/sci/ - Science & Math

Also fact
1 =~ 1

>>11509365
Why do you make this thread everyday?

>>11509421
People on 4chan are too dopamine fried to actually engage in science in real life, so they pretend.

0.999...+0.0...1=1

not because 0.999...=1 and 0.0...1=0 so 1+0=1
but because 0.999...=0.999...9 so 0.999...9+0.0...1=1

I surrender! You are the master. You had me at "Fact"

>>11509365
>>11509388
Based

>>11509365
1/3 = 0.333333333
1/3 * 3 = 1

also
1/3 * 3 = 0.9999999999

>>11509559
How does an infinite sequence terminate?

>>11509365
If I had an infinite number of dice and rolled all of them an infinite number of times, would I have any dice that rolled a 6 every single time?

>>11510962
It doesn't. It never reaches 1.

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

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

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

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

>>11510989
t. schizo

>>11510962
by being infinite

>>11509365
[math]0.999\ldots\leq1[/math]

>>11509365
oh look, it's THIS thread again.

>>11510989
so much hand waving it's a fucking helicopter

>>11509559
0.0..1 = 0

>>11510989
>.999 isn't the same as 1
No one is claiming it is, retard.

>>11510989
schizo thinks that 0.999... is an ambiguous symbol which means "0.999... = 0.9" or "0.999 = 0.9999" or "0.999... = 0.999999999" depending on our current situation.
schizo also thinks that numbers have legs and they're running around desperately trying to reach something
schizo also thinks that you need to literally perform an infinite process to work with an infinite process

>>11509365
Cringe and fraction pilled

>>11509365
I'm 99.999999...% sure you're wrong

>>11509365
>He doesn't understand the construction of the reals via equivalence classes of Cauchy sequences of rationals
Highschoolers and engineering majors need to leave

https://en.wikipedia.org/wiki/Zeno%27s_paradoxes

>>11509365
>>11509559
>>11510989
>>11511186
Fuck off.

>>11512970
less paradoxes and more simple statements.
>[math]\frac{1}{\infty} \neq 0[/math]
>[math]\sum_{n=1}^{\infty} \frac{1}{2^n} \neq 1[/math]

>>11513880
You being too retarded to understand basic calculus is not an argument against it.

>>11514046
You disagreeing with zeno?
Why?
you being too retarded to understand calculus is no reason to call others retarded.
Your mother should have been a spitter.

Question for all who say .999... = 1:

What is the largest number that satisfies the equation n<1?

>>11514065
This is like asking what's the smallest number greater than 0.

>>11514054
"Appeal to authority" is a fallacy for a reason, retard. Calculus solved the "paradox" because it showed that infinite sums can converge to finite numbers. I don't blame Zeno for being wrong in this regard, you have no excuse though.

>>11514065
1) That's an "inequality".
2) Let n be the largest number that is strictly less than 1. Now consider the average (1+n)/2. This ratio is strictly between n and 1, therefore it's larger than n and less than 1. But this contradicts the assumption that n is the largest such number. Thus there is no such number QED.

if by =~ you mean in the same equivalence class of Cauchy sequences, then yes

if you mean "approximately" then no

>>11509365
.999... is just shorthand for the limit of 9 * 1/10^n, which is 1.

.999... is not a number so much as it's a formula.

Consider base 3

1/3 = 0.1
2/3 = 0.2
3/3 = 0.1 + 0.2
1 = 1

Or base 9

1/3 = 0.3
2/3 = 0.6
3/3 = 0.3 + 0.6
1 = 1

>>11514239
>.999... is just shorthand for the limit of 9 * 1/10^n
Wrong

People who don’t believe infinity is a number shouldn’t believe 0.999... is a number

>>11514243
consider the possibility you were dropped on your head as a child.

>>11514254
>i have no argument

>>11514246
inf definition:
-unbounded
-larger than any number
so either inf isn't a number, or inf is larger than itself

>>11514206
>converge
math isn't a perspective painting.
If you have infinite degrees of accuracy, you're expected to use infinite degrees of accuracy. since doing so is impossible, all "infinite" degrees of accuracy are implicitly used finitely.
You're an actual literal retard if you fail to see the paradox created in modern math from zeno's "arrow paradox". it's really plainly simple. infinite divisions of time provides 0 time, and the arrow cannot move forward.
Because motion is in fact a thing, there must be smallest parts, smallest real non-zero divisions, which aligns with modern usage of "infinity" being finite.

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

Infinity is a concept made up by retards, for retards.

Anything bigger than 1,000 might as well be infinite to a brainlet retard who believes in infinity's usage as "a number", much less agreeing with wolframs definition.

>>11514263
schizo copy pasta

>>11514263
>unbounded quantity
>unbounded
lrn2read

I disagree I think even though they relate they are so fundamentally different they are not liken to.

Limit of x as x->1is equal to 0.999.. equal to 1

>>11513142

>>11514218
[math]0.999\dots \approx 1[/math]
that's the best you can hope for, take it or leave it.

>>11513142
>Proof by induction
What retard wrote this graphic? He clearly doesn't know what he's talking about

>>11510989
How is an infinite Abrahamic God incompatible with the concept of infinity? It literally relies on the concept of infinity, eternity, omnipotence, omniscience etc.

>>11514549
nah it's exactly 1

Also a fact :
9=~10

>>11514791
>i have no idea what infinity means
Godless retard.

>>11514268
define unbounded

>>11514246
and let me finish your clever argument for why this is the case

just ask this simple question:

how many 9's are there in 0.999... ?

the question starts with "how many" so the answer must be a number.
infinity is not a number, so infinity cannot be the answer
therefore there's only a finite number of 9's
clearly such a number is lesser than 1

>>11515945
Fact of the matter is, using "[math]\dots[/math]" notation is shitgarbage and invokes indeterminism.
There must be a finite amount of 9's, but it's completely indeterminate what finite amount of 9's there are.
The logic is sound, but the usage of "..." isn't.

>>11513142
>>11510954
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.
>>11509365
>>11509559
this

>>11510989
Jesus Christ this better be a shitpost

>>11514380
Is this a shitpost?

>>11516674
Everything in these threads is shitposting. Non-shitposters know to avoid these threads.

How the fuck is everyone on this board this retarded? Literally just use a convergent geometric sum and you can verify this 0.9999cont = 1 to be true. Please actually spend time learning math instead of shitposting.

>>11514260
Converge has a mathematical meaning AND an artistic meaning. The same word can have different meanings in different fields, retard.

>>11514549
No, it's exactly one. You're a fucking retard for not understanding this.

>>11516654
Read >>11516723

>>11516731
Shit wrong comment! >>11516701

>>11516654
>0.000...001>0
then also 1/0.000...001 > 0 and we can apply decadic log to it. log(1/0.000...001) is a real number and so can be bounded by some interger:

log(1/0.000...001) < N

take N as the index. for any j,k > N we will find

|x_j - x_k| < 10^N < 0.000...001

>>11516743
>10^N
should be 1 / 10^N, my bad

>>11516726
Might be the case if it were impossible to construct 0.999...

But it isn't impossible, so it must obviously be a real number.

>>11513142
>multiply 10*.999...9
>get 9.999...9
>not 9.999...0

>implying it's possible to have 1/3 of a glass of water when there are a finite # of water molecules which may or may not be divisible by 3

>convergence theorem
>just another approximation

Jesus Christ, you "close enough, so it might as well be equal to" mathlets should have confined yourself to MechE.

>>11509365
/hidethread

reminder that there is no smallest unit of space time and that the universe is infinite in expansion

>>11516801
Prove it

>>11510989
It's more a limit of decimal notation, retard. 1/3 can only be expressed in decimal notation as 0.333 (repeating), so 0.333 (repeating) • 3 = 0.999 repeating, even though (1/3) • 3 = 1. But in duodecimal, 1/3 can be expressed as 0.4, which fits into 1 quite nicely 3 times. Same concept for all rational numbers that can't be expressed well by decimal notation; change it to a different number system if it makes it easier to grasp.

>>11516809
whoops didn't mean to namefag, [s4s] habit

>>11514214
(0.999.. + 1)/2 = (0.999..)/2 + 1/2 = 0.4999...9(5)+ 0.5 = 0.999... . The 5 is out of precision. SOP is to floor to the valid degree of precision. Do they really give you guys math degrees when you can't even do basic algebra?

>>11516809
Repeating decimals exist regardless of base.
that some bases can cover a fraction easily while another can't is ultimately meaningless. Computers run on hexadecimal and there is no 1/3rd in there either.

the inability to convert 1/3 into an equal decimal is just a fact of the conversion process. It doesn't mean that they actually are equal though.

>>11516776
Stop putting 9's at the end of the ellipses.

It's not an approximation you moron. Secondly, the ".999...9" you used ACTUALLY IS an approximation of the value that we're talking about. If approximations were so uncouth, you wouldn't use them.

>>11517187
putting shit after ellipses is the only way to get away from using ellipses at all.

people use ellipses cause they don't want to write out 40 fucking decimal places in a repeating number, but nothing about the repetition explicitly implies "infinitely"

if we got 40 decimal places to write out, the better way of writing this shit is
[math]0.\overline{999}_{r40}[/math] or something like that. Something that actually conveys usefulness instead of inventing ambiguity.

>>11517215
>40 fucking decimal places
no, it's the sigma to infinity you retard

>>11516309
... means infinite decimals retard

>>11517232
>>11517225
infinite isn't an amount of things though, infinity isn't a number. it's finite, but it's arbitrary. more than arbitrary, it's ambiguous with the current notation.

>Fact
The fact is that "dot dot dot" really isn't very good notation. Saying, "Just pretend we can write an infinite number of nines," is a lot different than saying, "Just pretend there's an integer between 39 and 40," but it it's not as different as one might think.

>>11517238
>infinity, it's finite
wew lad

>>11517241
>we can write
lol no
it's "here is an infinite amount and idgaf how it happened"

>>11517243
it's less that "infinite is finite" and more "infinity doesn't even exist, and the things infinity is describing are finite"

>>11517248
Infinity exists, it's just not a number, nor can it's scope be captured and contained in something as easily understood as numbers.

>>11517248
meaningless meta bs
all you need is
-unbounded
-larger than any number

>>11517256
Unboundedness is a property of sets, which means infinity is a property of sets, such as used to describe the suze of the set of all numbers, of which excludes infinity because infinity is not a number.

It has no relation to numbers outside of describing a set of all numbers, which 1 is retarded, theres no need for a set of all numbers; and 2, means it can't be "larger" than any number.

>>11517264
sure bud
https://www.wolframalpha.com/input/?i=infinity

>>11517277
Oh yay its wolfram retard

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

Infinity is a concept made up by retards, for retards.

Anything bigger than 1,000 might as well be infinite to a brainlet retard who believes in infinity's usage as "a number", much less agree's with wolframs definition.

>>11517283
YA4SWKMTAM
yet another 4chan shitposter who knows more than all mathematicians

>>11517283
>unbounded quantity
>unbounded
lrn2read

>>11517287
google that word niggernogger, save humanity the shame of having to deal with you.

>>11517289
lol google
nah I'm staying with WA

>>11517300
go ahead and give me WA's definition of unbounded then, buckeroo

>>11517323
limitless, endless

>>11517325
hey come on now, don't be shy. copy and paste the definition buddybro

>>11517329
https://www.wolframalpha.com/input/?i=bounded
opposite of that

>>11517364
you're trying too hard.
let me help you out retard
https://www.wolframalpha.com/input/?i=unbounded
>seemingly boundless in amount, number, degree, or especially extent
>seemingly
gosh that's not a very empirically helpful word is it.

>>11509365
>>11509559
1/9 = 0.111...
2/9 = 0.222...
8/9 = 0.888...
9/9 = 1

>>11517387
>2/9 = 0.222...
prove it

>>11517374
no bound = endless
prove otherwise

>>11517410
lol what a retard
disprove it

>>11514736
Not that anon, but it's intrinsic to the faith that man can never fully comprehend the fullness of God. I'm an annihilationist deist myself, papists and protestants as a whole disappoint me.

>>11517431
no final digit means no equality.

> 2/9 > 0.2
> 2/9 > 0.22
> 2/9 > 0.222

repeating decimals and unending decimals slip through a crack in the language gap between Fractional to Decimal. for 2/9, it seems to want there to be an integer between 2 and 3, but there isn't one, so it just spits out 2's forever.

if we take the above greentext and expand it
> 2/9 > 0.2222
> ...
> 2/9 > 0.222...
remains valid.

but with all things of this expanding decimal nature, we hardly need more than 8 or 15 decimals of accuracy for a majority of scientific applications, and there is usually a smallest denomination that is insignificant enough to ignore it so we can just "say" that "0.222..." is close enough to the REAL value of 2/9 that it shouldn't matter.

But to have the kind of accuracy needed to achieve lightspeed, 8 or 15 won't cut it, and nor will not having that extra integer between 2 and 3.

>>11517466
Death to America are you fucking serious

>>11517467
Death to Humanity, I'm serious.

>>11517466
finite cases < 2/9
infinite case = 2/9

>>11517466
schizo thinks that 0.999... is an ambiguous symbol which means "0.999... = 0.9" or "0.999 = 0.9999" or "0.999... = 0.999999999" depending on our current situation.
schizo also thinks that numbers have legs and they're running around desperately trying to reach something
schizo also thinks that you need to literally perform an infinite process to work with an infinite process

>>11517515
so what, you imagine there are "infinite" 2's in 0.222-> ?
infinity is not a number. containing infinite 2's is indifferent from saying it contains unlimited 2's, which although is a reasonable assumption, is an assumption with definitions beyond it's scope.

[math]\frac{2}{9} > (\sum_{n=1}^{\infty} \frac{2}{10^n} = 0.222\dots)[/math]
there is no "infinite case". "infinity" is unreachable, unattainable, and would present issues even if it weren't. Such as, in this sum, if n=infinity, would provide [math]\frac{2}{10^{\infty}} = 0[/math], thereby making the rendered value something like [math]0.222\dots 0\dots[/math] in a similar way as [math]\frac{1}{4} = 0.25000\dots[/math], but that treats infinity as both reachable, incremented from the reals, as well as finite, an absolute end; which then begs the question of what is the largest real number before the +1 increment to [math]\infty[/math]?
It also makes the math even more believable that 0.999... !=1 because it would instead be 0.999...0, allowing for a smallest real part to exist 0.000...1.

the only thing the dots imply is continuation.
if
2/9 > 0.2
2/9 > 0.22
2/9 > 0.222
and this is continued
>...
then
2/9 > 0.222...

how long does it continue?
that's left up to the user to decide. It's not predetermined because there is no greatest number or greatest length in the scope of all things.

>>11517584
>0.999... is an ambiguous symbol
nope, it's >>11517246

big number is big hahahah brrrrrrr

>>11517610
>infinity is not a number.
that's precisely why it works

>>11517610
why scream >>11517466 again?
it was bs the first time, and still is

>>11517625
it's precisely why it doesn't work.
the continuation of an expanding decimal is inherently limited finitely, and that finiteness is a measure of the user's own willingness.

in a more abstract way, it's retarded to think
>[math]0.222\dots[/math]
contains a knowable, concise, identified object's worth of repetition. Treating it like that would be no different than treating 0.2222 as knowing it contains four 2's.

infinity is a method, not a solution.
What
>[math]0.222\dots[/math]
really contains is an undefined, unknown, unknowable amount of continuous arbitrary growth of elements that can be bijected with the set of all integers, of which all individual integers within the set are finite in their own utility. There is no [math]\infty[/math]'th integer, nor is there a [math]\dots[/math\'th integer; nor is there a final/greatest integer. It's all simply continuous, without end; and without end in this case is an important factor to determining why 2/9 is greater than 0.222..., because it is merely always a repetitive continuation of finite cases, and for any finite case 2/9 is greater than 0.2->

>>11517644
>infinity
>inherently limited finitely
just listen to yourself

>>11517644
Seems to me like you're just describing infinity in more pretentious terms.

First time posting on /sci/, btw, I've no idea what's going on here. I misclicked.

>>11517649
the "infinite" set of """all""" integers contains integers which are finite. infinity is less a distinction of the "size" of the set and more a property of the set's expanding, endlessly growing nature.
Any test of measuring any single arbitrary element within the set will decisively return a finite integer, however.

>>11517644
>infinity is a method
nah infinity just is.
the method, lim, is real numbers increasing towards it, never reaching
inf isn't in R, it's separate and bigger (duh)

if [math]\frac{1}{\infty} = 0[/math] it becomes a 0% probability of determining any single element of the set. Put it another way, if you were to "randomly pick" a number within the set of all numbers, it has a 0% chance of being ANY identifiable number. This creates a contradiction whether or not it's even possible to "create" or "instantiate" an "infinite set" if you know even a single value within the set.

So this must mean [math]\frac{1}{\infty} = 0[/math] is a false statement for any variety of reasons.

>>11517652
>endlessly growing
nah it just is what it is, there's no cute little engine chugging along

>>11517669
>1/∞=0 is a false statement
[citation needed]
because any academic source claims your talking bs

>>11509365
>>11509421
>>11509559
>>11510910
>>11510975
>>11510989
>>11511116
>>11511803
>>11513142
>>11514243
>>11514246
>>11514260
>>11516654
>>11516743
>>11517241
>>11517374
>>11517466
>>11517652
>>11517669

https://strawpoll.com/fz4g5wxa

>>11517669
>1/∞=0 is a false statement
[citation needed]
because any academic source claims you're talking bs

>>11517672
well good thing infinity isn't.
there's no magical space number that solves all problems.

>>11517679
>academia

>>11517680
>magical space number
nope, it's defined and universally used
>>11514258

>>11517684
found the dropout

x=0.99999...
10x=9.99999...
9x=9
x=1
prove me wrong

>>11517691
nigga the proof was provided to you in the post you quoted the end of, what is your issue? You have the gall to call me a dropout and you can't even process a 100 word post?
let me expand
[math]\frac{1}{4}[/math]. If you were to randomly pick a number between 1->4, you have a 25% chance of guessing right.
[math]\frac{1}{100}[/math] if you were to randomly pick a number between 1->100, you have a 1% chance of guessing right. If you were to say the number must exist in the range between 1->50, you have a 50% chance of being right.

[math]\frac{1}{\infty}[/math] now you got this issue. If you were to randomly pick a number between 1->inf, you have a 0% chance of guessing right. Alternatively, if you were to say the number must exist in the range between 1->50,000,000,000 - then you still have a 0% chance of being right. If you extend that range to anything, it still holds that you have a 0% chance of the randomly picked number existing in that range.

If you knew even 1 value within the set, and claimed the set was infinite, [math]\frac{1}{\infty} = 0[/math] would be required to be false, otherwise the falsity lies on the ability to create an infinite set while knowing any values inside it.

>>11517709
schizo wall-of-text
>random choosing, guessing
rambling holy shit, take your pills

>>11517713
bravo retard
>>11517622

>>11517717
>infinity is about 4
k

>>11517713
1/infinity = 1/infinity

Ur dumb

>>11517729
even your retardation is bounded by your eventual death, you weird little bugman.

>>11517733
>happy random grabbing
look mom i'm mathing

>>11517738
i swear you learned english from a chatbot. you make no sense.

>>11517741
let go of my ass you little perv
t. mom

>>11517746

>>11509559
.0...1 isn't a cauchy sequence and hence isn't a real number. fuck off

>>11517755
>not grabbing that, nossir

>>11517709
This confirms it. Infinity is meaningless in math.

>>11517792
no u

>>11517875
If [math]\frac{1}{\infty} = 0[/math] then a set containing infinite numbers contains no knowable numbers, unless [math]\frac{\infty}{\infty} = 1[/math], allowing for a randomly picked number to 100% exist within the scope of the set.

if [math]\frac{\infty}{\infty} \neq 1[/math] then [math]\frac{1}{\infty} \neq 0 [/math]

>>11517951
inf/inf undefined
1/inf=0

>>11518033
>1/inf=0
then it's impossible to have an infinite set containing any known elements.

Once again infinity is used to prove it doesn't exist.

>>11509559
Correct
>>11510962
It doesn't because infinity doesn't exist, but if we're even dealing with "infinite sequences" then we're treating infinity as a number and in this fictional scenario it can terminate. Retard.
>>11510989
based

>>11514239
[0,1) and [0,1] are not the same, retard

>>11520252
No one said they were, retard.

>>11510989
ok numbnuts

>>11517709
oh wow this is a completely different kind of retardation than the 1/3 > 0.333... schizo
tell us something more