is not a number, it is a sequence denoted by the (...) ellipsis notation, tard.

>no you cannot, infinite means, without end
Does not follow. Using truncation, (0.3+x)- where x is a natural number, larger than 0 and extends to positive infinity- 0.3 is always recoverable from the total, no matter how large it becomes.
Where did you get your mathematics education, little man?

>>11950330
>0.00...0001 [...] is a sequence denoted by the (...) ellipsis notation, tard.
That is not what that notation means, anon.

>>11950343
Yes it is.

Inb4 you post the defaced Wikipedia page where embarrassed tards changed it to mean "limit" only in this very specific circumstance. For hundreds of years, the ellipses has denoted a series extending intuitively from the given pattern to the end result.

Either way, limit or not, everything else you said was wrong and easily outable as tardmaths.

>>11950330
>0.00...0001 is not a number, it is a sequence denoted by the (...) ellipsis notation, tard.
>its a sequence
then why the fuck did you say it doesnt equal 0
if its a fucking sequence theres no point in distinguishing it from a number, theyre trivially different

>>11950330
>Does not follow. Using truncation, (0.3+x)- where x is a natural number, larger than 0 and extends to positive infinity- 0.3 is always recoverable from the total, no matter how large it becomes.
>Where did you get your mathematics education, little man?
what the fuck are you saying and how is it supposed to relate to what we're talking about?

>>11950372
>what the fuck are you saying
Hello brainlet.

>>11950383
youre saying that in the sequence .3, 1.3, 2.3, 3.3...
its always possible to take .3 out of it at any term
that has fucking nothing to do with what we're talking about
so yeah, what the fuck are you saying retard

>>11950357
>For hundreds of years, the ellipses has denoted a series extending intuitively from the given pattern to the end result.
Are you sure you know what a series is, anon? Because a series is a type of limit. Did you mean a sequence?

>Yes it is.
No, it is not. A decimal expansion with "..." in it refers to a real number whose decimal expansion is such an intuitively extending sequence. There is a sequence involved here, yes; but the thing as a whole refers to a real number defined by that sequence, not the sequence in isolation. And the real number so expressed can be defined as the limit of a sequence. Meaning the notation refers to a real number that is the limit of a sequence, not the sequence itself.

>Either way, limit or not, everything else you said was wrong and easily outable as tardmaths.
I'm not the person you were talking to before. Sorry for the confusion.

>>11950395
The endianness of a number is always mathematically reverseable. What it starts with, is expressible as the termination. This is the case for any number.

>>11950412
0.9999... as an infinite sequence, does not equal one

lim(0.99999....) as a limit, does equal one.

One does not feature in the domain of 0.9999....

>>11950413
>The endianness of a number is always mathematically reverseable.
what the fuck is the endianness of a number

>>11950421
>lim(0.99999....) as a limit, does equal one.
thats not how limits work you fucking mong

>One does not feature in the domain of 0.9999....
has no bearing on anything

>>11950433
>thats not how limits work you fucking mong
Yes it is.

There's no reason to get angry, tardlet.

>>11950447
>Yes it is.
no it isnt

no reason to get angry tardlet

>>11950450
lim(1-0.5-0.25-0.125-0.0625...+2^-x) where x->inf

Problem?

>>11950464
>this is how limits work
>see, look at this totally different example

>>11950468
lim(1-0.5-0.25-0.125-0.0625...)

Problem?

hehe I love it when they out themselves

Where are you, >>11950468?

It's impossible to calculate any difference between 0.999... and 1

>>11950547
0.9999....+0.000....1 = 1

1 + 0.000...1 != 1

>>11950590
0.9...+ 0.0...1 = 1 + 0 = 1
1 + 0.0...1 = 1 + 0 = 1

>>11950590
>0.9999....+0.000....1 = 1
No, that's wrong.
0.999...9 + 0.000...1 = 1

>>11950590
>>11950609
To clarify further:
0.999... + 0.000...1 = 1.000...0999... ≠ 1

>>11950609
>No, that's wrong.

>>11948527
_
2/3= 0.6

>>11950842
>No, that's wrong

>>11950547
true, there is no difference. glad to see this catching on.

>>11950892
>No, that's wrong

>>11949861
>infinitessimals are an ALGEBRAIC concept, limits are a GEOMETRIC concept

based and redpilled

>>11950921
what’s wrong?

>>11950637
this
>0.999... + 0.000...1 = 1.000...0999... ≠ 1
no difference calculated

>>11950279
>0.0....0001 does not equal zero. Its limit does, however.
no, the limit of that is 0.0....0001

>>11950273
>which is why .000...1 is just equal to 0
no, 0.000...1 is not 0

>>11950950
What framework are you using to define 0.00....01? If it's not a limit of 1/(10^n), then what is it exactly? In rigorous terms please.

>>11950950
if .000...1 isnt zero, then what is 1/.000...1

>>11950957
any decimal representation that ends isn’t zero.

>>11950961
1000...0

>>11950966
Okay, so it's ambiguity on what the "..." means then? Because it means infinite zeroes to me, how are you interpreting it?

>>11950971
no ambiguity, 0.000...1 literally ends in a 1. doesn’t matter how the ... is interpreted

>>11950971
you're right, anything after the ... is meaningless

>>11951006
no, and it doesn’t matter

>>11951006
>you're right, anything after the ... is meaningless
Retard

>>11947555
>0.999...8
you're joking right?
how can there be an 8 if the 9s never end?

>>11951010
1.0,,,x = 1
anything after the ... is meaningless

>>11951013
just go with it, it doesn’t matter

>>11951012
hillbilly

>>11951014
>1.0,,,x = 1
if you explain what this comma notation means i’ll let you know if i agree or disagree

>>11951013
Quite easily. You define that the number ends with an 8.

f(x)/g(x) will always equal 4 where
f(x)=8*10^-x
g(x)=4*10^-x

even when x tends to infinity

>>11951022
It means he's a britfag

>>11951046
f(x)/g(x) will always equal 2*

>>11951046
it’s impossible to calculate a difference between 0.999... and 1

>>11951048
32*10^(-2x)=2
your fields medal is in the mail

>>11951047
>>11951014
ok then no, 1.000...x = 1+ 0.000...x so it obviously isn’t equal to 1

>>11951076
0.000...x = 0
anything after the ... is meaningless

>>11951084
why?

>>11951085
1/inf=0

>>11951088
>0.000...x
>1/inf=0
you’re not making sense, i don’t get how this calculates a difference between 0.999... and 1?

>>11951097
>i don’t get
happens a lot to some

>>11951054
>it's impossible to calculate the difference

No it isn't

1-0.999...=0.0...001

>>11951105
i’m happy to be wrong, just explain how to calculate the difference between 0.999... and 1

>>11951107
no,
1 - 0.999... = 0.000...

>>11951113
...1

keep up, chap

>>11951118
...9
can’t have one without the other

>>11948570
Different anon; perfect explanation here. The concept of a closure really helped clear up my confusion about the equality in question.

>>11951148
that just means you’re susceptible to an axiom brainwash, who cares. the only thing that matters is that it’s impossible to calculate a difference between 0.999... and 1

>>11948570
(0,1) contains 0.999... but not one
(0,1] contains 0.999... and one

[math](0,1]\cap(0,1)^c=A=\{1\in A|0.999...\notin A\} \implies 1\neq0.9.... [/math]

Thanks for the proof, mathtard.

>>11947555
>0.999...8 (an infinite number of nines with an 8 in the end)

>>11951198
/thread

>>11951198
>(0,1) contains 0.999... but not one
Prove it

>>11951255
doesn’t matter, the only thing that matters is that you can’t calculate difference between 0.999... and 1

>>11951264
it does matter, because he's wrong

>>11951311
doesn’t matter if he’s wrong, you can’t calculate a difference between 0.999... and 1

>>11951323
the difference is 0

>>11951001
>no ambiguity, 0.000...1 literally ends in a 1.
is .000...10 the same thing as .000...1, or is it 10 times as much
what about .000...01?
you cant assign positions to the digits after having infinitely many digits

>>11951198
>(0,1) contains 0.999... but not one
>calling me a mathtard
>and hes actually dumb enough to assume what hes trying to prove

the difference between .999... and 1 is 0.

>>11951416
Your trolling technique of repeating the same sentence over and over is stale, I already fell for that 10 threads ago.

>>11951463
im not even the guy repeating the difference sentence, i just added it in for extra frill

>>11951198
>assume your conclusion
CHAD

>>11948485
Not if you put something after them.

>>11951959
anything after the ... is meaningless

>>11947788
It doesn't "get closer" it's a number. It doesn't move or change value. Whatever function you're picturing in your mind, that number is its limit.

Okay fine, assuming you CAN have a 1 after an infinity of 9s, which one of these would be greater:
>9.99999...1
or
>9.99999...11

>>11952104
if its after an inifnity of 9s its infinitely unimportant, and just equals 0
those both equal 10

>>11952110
That's kind of my point.

>>11947555
Why is this board so goddamn stupid

0.999... is greater than any number smaller than 1. If 0.999... is a real number then it cannot be anything else than 1.

This thread has been repeated everyday for years. It's basically the flat earthism of mathematics.

>>11950957
[math] \displaystyle
0. \bar{0}1
= \lim_{n \to \infty} 0. \underbrace{0 \dots 0}_{n ~ \text{times}}1
= \lim_{n \to \infty}
\left [
\left (
\sum_{k=1}^n \dfrac{0}{10^k}
\right )
+ \dfrac{1}{10^{n+1}}
\right ]
=0
[/math]

>>11952303
fuckin kek

american education

>>11950249
>infinitesimals only exist in the context of limits.
ok sweetie
[math] \displaystyle
\lim_{x \to \infty} \dfrac{x+1}{x} =
\lim_{x \to \infty} 1+ 1/x = 1+0 = 1
[/math]

>>11947555
I left 4chan for two months and this bullshit still exists

>>11951327
right, so you can’t calculate a difference. there’s no difference.

>>11951411
doesn’t matter if you can assign positions, 0.000...1 unambiguously ends and therefore can never represent the same number as 0.000...

>>11952740
It's smaller than any number bigger than 0 therefore it's zero.

>>11952740
>unambiguously ends
nope
anything after the ... is meaningless

>>11952959
no, 0.000...1 in any base b can only possibly refer to b^-n for some arbitrarily large finite integer n. all such numbers are > 0
>>11953002
how so?

>>11953034
>0.000...1 in any base b can only possibly refer to b^-n for some arbitrarily large finite integer n. all such numbers are > 0
0.999... doesn't refer to "1 - 1/10^n for some arbitrarily large finite integer n" though

>>11953034
anything after ... has -inf as an exponent
1/inf=0

>>11953116
correct, 0.999... doesn't end.

>>11953121
... can't possibly be referring to an infinite string of digits in the abbreviation 0.000...1, because that abbreviation clearly ends with a 1.

infinite string of 0's followed by a single 1 actually makes perfect sense. arguments like "nothing can come after infinite zeros because infinity doesn't end" are flawed. it's just that this object doesn't represent any real number.

>>11953202
>infinite string
>followed by
no, as soon as you add the follow by, the original string is no longer infinite since it clearly ends

>>11953212
>what is ω+1

If 0.999...= 1, then why isn't it just called 1? Checkmate atheists.

>>11953240
>if 2/2 = 1, then why isn't it just called 1?

>>11953228
limit ordinals aren't real, it's meaningless nonsense

>>11953268
>ordered sets aren't real, it's meaningless nonsense

>>11953278
>meaningless greentext
wow you convinced me

>>11950927
that is.

>>11953342
No, that's wrong.

>>11953313
>wow you convinced me
I'm glad

>>11953370
no, I'm glad

>>11953156
anything after the ... is meaningless

It's very cute and endearing how some people can't wrap around their head that 1 doesn't represent the symbol of 1. 1 can be written as 1, or as 5/5, or as 5*0.2, or as 0.999.... Symbols are completely arbitrary. I now redefine 4 to mean 1. So 0.999... = 4. The glyph used doesn't matter on iota.

>>11953538
what's the point of interpreting the 1 to be meaningless, instead of interpreting the ... to be finite?

>>11953585
>>11952303

>>11947555
0.999... =/= 0.999...8

>>11952740
>doesn’t matter if you can assign positions
the definition of a decimal representation requires that the digits have an assigned place
>>11953585
>what's the point of interpreting the 1 to be meaningless, instead of interpreting the ... to be finite?
because thats not what we're talking about
>>11953228
omega is not an infinite string, we arent putting anything at the end of it by adding 1

>>11953643
>omega is not an infinite string, we arent putting anything at the end of it by adding 1
no, but it captures the pattern. map omega+1 to {0,1..,9}, you get an infinite string followed by a single digit.

>>11953643
>the definition of a decimal representation requires that the digits have an assigned place
yes, but every decimal representation that conforms to the pattern 0.000...1, where ... is an arbitrarily long string of digits, is a finite decimal ending in 1 and as such > 0
>because thats not what we're talking about
yes, that's what I've been talking about, the only interpretation that makes sense. why would you bother talking about an interpretation that doesn't make sense?

>>11953607
the post you linked has nothing to do with my question

>>11953664
>yes, that's what I've been talking about, the only interpretation that makes sense.
yes, but theres retards in this thread using ... to represent infinitely many digits

>>11953667
>beyond help
sad

>>11953685
>doesn't know what a limit is
sad

>>11953607
>using limits is the same as not using limits

Everyone here knows that the LIMIT of 0.00...01 is 0, but the actual number itself is not zero. Retard

>>11953763
>actual number itself is not zero
lol
retard

>>11953763
correct, no number that fits the pattern 0.000...1 is equal to zero.

>>11953776
>
citation needed

>>11953786
>1>0
>citation needed
(You)

>>11947555
0.9999...8 (an infinite number of nines with an 8 at the end) does not exist.
You can't have an infinite amount of digits and then a last digit because then it isn't infinite. INFINITE MEANS THERE IS NO END.

>>11953763
>Everyone here knows that the LIMIT of 0.00...01 is 0, but the actual number itself is not zero. Retard
you are using 2 different fucking terms to describe .000...1
a SEQUENCE has a limit, a NUMBER does not
so if the LIMIT of .000...1 is 0, then that means youre talking about .000...1 as a sequence of 0s followed by a 1
but then that means, that .000...1 isnt a fucking number, its a sequence
so it isnt an AcTuAl NuMbEr
youre using contradictory terms

>>11953763
>limit of a number
kys

>>11953798
>has no citation
kek

>needs a citation
>>>/x/

>>11953971
what exactly do you need citation for?

>>11953975
for you>>11953971

>>11947757
Maybe this is the issue. Infinity is not an easy thing to accurately describe for brainlets, evidence being this hilarious absolute abomination of a thread. Dumber than water not being wet. Dumber than how dumb you perceive .999...=1 is to you. No wonder you think .999...8 is even a concept because you didn't understand .999... either. Infinity, when describing a range, is just saying all of this.

Why does .999... even exist? Necessity. Necessity doesn't necessarily make something true but there are plenty of reasons, the simplest being dividing any base 10 number into 3. As you progress, yes, there is a continuous .000...1 but that 1 is not there in the end it only exists while you are performing the division.

1/3 x 3 = 1 each digit only has 9 "holes". 0 is no holes filled. Nine is all holes filled. Every whole of every digit is filled. If at any point the digits stopped you would have a .1 but you cannot have a .1 at the end of infinity. You can't have a ... and then terminate with a number other than the number before the ... because that would mean the ... is not actually infinite.

I'm convinced it is the assumption that there is a belief in a tenth hole in the digits. There are only nine holes. If you wanted 10 you would write a zero and a 1 to the left.

It may seem to be unnecessarily redundant but .999... is the same as saying 1.0. It's like writing five tally Mark's instead of four and a slash.

Bros, give it up. His understanding of 0.999... is that it's the class of numbers which have arbitrarily many 9s following the decimal place, he's never gonna agree.

>>11947555
Wait, by 0.9999...8, do you mean
>0.9999... + 0.0000...8
or
>0.9999... - 0.0000...1
?
If you can't answer that, or explain why it would be one rather than the other, your argument is void.

>>11955016
>YOU hAvE TO ChoOSE betWEEN diFFERNECE A AND difFERENCE B
Both.

>>11955198
/thread

>>11955016
0.999... + 0.000...8 = 1.000...7999...
0.999... - 0.000...1 = 0.999...8999...
how could these possibly be the same?

>>11955231
no one is laughing