/sci/ - Science & Math

[Anonymous No.11473744]

as you all know, the math undergrad cultists have for some time told us that 0.999=1. Effectively the 0.999=1 meme is claiming that the sequence of partial sums 0.9,0.99,0.999... is convergent. Since a real valued sequence is convergent iff it is cauchy (Barnett 2015), I shall disprove that this sequence is cauchy to put this matter to rest. Let xn=0.99999... be a sequential term with n 9s. Let N be an arbitrary index. We take epsilon to be 0.000...001>0. now consider any indices j,k >= N. Then,

|xj-xk|=|0.999...(j times)-0.999...(k times)|
=0.000(min(j,k) times)...999...(|j-k| times)
>0.000...(max(j,k) times)...1
>epsilon

Hence 0.999... is not cauchy. I do not know why so called mathematicians still spew this propaganda. Personally I think it's an element of societal control, but feel free to discuss your own theories.

[Anonymous No.11473750]

>>11473744
Go ahead and convert 0.999999... to any other base.

[Anonymous No.11473751]

>>11473744
Limits, motherfucker.

[Anonymous No.11473771]

>>11473744
>(Barnett 2015)
Almost had me

[Anonymous No.11473773]

>>11473744
Epsilon is not well specified. Furthermore, in the definition of a Cauchy seqeunce, N is not arbitrary given epsilon.

[Anonymous No.11473775]

>>11473773
Thought I was smart for pointing out the flaws and then >>11473771 made me realize I was a brainlet.

[Anonymous No.11473803]

>>11473751
Yup, it approaches but never becomes 1. No matter how far to the right you go, it never become 1. This is as intuitive, as axiomatic, as adding zero to a number and knowing its value will not change.

How something as patently obvious as this can be denied by the 0.999...= 1 faggots is one of the best examples of blatant intellectual dishonesty in history.

The fact that you get asshats proclaiming such absurdities to be true illustrates how maths has become more of a religion rather than being a rigorous discipline.

[Anonymous No.11473807]

>>11473773
riddle me this, if 0.000...1 isn't well defined then how can 0.999.... be? math cultists truly have no shame

[Anonymous No.11473838]

>>11473744
1/3 = 0.3333....
1/3 * 3 = 0.3333.... * 3
3/3 = 0.9999....
1 = 0.9999...

OP BTFO with highschool math

[Anonymous No.11473955]

>>11473807
Epsilon goes to 0 if you play his game long enough. Even if it doesn't, it isn't stated where it's going to terminate. If there's 5 zeros, 500, or a million. You can just snake your way round by saying "oh but I mean that it had a hundred more zeros than what you thought jk"

[Anonymous No.11473984]

>>11473803
Find me a number between .9 repeating and 1. Go ahead; I'll wait.

[Anonymous No.11474030]

>>11473984
0.999...1

[Anonymous No.11474038]

>>11473807
0.1 = 10^-1
0.01 = 10^-2
0.001 = 10^-3
:
0.000...1 = 10^-inf = 0

[Anonymous No.11474137]

type "convert .999... to base 10" in wolfram alpha and it gives 1 for whatever that's worth

[Anonymous No.11474187]

Hot take: Converging numbers shouldn't be treated as traditional numbers. Infinite decimal holds it's own purpose.

[Anonymous No.11474196]

>>11473838
Prove that 1/3 is 0.3333...

[Anonymous No.11474202]

>>11474038
Prove that 10^-inf = 0

[Anonymous No.11474217]

This is why Arabic numerals are a shit system.

[Anonymous No.11474241]

>>11474217
What else do you have in mind, mister Roman?

[Anonymous No.11474272]

>>11474202
same as 1/inf

[Anonymous No.11474274]

>>11474196
1/3 = 3/10 + 1/30
= 0.3 + 1/30
= 0.33 + 1/300
= 0.333 + 1/3000
:
= 0.3... + 1/inf
= 0.3... + 0
= 0.3...

[Anonymous No.11474406]

when you define the real numbers as corresponding to the collection of Dedekind cuts of the rationals, then get the Cauchy sequence convergence property from the reals being a complete metric space, and then defining the reals as corresponding to the equivalence class of rational Cauchy sequences is equivalent to the Dedekind cut definition. now 0.999... = 1 is necessitated by definition.

[Anonymous No.11474658]

>>11474030
That's not .999... then, dude.

[Anonymous No.11474903]

>>11473807
[math] 0.999...= lim_{n \rightarrow \infty} \sum_{i=1}^n \frac{9}{10^i} = lim_{n \rightarrow \infty} 9 \sum_{i=1}^n \left(\frac{1}{10}\right)^i[/math]. Now how could we define [math] 0.000...1 [/math]? [math]
lim_{n \rightarrow \infty} \frac{1}{10^i} [/math]. Now is that bigger than zero, or equal to zero? I'll give you a hint, it's the latter.

[Anonymous No.11475415]

Shitty bait.

[Anonymous No.11476191]

>>11474272
Obviously, retard, but now you have to prove that 1/inf = 0
>>11474274
Same thing
>>11474903
Same

[Anonymous No.11476200]

>>11473803
>it approaches but never becomes 1
What process in time are you describing?

>No matter how far to the right you go, it never become 1.
That can describe a function whose limit equals 1. What is your point?

[Anonymous No.11476203]

>>11476200
The definition of limit is not getting there? What are you even talking about?

[Anonymous No.11476205]

>>11474406
if you make up a bunch of definitions you can define anything as anything, that doesn't make it true.

[Anonymous No.11476208]

>>11476203
>The definition of limit is not getting there?
What?

>What are you even talking about?
I'm saying nothing you said describes 0.999..., you are describing the function 1-1/10^n

[Anonymous No.11476211]

>>11476205
Math is just the implications of certain definitions. The definitions are the only thing that makes it true.

[Anonymous No.11476212]

>>11476208
Ok, nvm, my misunderstanding

[Anonymous No.11476286]

>>11476191
I'll prove that [math] \frac{1}{n}\rightarrow\infty [/math]. Let [math] \epsilon >0 [/math] be given, then let [math] N>\frac{1}{\epsilon} [/math], observe that [math] |\frac{1}{n}-0|=|\frac{1}{n}|<\frac{1}{\frac{1}{\epsilon}}=\epsilon [/math] for all [math] n \geq N [/math] So for an arbitrarily small epsilon, n can always be chosen so that one over n is less than epsilon. By definition of the limit [math] lim_{n\rightarrow \infty}\frac{1}{n}=0 [/math]. Notice that [math] \frac{1}{n}>\frac{1}{10^n}>0 [/math], so obviously it holds for that one as well.

[Anonymous No.11476299]

>>11476205
>if you make up a bunch of definitions you can define anything as anything, that doesn't make it true.
Yes but this is the definition of the real line that we all use. So, if you want to talk about analysis on the real line, you have to play the game of this construction
>>11474038
>>11474202
>>11474274
most of the misconceptions that allow OP to shitpost come from abusing infinity in notation. The core idea of analysis is that when we admit arbitrary precision, convergence is a meaningful tool that generalizes equality from the standpoint of behavior. It's not that 1 / inf = 0, but that 1 / n tends to zero as n blasts to infinity, so we understand it. The reason we can do this and study this is because of the completeness (every Cauchy sequence converges) of the real line.
TL;DR use an epsilon argument, don't use fucking substitutions with infinity. This is a freshman mistake,
Also
>>11474406
What this person said is more or less correct. The construction of the reals that demonstrates how we can claim 0.99... = 1 is most present in classes of Cauchy sequences.

[Anonymous No.11476310]

They haven't. They know it's not equal, but for practicality rounding is simpler.
>posting bait that's literally a decade old

[Anonymous No.11476484]

>>11476191
directly follows from definition
inf is unbounded
any >0 value would bound inf

[Anonymous No.11476489]

>>11476310
>it's not equal
nope
it's equal

[Anonymous No.11476492]

infinity is not a numeral concept and actually as nothing to do with math.

there is no sensible meaning behind what "0.999..." even means.
repeating decimals are a calculation error and that's all.

[Anonymous No.11476510]

>>11476492
>not a numeral concept
true, from definition follows it's not a real number
>nothing to do with math
false, by definition it's larger than any real number

[Anonymous No.11476514]

>>11476510
Infinity is not a number. Best you can say is that it is an object, and the best you can figure of that object is that it is incomprehensible. If you think you understand it, you're encouraged to make it more incomprehensible so your understanding no longer applies.

One way or the other, it's got nothing to do with numbers. You can't count to it or anywhere near it. It's like putting a photo of a red car on a number line. Where does the red car go on the number line? Is it bigger than 10? Bigger than 100?
You don't put the red car on the number line cause the red car has nothing to do with the number line. Same goes for infinity.

[Anonymous No.11476516]

>>11476514
>from definition follows it's not a real number
did i fucking stammer?

[Anonymous No.11476518]

>>11476516
it has nothing to do with numbers. Real, complex, imaginary, or otherwise. Read.

[Anonymous No.11476523]

>>11476518
sigh

https://www.wolframalpha.com/input/?i=infinity
An unbounded quantity that is greater than every real number.

[Anonymous No.11476532]

>>11476523
oh no, you're retarded...
https://www.wolframalpha.com/input/?i=sum%5B9%2F10%5En%2C+%7Bn%2C1%2C1.7*%2810%5E308%29%7D%5D

[Anonymous No.11476536]

>>11476532
forcing WA to fiddle with real numbers doesn't change inf's definition

[Anonymous No.11476558]

>>11476536
infinity in calculable math is a real finite number. Relative to wolfram, it's just the upper limit of a 64-bit Float.
https://docs.microsoft.com/en-us/cpp/cpp/data-type-ranges?redirectedfrom=MSDN&view=vs-2019
>double: 1.7E +/- 308 (15 digits)

https://en.wikipedia.org/wiki/Arithmetic_underflow
>Arithmetic underflow can occur when the true result of a floating point operation is smaller in magnitude (that is, closer to zero) than the smallest value representable as a normal floating point number in the target datatype.[1] Underflow can in part be regarded as negative overflow of the exponent of the floating point value.
Wolfram's result here stretched to within the confines of a single operation force it to do disingenuous shit by simply adding "1" arbitrarily to it's result, because the math coding merely assumes that [math]\sum_{n=1}^{\infty} \frac{9}{10^n}[/math] ought to "equal" 1, showing both that neither can a computer understand infinity, it also has to do disingenuous calculations to produce a result that aligns with preconceived assumptions. Here, we assume the limit of the sum taken to infinity under classical definitions should produce the result of "1", but wolfram, the computer, believes "infinity" is the same number as the largest value of a 64-bit Float, being ~1.7x10^308, which is very much definitely a finite number. Wolfram attempts to iterate through the calculation and finds itself accumulating number errors it can't do math on because the values are so small, resulting in the underflow rather than an actual value, so the programmer decided in this situation to simply make wolfram "add 1" to this non-value. The programmer was a retard sure, cause they thought adding 1 to NaN value was the same as adding 1 to "nothing" AKA "0", so the result is printed as Underflow +1 when they probably intended it would look more like "0+1" and thus just print "1" to align with assumptions.

[Anonymous No.11476559]

>>11476536
>>11476558
Point is, infinity has no real definition because it cannot be practically applied. Doesn't matter what wolfram's "definition" of it is if Wolfram itself can't work with it.

[Anonymous No.11476567]

>>11473744
>but feel free to discuss your own theories.
It's that bitchass satan trying to be like God. Just think on it; it's exactly the same.
>if i am this incomplete thing an infinite number of times, then i am this complete thing
>.999...
>666=7

[Anonymous No.11476568]

>>11476559
>t. retard

[Anonymous No.11476571]

>>11476484
Holy retard
How about this: you’re wrong. Why? It follows from definition

[Anonymous No.11476572]

>>11476568
>>>11476559
>>t. retard

[Anonymous No.11476573]

>>11476558
>confusing geometry with limitations of a ruler
kek, thanks for the laugh

[Anonymous No.11476576]

>>11476571
Because his brain is unbounded by his skull

[Anonymous No.11476577]

>>11476573
I don't believe for a moment you actually understood anything about that miserably tiny post you just made.

[Anonymous No.11476578]

>>11476571
lazy.
how about giving the counter-example

[Anonymous No.11476662]

>>11473744
>(Barnett 2015)
okay heres tour (You), you earned it

[Anonymous No.11476690]

>>11473744
N=0.999...
10N=9.999...

10N-N = 9.999... - 0.999...
9N = 9
N=1
1=0.999...
Case Close common /sci/

[Anonymous No.11476715]

>>11476690
N = 0.999...
10N = 9.99...0
10N-N = 8.99...1

[Anonymous No.11476723]

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

[Anonymous No.11476733]

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

[Anonymous No.11476740]

>>11476690
N=0.99999
1.5N=1.499985
1.5N - N = 0.499995
0.5N = 0.499995
0.499995 ×2 = 0.99999 = N

Math is done right to left nigger, you can't leave a repeating decimal repeating else you can't do any math on it cause it has no right-most end.

[Anonymous No.11476746]

N = 9
10n = 99
10N-n = 90
9n = 90
N = 10
9 = 10

[Anonymous No.11476747]

>>11473803
Lot's of numbers are defined as limits, you faggot. Do you deny the existence of pi an e?

[Anonymous No.11476762]

>>11476740
>Math is done right to left
>hurr durr 2+3=5 only right to left
[citation needed]

[Anonymous No.11476766]

>>11476746
>10n = 99
wew lad

[Anonymous No.11476796]

>>11476762
0.999 +
0.001 =
>L2R: 0+0=0
0_____
>L2R: 0+9=9
0.9___
>L2R: 0+9=9
0.99__
>L2R: 1+9=10
0.9910
>uhh wait fuck no, i did the math wrong

0.999 +
0.001 =
>R2L: 1+9=10
____0
>R2L: 0+9+1=10
___00
>R2L: 0+9+1=10
__000
>R2L: 0+0+1=1
1.000

>>11476766
>n=9
>10n=99
>wew lad

>n= 0.999...
>10n=9.999...
wew lad

[Anonymous No.11476806]

>>11476747
How is pi a limit?

[Anonymous No.11476807]

>>11476766
10N = 11 you fuckking brainlet. get out of tjis sub you fucker

[Anonymous No.11476840]

If n=0.999...
then 10n is NOT 9.999...

the dots imply repeating, but nothing about that repetition is countable, and also not equatable. This is the problem with infinity in math, people just seem to treat it like a fixed contained object even though it isn't.
If it's written like
n = 0.(n 9's)
then 10n = 9.(n-1 9's)
and the math remains true.

the wrong math is
n = 0.(∞ 9's)
10n = 9.(∞ 9's)
that is for certain, but is commonly ignored through the trap of then admitting ∞ is not a number and ideas such as ∞-1 have no numerical value or meaning, which altogether adds up to retardation cause you're trying to say ∞ is a number by "counting" (∞ 9's) followed by immediately claiming ∞ isn't a number cause it fails as a substitute for n in "(n-1 9's)".

It'd make as much sense as merely claiming:
n = 0.(two 9's)
10n = 9.(two 9's)
as if "(two 9's)" is an immutable fixed object that must remain true, and therein lies the "infinity is an immutable fixed object" idea.
Infinity is unbounded. It cannot be contained or restrained. It cannot exist inside a set, because it cannot be contained. Infinity cannot describe an amount of something.
There are not "infinity" numbers, but that doesn't automatically mean there is a single largest finite number applicable to all circumstances.

[Anonymous No.11476877]

>>11476840

At this point its impossible to even start arguing with you since you reached levels of retardation I have never seen before.

> There are not "infinity" numbers, but that doesn't automatically mean there is a single largest finite number applicable to all circumstances.

Lets try the easiest: If there are not "infinity" natural numbers as you say there has to be an end to it, so to say a biggest natural number since you can always sort them by size. But in the same sentence you say that there isnt a single largest finite number thus contracting your own statement.

Just stop doing math or anything math related because you might hurt yourself at this point.

[Anonymous No.11476897]

>>11476877
>>There are not "infinity" numbers, but that doesn't automatically mean there is a single largest finite number applicable to all circumstances.

> If there are not "infinity" natural numbers as you say, there has to be an end to it
nigga you can't read at all.

Let me make it easier for you:
If you want to say there are "infinity" numbers, what you're really saying or wanting to express is that there is a finite maximum of which there can be no greater. Finite, so you can understand it (as you can't understand infinite), and maximum, so you can get to the end of something before you die from old age.

You aim to use infinity as an unspecified arbitrarily large finite maximum. Let's call this idea "ㅅ". Because it's the maximum, you enjoy the convenience of there being no sense in adding to it, because it's the maximum and can't go any higher, so "ㅅ+1" is meaningless. Because you haven't specified where the number is, you also get to enjoy the convenience of not being able to subtract from it and come to a specified real number, so "ㅅ-1" is also meaningless.

now replace ㅅ with ∞ and there you go.
The definition of infinity does not match the usage of it's symbol.

[Anonymous No.11476907]

>>11476897
Meh, I tried but seems like you are really beyond saving.

Have a nice life and god bless you.

[Anonymous No.11476913]

>>11476907
you're a sad bitch if you virtually immediately get reduced to acting superior.

but that was obvious from the getgo since you can't actually comprehend math.

[Anonymous No.11476970]

>>11476897
I kinf of get it, you are saying inf+1 has no mathematical sense bc obv inf+1=inf thats the whole paradox behind the 0.999..=1 meme, because it is a meme right?

[Anonymous No.11476987]

>>11476840
>people just seem to treat it like a fixed contained object even though it isn't.
but it is

[Anonymous No.11477015]

>>11476806
Wow you're dumb. I'll give you a simple example:

pi = lim as n->inf of 4/1-4/3+4/5-4/7+...4/(2n-1)

[Anonymous No.11477017]

>>11473744
what is the result of 1/0.99999...

[Anonymous No.11477022]

I think there are unlimited numbers.
But there are not infinite numbers.
Infinity is a thing.
Unlimity is not a thing.
But at the same time if mathfags used "unlimited" everywhere where they'd use infinity, they'd realize pretty quick what they do with infinity makes no sense. Just using the word "unlimited" alone would crush a majority of calculus cause having an unlimited limit is illogical.

[Anonymous No.11477029]

>>11477022
based schizo post
exactly what do you propose is the difference between unlimited and infinite? If we're going to talk about unbounded, in that case, we have to address infinity.
It's not that infinity doesn't make sense. It's that when you're an amateur in mathematics, infinity is a tricky concept to tackle with your tools and intuition, and as a you get more mature, it becomes apparent even when your peers start to mangle it. The way we use infinity is fairly consistently precise and well defined in mathematics. What exactly about a delta-epsilon proof reads as "making no sense?'

[Anonymous No.11477081]

>>11477029
"unlimited" is what makes sense relative to the math concept of infinity.
Unlimited is an adjective, so it's a property. Infinity is a noun, an actual thing (that happens to have no relation to math)
Infinite is non-word that doesn't make sense cause it's only utility is describe infinity, and yet mathfags will say completely psychotic retard shit like "an infinite amount of [...]", when infinity is not countable or numerable and has no logical connection to describing something that actually can be described by counting or enumerating.
Unlimited is a far more sensible word than Infinite, but "unlimited" defies whatever logic exists in higher math limits that are undefined as "infinite".

lim->10, lim->100, lim->1000, all these make sense. the point of notating lim is to define an arbitrary restriction or rule that wouldn't exist otherwise, so setting lim->unlimited stops making sense because it's announcing the application of the limit rule then immediately renouncing it by not actually giving an actual limit to confine the process.

For anything that isn't assuming convergence upon a real number limit, it seems the general usage of lim->∞ really just means the limit is to an arbitrary value of the user's discretion which provides a desired level of useable accuracy. If we just called that "TUD" for "to user's discretion", then lim->TUD solves what needs to be solved in any desired situation to a desired degree of accuracy. You can get degree measurements with 15 decimals of accuracy to launch a rocket into the orbit of jupiter, so any math involved in figuring the process to get that rocket to jupiter would only need 16 decimals: The 15 required and another for potential carry, and the TUD would be whatever obviously finite number will accomadate 16 decimals of accuracy.

Point is, if you don't treat "infinity" as being logically interchangeable with "unlimited", then you're not looking at "infinity" correctly.

[Anonymous No.11477084]

>>11477081
do you actually know the definition of the symbol [math]\lim_{x \to \infty}f(x)[/math] ?

[Anonymous No.11477091]

>>11476796
Please translate into non-autistic

[Anonymous No.11477095]

>>11473744
It is Cauchy you moron.
[math]|x_n-x_m| = |\sum_{k=1}^n\frac{9}{10^k}-\sum_{k=1}^m\frac{9}{10^k}| =9\sum_{k=min(n,m)+1}^{max(n,m)}\frac{1}{10^k}<9\sum_{k=min(n,m)+1}^{\infty}\frac{1}{10^k} = 9(\sum_{k=0}^{\infty}\frac{1}{10^k} - \sum_{k=0}^{min(n,m)}\frac{1}{10^k})[/math]
Using geometric series you find:
[math]|x_n-x_m| < (\frac{1}{10})^{min(n,m)}[/math]
So whenever [math]n,m > N = -\log_{10}(\varepsilon)[/math]:
[math]|x_n-x_m|<(\frac{1}{10})^N < \varepsilon[/math]

[Anonymous No.11477097]

>>11477084
Do i know your definition? No.
I've gone over that many times.
The usage of infinity in higher math is illogical incalculable nonsense that doesn't align with the definition. It's not that it's counter-intuitive, it's simply wrong.
The mathematical symbol ∞ and the word "infinity" are not actually related.
∞ ≠ "infinity".
You ask for a definition of "infinity" and you get something that says unbounded, uncountable, greater than everything.
Then you turn around and use ∞ in lieu of where a real number would be.

It's a tard wrangling party.

[Anonymous No.11477108]

>>11477097
>Do i know your definition? No.
so you have no idea what you're talking about. ok

[Anonymous No.11477119]

>>11477108
I answered your question in the text following "no" with an affirmation.
I can tell you right now that you don't know what lim->∞ means cause your only interaction with it is pressing the buttons on a calculator or typing it into wolfram.
I can tell you what your calculator is doing though. It's treating ∞ as a large finite number, the aforementioned TUD that will produce a degree of accuracy the hardware is equipped to display you, for example 16 digits.

[Anonymous No.11477123]

>>11477097
>∞ ≠ "infinity
retard

[Anonymous No.11477128]

>>11477119
>t. no idea what I'm talking about

[Anonymous No.11477132]

>>11477128
lim x-> 4, f(x)

you can do that much at least, right?

[Anonymous No.11477142]

this thread is the fucking equivalent of the "i don't tip" thread on /b/

It has always been there, it will always be.

It is comforting in a way.

[Anonymous No.11477331]

>>11476690
>0.999...*10=9.999...
Cool it with these math proofs you find on the bottom of snapple lids. All such math "proofs" merely presuppose the metaphysical assumption that 0.999=1, and then pretends to arrive at that same conclusion organically.
Alternatively, pop-math regurgitating brainlets say
>there are no numbers between 0.999... and 1, therefore...
Yes there are. There's an infinity of numbers between 0.999... and 1: an infinite number of 9s; where 0.999... be 1, then there is simply more infinity.
Honorable mention to the ultra super mega brainlet who thinks
>0.999... and 1 are just two ways to represent the same thing
is advancing a novel argument. Well yes, that is indeed what's in dispute.

[Anonymous No.11477338]

>>11477331
>>11476690
>0.999...*10=9.999...
Cool it with these math proofs you find on the bottom of snapple lids. All such math "proofs" merely presuppose the metaphysical assumption that 0.999=1, and then pretends to arrive at that same conclusion organically.
Alternatively, pop-math regurgitating brainlets say
>there are no numbers between 0.999... and 1, therefore...
Yes there are. There's an infinity of numbers between 0.999... and 1: an infinite number of 9s; where 0.999... would be 1, then there is simply more infinity.
Honorable mention to the ultra super mega brainlet who thinks
>0.999... and 1 are just two ways to represent the same thing
is advancing a novel argument. Well yes, that is indeed what's in dispute.

[Anonymous No.11477344]

Based schizo poster introducing me to the word unlimity
Will be using it to teach 1st years about limits

[Anonymous No.11477345]

>>11477338
>between 0.999... and 1: an infinite number of 9s;
just listen to yourself

[Anonymous No.11477350]

>>11477344
says the idiot who can't figure out how to reply

[Anonymous No.11477354]

>>11477345
inspired by this brainlet
>>11477331 (Dead) (You)
>>11476690
>0.999...*10=9.999...
Cool it with these math proofs you find on the bottom of snapple lids. All such math "proofs" merely presuppose the metaphysical assumption that 0.999...=1, and then pretends to arrive at that same conclusion organically.
Alternatively, pop-math regurgitating brainlets say
>there are no numbers between 0.999... and 1, therefore...
Yes there are. There's an infinity of numbers between 0.999... and 1 -- an infinite number of decimals -- where 0.999... would be 1, then there is simply more infinity.
Honorable mention to the ultra super mega brainlet who thinks
>0.999... and 1 are just two ways to represent the same thing
is advancing a novel argument. Well yes, that is indeed what's in dispute.

[Anonymous No.11477378]

>>11477095
as shown in the OP, there is never a point in the sequence wherein d(xn,xm) < 0.000...1 for arbitrary n,m. this is a direct proof and is irrefutable. your proof is reliant on log being bijective for your statement to apply to any epsilon

[Anonymous No.11477386]

>>11477354
what is the result of 1/0.99999..

[Anonymous No.11477397]

>>11477386
1.000000000....1...0000....1....0000....1....

retard

[Anonymous No.11477410]

>>11477386
Oh shit iono. wtf 0.999...=1 now. Proof from irrelevant question. Maybe something like infinitesimal-1, if there were a math symbol for that. In practice, it's find to proceed AS IF 0.999...=1. But if we're talking about what is actually true or false, it's false.
>herp derp truth is only what is practically useful
1) interesting, 2) This is equivalent to saying
>then until a practical use for "infinitesimal-1" is found, it IS true that 0.999...=1
The truth of this sentiment seems to be contingent on whether you're an NPC or actually alive.

[Anonymous No.11477417]

>>11477397
Report type
⦿ This post violates a rule.
∟This post is extremely low quality.

[Anonymous No.11477420]

>>11477410
>>11477397
>Oh shit iono. wtf 0.999...=1 now. Proof from irrelevant question. Maybe something like infinitesimal-1, if there were a math symbol for that. In practice, it's fine to proceed AS IF 0.999...=1. But if we're talking about what is actually true or false, it's false.
>>herp derp truth is only what is practically useful
>1) interesting, 2) This is equivalent to saying
>>then until a practical use for "infinitesimal-1" is found, it IS true that 0.999...=1
>The truth of this sentiment seems to be contingent on whether you're an NPC or actually alive.

[Anonymous No.11477422]

>>11477420
holy fuck, lol
take your medicine

[Anonymous No.11477428]

>>11477420
>>11477410 (Dead) (You)
>>11477397
Oh shit iono. wtf 0.999...=1 now. Proof from irrelevant question. Maybe something like infinitesimal-1, if there were a math symbol for that. In practice, it's fine to proceed AS IF 0.999...=1. But if we're talking about what is actually true or false, it's false.
>herp derp truth is only what is practically useful
>1) interesting, 2) This is equivalent to saying
>then until a practical use for "infinitesimal-1" is found, it IS true that 0.999...=1
The truth of this sentiment seems to be contingent on whether you're an NPC or actually alive.

[Anonymous No.11477435]

>>11477422
>>11477420 (You)
>>11477410 (Dead) (You)
>>11477397
Oh shit iono. wtf 0.999...=1 now. Proof from irrelevant question. Maybe something like infinitesimal-1, if there were a math symbol for that. In practice, it's fine to proceed AS IF 0.999...=1. But if we're talking about what is actually true or false, it's false.
>herp derp truth is only what is practically useful
1) interesting, 2) This is equivalent to saying
>then until a practical use for "infinitesimal-1" is found, it IS true that 0.999...=1
The truth of this sentiment seems to be contingent on whether you're an NPC or actually alive.

Fuck this stupid website.

[Anonymous No.11477448]

>>11477428
>>11477435
https://youtu.be/c6Zh2OdhBTI?t=2m

[Anonymous No.11477454]

>>11477397
"..." means that 0 continues without end, so how can you place a number after it as if it has an end?

[Anonymous No.11477472]

>>11473744
Is that you Wolfgang? You really ought to study how to deal with quantifiers sometime, it might spare you from being such a laughing stock.

[Anonymous No.11477474]

>>11477454
Holy shit you're dumb

1+1^-x+1^-(x^2)+1^-(x^3)....+1^-(x^n)

where x, n tend to infinity

[Anonymous No.11477480]

Hey! Lets count!
1,2,3..whoah, it must go for like FOREVER!
Wow, that means infinity exists!

[Anonymous No.11477484]

>>11477474
You are a very smart parrot. Wanna a cracker?

[Anonymous No.11477558]

>>11477474
>dumb
says the retard who can't do latex

[Anonymous No.11477680]

>>11477474
>holy shit you're dumb
>here's this thing that demonstrates the exact same concept in dispute as 0.999...=1
I'm pretty sure """people""" like you think people are just too stupid to properly download textbook information, like
>you can just google it. people are just so stupid that they can't read information freely available on google
And your """thoughts""" never go beyond that point.

[Anonymous No.11477694]

>>11477474
>1+1^-x+1^-(x^2)+1^-(x^3)....+1^-(x^n)
This describes a finite sequence.

>where x, n tend to infinity
This is gibberish. Are you trying to describe a limit?

You understand that the limit isn't the sequence as you've written it, it's the limit of the finite sequences you've described.

The infinite sequence equal to the limit would just be

1+1^-x+1^-(x^2)+1^-(x^3)....

Thanks for proving my point.

[Anonymous No.11477708]

>>11477480
>the physical act of counting determines anything

[Anonymous No.11477729]

>>11477694
exactly, so you would yield a number

1.000000000....1...0000....1....0000....1....

like that. Problem?

[Anonymous No.11477773]

>>11477729
Yes, if by "..." you mean some finite amount of digits.

[Anonymous No.11477782]

>>11473744
>(Barnett 2015)

[Anonymous No.11477904]

>>11477350
Lmao, I'm just throwing peanuts in the ring

[Anonymous No.11477928]

>calling someone else a schizo while claiming to be a math teacher
>on 4chan
NPC's and their complete lack of spacial awareness will never get old.

[Anonymous No.11477936]

There are no numbers greater than infinity...
... but also there are no numbers less than infinity...
so infinity isn't a number or a thing that can replace a number in any equation.

[Anonymous No.11477945]

>>11477708

>I have trouble distinguishing between a physical manifestation of a concept and the concept itself!
>( I am so smart )

Go forth and multiply. The world needs more lawn mower mechanics.

[Anonymous No.11477946]

>>11477936
>but also there are no numbers less than infinity...
Wrong.

[Anonymous No.11477959]

>>11477928
You are a schizo and I'm a math teacher.

Deal with it, schizo.

[Anonymous No.11477962]

>>11477946
It's true...
0.5×n = b; b<n
test n->infinity
b<n
but test n @ infinity... oh no...
>0.5×infinity = infinity
>b=n
>less-than-infinity = infinity
no numbers smaller than infinity...

[Anonymous No.11477964]

>>11474903
Anyone with half a brain knows the geometric series has an addition of -(x^(n+1))/(1-x). That's why it diverges, when x>1, dumbass.

[Anonymous No.11477965]

>>11477945
>>I have trouble distinguishing between a physical manifestation of a concept and the concept itself!
Are you talking about yourself? The only one who brought up counting was you.

[Anonymous No.11477972]

>>11477962
>0.5×n = b; b<n
False. Let n=0

>>0.5×infinity = infinity
False. It's undefined.

>no numbers smaller than infinity...
How does that follow? What a brainlet.

[Anonymous No.11477976]

>>11477964
That didn't respond to anything he said. Nice try retard.

[Anonymous No.11477981]

>>11477972
>0.5×n=b; b<n for all non-zero values
>b=n for n=0
>b=n for n=infinity
>infinity = 0
>infinity is nothing
>infinity doesn't exist
oh no bro...

[Anonymous No.11477998]

>>11477972
[math]\sum_{n=1}^{x} 1 = x [/math]
the purpose of this function is sequential iteration, which is a countable enumerating property, reiterating X amount of times.

plugging in [math]\infty[/math] in for X no longer provides a solveable equation because infinity is not countable or enumerable.

[Anonymous No.11478000]

>>11477981
>>b=n for n=infinity
Incorrect, 0.5*inf is undefined. Are you illiterate?

>infinity = 0
Just like 2 = -2 since both solve x^2=4 right? Wow, you're dumb. You appear to be about 12 years old.

[Anonymous No.11478003]

>>11477998
How does that respond to anything I said?

[Anonymous No.11478023]

>>11478000
2 = 2 bro...
doesn't matter if it's positive or negative. it's still 2...

v = -2
2v = 2-2 = 0
2v = 2×-2 = -4

negative numbers aren't a real thing bro...
you can't have a negative amount of things...
everything you believe in is a lie bro...

[Anonymous No.11478027]

>>11473803
1/3 is .333~
2/3 is .666~
3/3 logically must be .999~ and equal to 1.
To argue against this would be to argue that 3 divided by 3 isn't 1.

[Anonymous No.11478032]

>>11478023
>2 = 2 bro...
>doesn't matter if it's positive or negative. it's still 2...
You ruined it. You almost had a good troll going and you ruined it.

[Anonymous No.11478039]

>>11478003
There are no numbers smaller than infinity because it is impossible to count to infinity through any and all numbers.
Even the sum of all numbers has no identifiable relation to infinity.

if infinity is a number, then undefined is a number.
if undefined isn't a number, then infinity isn't a number.

[Anonymous No.11478042]

>>11478027
To argue it is to argue that 1÷3 isn't actually 0.333..., which is easy enough to prove is the case.

[Anonymous No.11478293]

>>11478042
prove it then if you think you're so smart
0.33333...=1/3
go on, I dare you

[Anonymous No.11478318]

>>11478293
1÷3 > 0.3
1÷3 > 0.33
1÷3 > 0.333
1÷3 > 0.3333
1÷3 > 0.33333
1÷3 > 0.333333
... ad infinitum

1÷3 > 0.333...

[Anonymous No.11478366]

>>11478318
ad finitum, retard

[Anonymous No.11478565]

>>11473984
Find me a value between the natural numbers 3 and 4. Does this now mean that 3 = 4?

[Anonymous No.11478600]

>>11478318
but you'll never reach infinity with that method. Your numbers will always be finite

[Anonymous No.11478694]

>>11478565
>natural

[Anonymous No.11478948]

>>11478039
>There are no numbers smaller than infinity because it is impossible to count to infinity through any and all numbers.
Non sequitur.

>Even the sum of all numbers has no identifiable relation to infinity.
There's no such thing.

>if infinity is a number, then undefined is a number.
>if undefined isn't a number, then infinity isn't a number.
Non sequitur.