/sci/ - Science & Math

>0.999... gets close
0.999... is static, the length is aleph_0 from the get go.
Your naive cartoon vision of a diesel engine chugging along is ridiculous. Embarrassing even.

>>12284647
>0.999... is static, the length is aleph_0 from the get go.
i dont know what aleph zero is so it does not matter

>Your naive cartoon vision of a diesel engine chugging along is ridiculous. Embarrassing even.
Diesel engine? What the fuck are you talking about?

>>12284655
>i dont know what aleph zero is
shocker

>>12284637
Nigger, if there is a salt impurity in the water, the volume will never be 0.999..., it will always be 0.999...8

>>12284678
>Nigger, if there is a salt impurity in the water, the volume will never be 0.999..., it will always be 0.999...8
why? you can do the reverse, take a 100% pure body of water that is infinite
now put 1 gram of salt in it, how pure is it now?

>>12284711
100%

It is a game of semantics. .33 infinitely repeating is different from 1/3. Simple as that

>>12284637
When is this information relevant?

it's funny how this board can have the same exact thread for almost a decade now

>>12284776
chemistry

>>12284637
You are correct 0.9999... does not equal one.

The limit does, but the sum does not. Retards struggle with this nuance.

Imagine walking down a hallway but you take smaller and smaller steps infinitely

Checkmate

>>12284711
It is an infinitely large, impure body of water.

>>12284771
wrong

>>12284783
>The limit does
the limit of what?

>>12284806
No, actually he is based and pilled. Try again.

>>12284637
>0.99999999999999 doesn’t equal one
In all real world allocations it does. You’re autistic anon.

>>12284783
>let's pretend finite is infinite

>>12284813
Infinity only exists in your head anon.

>>12284817
that's where math is done, duh

>>12284824
Infinity isn’t a thing that exists, nothing is infinite.

>>12284829
>nothing is infinite.
except your stupidity

prove me wrong
okay, 0.999...999, 0.999...998, 0.999...955 etc are all different numbers, differing by infinitesimals, but no matter how many infinitesimals you add/subtract from the number, they will never leave the ellipsis and change non-infinitesimal digit places so you can just ignore what happens to the infinitesimals and equate 0.999...<insert infinitesimal digits here> and 1, as they only differ by infinitesimals, which don't matter because see above

>>12284637
>Now increase the volune of water to infinity, like the never ending 0.999...
>Even if salt in relation tothe total approaches zero, it cannot be zero
Yes it can, because you increased the volume of water to infinity. This will also probably blow your mind: events with probability 0 may occur over infinite trials.

>>12284783
0.999... is not a limiting process.
0.9 + 0.99 + 0.999 + ... is a limiting process.

0.999... is simply a static object.
It doesn't change.
It's just a zero, a decimal point, and nines that don't end.
There is no difference between 0.999... and 1. It's the exact same thing.

>>12284637
>0.999... isn't 1 because it has a gram of salt
It doesn't. It's all nines forever, there's no salt.

>>12285728
anything after the ellipsis =0 and can be ignored

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

>>12284783
So what you're saying is that 0.999... is not a number?

>>12285779
no, it's a different way of writing Sum_{k=1..∞} 9 * 10^(-k)

>>12285782
same with 1.000..., it equals 1, but it's not 1 itself

>>12285728
Numbers that include infinitesimals are explicitly two strings of digits, not one string of digits.
Their ordinal structure is ω+c, ranging from ω+1 to ω+ω.
This is entirely unrelated to the ordinal structure of 0.999..., which is simply ω.

>>12285779
>>12285782
>>12285784
You and the poster you replied to are both wrong.
0.999... is not a sum.
0.999... is exactly 1.

>>12285788
every number written with digits is a sum, anon

how can 0,999 and 1 be the same thing?
t. brainlet

>>12285791
Nope.
You can describe a sum that adds up to any number, but the sum is not the number.

>>12285794
They're not. Any number of 9s that stop isn't the same thing as 1

>>12285797
so what are these people discussing about?

>>12285798
9s that don't stop.

God cursed SODOMITES insisting that 0.999...= 1
Christ. I have had enough of this bullshit. Hear me now. I call for...

A HOLY CRUSADE!

First we retake Constantinople, then we reclaim mathematics for the GLORY OF GOD, putting to the sword any heretic who claims infinity can exist. EVEN AS A CONCEPT!

HEAR ME BROTHERS! We shall cleanse the Earth of HERESY!

BROTHERS OF THE ONE TRUE FINITE AND DISCRETE UNIVERSE! SAY IT WITH ME!

DEUS VULT!
DEUS VULT!
DEUS VULT!

>>12285800
well, if they dont stop, they cant be 1

>>12285806
No, they can't not be 1.
The difference is always 0.
1 - 0.999... = 0.000...

DEUS VULT!
DEUS VULT!
DEUS VULT!

>>12285795
so 1+1 is not 2 is what you're saying?

>>12286022
2 is a number.
2.000... is a number.
1.999... is a number.
1+1 isn't a number, it's two numbers and a binary operator which tells you to add the two numbers together.

1+1 is a sum which gives you the number 2.

>>12285782
>>12285765
brainlet, the symbol [math]\sum_{n=0}^{\infty}a_n[/math] stands for both the sequence of partial sums and the limit

>>12286058
1/inf=0

>>12286073
so?

>>12284637

.999999... is basically a made up number just for the sake of a hypothetical.

There's no fraction that comes out to .999999...., like 8/9=.8888888....

>>12286087
0.9...=1

>>12286097
1/9=0.111...
+
8/9=0.888...
=
9/9=0.999...

>>12286097
>no fraction that comes out to .999999....
Sure there is. 1/1, for example.

>>12286111
Holy trips

>>12286105
so?

>>12286111
Bravo! That is cool, hope it will put all similar threads to an end

>>12286111
1-1+1-1+...=1-(1-1+1-1+...)
s=1-s
s=0.5

1-1+1-1+...=1-(1-1+1-1+...)
s=1-s
s=0.5

1/9 = 0.111...
2/9 = 0.222...
3/9 = 0.333...
4/9 = 0.444...
5/9 = 0.555...
6/9 = 0.666...
7/9 = 0.777...
8/9 = 0.888...
9/9 = 0.999...
QED

>>12287508
>4/9 = 0.444...
>6/9 = 0.666...
>0.444... + 0.666... = 1
>10/9 = 1
Imagine being this retarded. Your "proof" is easily debunked.

>>12287529
>>0.444... + 0.666... = 1
0.444... + 0.666... = 1.111...
Imagine being this retarded. Your "counterproof" is easily debunked.

In case brainlet anon doesn't know how to do maths:
0.4 + 0.6 = 1
0.04 + 0.06 = 0.1
0.004 + 0.006 = 0.01
...
in the end you get 1.111..., which is 10/9 indeed

>>12284829
honestly anon, in a real setting, both finite AND infinite are impossible. by human understanding, the universe is paradoxical.

>>12284637
The only way that 0.999... could be different to 1 would be if one of the digits in the line of 9s was not a 9. They are all 9s, therefore 0.999...=1

>>12287629
0.999... is an infinite set that is infinitely smaller than one.

If you add .999... to .999... infinitely you get INFINITEY MINUS ONE

>>12287941
>inf=3
hurr durr

>>12284637
Jesus fucking christ how did this retarded meme get so widespread
OBVIOUSLY we can say that practically speaking the two are equal for many but not all applications
but just looking at the two numbers you know in your fucking brain that you’re talking about two different things!

>>12284771
This anon gets it. Semantically, they're not the same. Mathematically they're identical.

>>12287529
>>12287536
>>12287552
>>12287629
If I fuck your mom and pull out when I'm 0.999... of the way toward cumming in her rotten cunt, would your mom still give birth to you? No, because I pulled out before being 100% of the way to splooging. Clearly, 0.999... is not equal to 1. If you still believe that 0.999...=1 then what if I rape your mom two more times and give you 1.999... more siblings? That doesn't make sense, does it? Because you can only have a whole number of siblings, you can't have a decimal number. But if 0.999...=1 then 1.999...=2, so it is possible to have a decimal number of rape babies. You fucking moron.

>>12284711
>1 gram
Why stop there? You could dump truckloads of salt into it forever and it would stay 100% pure right up until the amount of salt becomes infinite when it would drop suddenly to 50% or whatever ratio of salt it ends up as.

>>12285804
I laughed. Thanks anon.

>>12288271
what you're saying here makes the concept of infinity sound even more retarded

>>12288816
That's because he's a retard.
0.999... has no salt at all.
And there's no line between infinity and not infinity.

>>12288022
No, semantically they're also identical.

>>12288015
No difference at all.
Literally the same number.
Literally the same thing.

>>12284783
the infinite sum literally does equal 1 retard

>>12284637
>increase the volume of water to infinity

theres your flaw, if you could increase to infinite water (you can't) then the volume of salt would actually be zero.

stop trying to apply finite intuition at the infinite level, that's why you keep misunderstanding.

>>12286097
>no fraction that comes out to .9999....

kek

>>12284829
Space is quite likely actually infinite. You could keep travelling in one direction and never stop, it's infinite.

>>12289069
Suppose there exists a number in the series 0.9, 0.99, 0.999 ... that equals one. Let that number be a(n). Then a(n+1)>a(n) by definition, then a(n+1)>1, which is impossible.

>>12285795
what is e then fucking retard

>>12289083
>Suppose there exists a number in the series 0.9, 0.99, 0.999 ... that equals one.

there isn't, are we just making up arbitrary axioms now? .999... is not an element of the set {0.9, 0.99, 0.999, ... }

>>12289083
infinite sum is the limit of this sequence you retard

what do .999... does not equal 1 fags do when they take calc 2? do they just fail?

>>12289085
It's a number, why?

>>12289098
how so? {0.9, 0.99, 0.999} is an infinite set and thus contains numbers with all possible lengths of (99999)s after the (0.)

>>12289143
first of all, your reasoning is retarded. {0.99, 0.9999, 0.999999,..} is an infinite set, but it doesn't contain numbers with all possible lengths of (99999)s after the (0.). for example it doesn't contain 0.9
second of all, this set only contains all FINITE lengths of (99999)s. 0.999... is not in this set

>>12284637
>Physical appeal to a purely mathematical construct
Your mistake was assuming that math and reality exist within the same ruleset. They don't.

>>12289150
How many (9)s are there in the a(inf) of {0.9, 0.99, 0.999, ...} then?

>>12289143
Different poster, but let's say 0.999... is in the set you describe.
What number in your set are you saying would come "after" 0.999...?

>>12289162
[math]a(\infty)[/math] is a priori undefined. it is however very reasonable to put [math]a(\infty) = \lim_{n\to\infty}a(n) = 1[/math]. then the answer to "how many (9)s are there in [math]a(\infty)[/math]" is [math]\aleph_0[/math].

>>12289166
0.9999... +(9/10^inf)

>>12289178
And what number are saying would come "before" 0.999...?

>>12289178
so 1+0, got it

>>12284771
>>12285784
>>12289062
>>12288022
>>12284806
What is semantics? Is there a book about this semantic matters in mathematics?

>>12289263
Semantics is what something means.
1 and 0.999... don't mean anything different, so they are semantically the same thing.

>>12289268
Any book, article or citation? I understand the math, sometimes its syntax doesn't even require the interpretation so i don't really care about the pseudo-controversy of 1 =0.(9) in math. What i need is linguistic analysis of this asap!

>>12289280
Book, article, or citation of what?
Semantics isn't a math term. It's a word we use to describe the study of meaning. It comes from an old greek word for indicating something, pointing something out.

>>12284637
It's different than that. It's like you have 1L of water, and you check if any of it is salt. Check if there's a 0.1 L portion of salt. No? Then it's 0.9 water. Check if there's 0.01L salt. No? So 0.99. You keep checking, and you never find salt, so you get 0.9999... which is pure, saltless, and equivalent to 1.

>>12289156
Un-meditated take.

>>12289344
finally someone who understands how decimal expansion works

>>12289344
Circular reasoning.

>>12284637
>Even if salt in relation tothe total approaches zero, it cannot be zero
show me. Pick a random molecule from the stack. What’s the probability of it being either a sodium or chloride ion? It is literally impossible. No matter how much water you take from the solution, you won’t find any salt, because there is none.
>b-b-but anon, how can it magically disappear?
by magically adding an infinite quantity of water.

>>12289439
Not the same poster, but there is no salt in 0.999...
It's 0.000... salt forever.

>>12284637
Distance to one is 0 but it's not same point as one, and if you divide this zero in half you can get another different point.

>>12284771
nice failed assumption

>>12290897
>Distance to one is 0 but it's not same point as one
wew lad

>>12284637
>so far salt is 1/101
It doesn't work that way. The salt is 1/100.

>>12284637
There is no number between .99... and 1. They are the exact same number. They do the same things when manipulated. They are the same number. Using a physical model like this tells us nothing, you can't have an infinitely large body of water. Also, idk why nobody pointed this out, your equation is wrong. A ml of water is a gram, so your initial math is correct, however, a gram of salt is not a milliliter of volume, but this isnt the priblem with what you said haha.
Would it help you to visualise that no matter how you sampled it, you would never get the salt? Like, if you had a house to get to, but you had to drive across an infinite plane to it, it literally could not be anywhere. Any placement of the house a distance away from you would negate its infinite distance from you.
In the same way, a limit is just saying what has to be. If I have the parabola y = x^2 and the line y =0, and some equation that is less than or equal to y = x^2 and greater than or equal than y = 0, can you see how it would have to be zero at zero? That is the only possible value that satisfies this relationship. With a limit, we can ask a similar question of any equation. When we approach x value, what, if anything do we approach? For .99... the number we approach is 1, at any possible finite sequence, it is not 1, qbsolutely, but at the end of infinity, the only value possible for this value is 1. Any .99999 would have already have been reached. The value when all .99999s have been gotten rid of is 1. It is indistinguishable from this infinite set of .99s.
With your hypothetical, the salt can not take up any amount of volume relative to this infinity. If it did so, it wouldnt be an infinity. There isnt a bound to point at and say, we are this % of it. Anon, imagine I have a finitearrangement of 1s and 0s, say 01. Surely, you would not say this arrangement is some percentage of the 0s and 1s possible? There is no control on how many patterns there can be. They are infinite.

>>12291992
YOU WILL BURN IN THE DISCRETE FIRES OF FINITE HELL, HERETIC!

DEUS VULT!

>>12289062
Take three cakes, circle one and you have 1/3. Take one cake and cut it into three pieces, circle one and you have 0.333...

>>12292060
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...

>>12289268
correct about semantics definition but the exact opposite about the difference, mathematically it can be disputed if they are the same thing, but semantically they definitely arent the same

>>12292091
What do you think is the difference in what they mean?

>>12292060
Correct. 0.333... is also semantically (and mathematically) the same as 1/3.

>>12292114
mathematically the same thing = homosexual

>>12292123
? Your train of thought is a bit too jumpy to follow here.
What are you agreeing or disagreeing is or isn't the same thing.

Are you proposing a difference between 1 and 0.999... in terms of math? If so, what?

Are you proposing a difference between 1 and 0.999... in terms of meaning? If so, what?

>>12292142
shut up faggot

>>12292272
No.

>>12292280
>t. noisy faggot

>>12292283
No.

Assume to contradiction that x is a rational number such that

0.999... < x < 1

0.999... is greater than any finite string of 9s so for any natural number n

1-1/10^n < 0.999... < x < 1

1-x < 1/10^n

10^n < 1/(1-x)

n < log(1/(1-x))

Let n = ceiling(log(1/(1-x)))+1

ceiling(log(1/(1-x)))+1 < log(1/(1-x))

This is a contradiction, so x does not exist and 0.999... = 1.

>>12292332
>t. repetetive noisy faggot

>>12292391
No.

>>12292336
It's not same point, it's point right next to one.

>>12286111
Now do that in base 9.
#DEBOONKED

>>12287589
COPE

>>12285743
>This will also probably blow your mind: events with probability 0 may occur over infinite trials.

Only theoretical, but the chance of it happening is infinitely small, collapsing both infinites back into zero. So yes, but only on paper, never in the real world.

>>12292439
Where is (1+0.999...)/2 then?

>>12292448
>Now spell zzz without a z.

>>12292336
hey i found a number that fits inside 0.999... < x < 1
0.999... is nothing but
[math]\sum_{n=1}^{\infty}\frac{9}{10^{n}}[/math]
the number is
0.AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA... (base 11)
which is merely
[math]\sum_{n=1}^{\infty}\frac{10}{11^{n}}[/math]
u mad?

>>12284637
Faggotry, Faggotry everywhere.

>>12292471
In decimal, that works out to .9090909090...
Nice try, sweatie. Thank you for playing.

If 0.999... = 1 doesn't that mean that infinity doesn't exist?

>>12292481
How are those concepts related?

>>12292478

>>12284637
>picks up a rock
at least the inside of it is 100% inorganic material

>>12292457

>>12292489
Well, you call 0.999... an infinite number yet it equals 1 a finite number. Something that's infinite can't be finite.

>>12292500
do it, spell zzz with a z hotshot

>>12292505
No, I don't call 0.999... an infinite number.

>>12292508
>I don't
Then why did you put ... after 0.999 just now. You clearly do.

>>12292515
Because the nines never end.

So what's 1 minus 0.999... then?

0.999 = 1 (0.999)

>>12292528
Exactly, anon. That's why it's called infinite number.

>>12292542
No, that's like saying "infinite" means finite because it's 8 letters long.

>>12284637
If they are NOT the same then please show how they differ from each other

>>12292547
Anon, are you saying that 0.999... doesn't represent infinity?

>>12292552
How could it? Considering it only ever approaches 1.

>>12292552
No, it represents 1.

>>12292448
1/10=0.1
+
8/10=0.8
=
10/10=1

>>12292556
It never approaches 1, it is 1.

>>12292556
>>12292564
So, looks like we agree that infinity doesn't and can't exist, after all 0.999... equals 1.

>>12292580
What is infinity, anyway?

>>12292580
My question was how are those concepts related?
If you don't have an answer, I guess it means they're not related.
>>12292481
>>12292489

>>12292588
They discuss aspects of Maya.

>>12292590
Maya herself dismissed those allegations as cobalt blue.

>>12292583
Infinity is an unbounded quantity greater than every real number.

>>12292588
You are asking how a infinite number is releated to infinity? Anon...

>>12292600
What’s a number? What’s infinity? What’s a quantity with no bounds? You have nothing.

>>12292595
>color

>>12292495
xd

>>12292621
What infinite number?

>>12292637
>what’s a number
A letter from the mathematical language.
>what's infinity
Continuous repeating of something indefinitely.
>what’s a quantity with no bounds
Infinity.

>>12292657
Exactly.

>>12292675
Thank you.

>>12292637
> schizo having a tantrum
lol, it's the definition

>>12292667
> A letter
L.
>Continuous repeating
L.
>Infinity
Unfinity.

>>12284637
Top quality larping.

Had a kek, thanks friend.

>>12292689
What is the definition?

>>12292697
https://www.wolframalpha.com/input/?i=infinity

>>12292704
Without using numbers describe infinity.

>>12292707
no can do
this isn't a poet festival, retard

>>12292716
Use language to describe numbers or is math incoherent?

>>12292707
No end.

>>12292719
no u

>>12292720
Where does it begin?

>>12292722
>no u.
Fixed.

>>12292725
what's your point

>>12292439
There is no such thing, the reals are a densely ordered set.

>>12292723
In the beginning.

>>12292723
Wherever you want, or nowhere.
Infinity just means no end, doesn't say anything about a beginning.

>>12292732
The beginning of the end.
>>12292736
>Infinity just means no end
So... the end.

>>12292743
>So... the end.
Of what?

>>12292751
What.

>>12292755
Noon.

>>12292759
Death toll.

>>12292763
Ivy.

>>12292765
Poise.

>>12292768
Porpoise.

>>12284637
>Imagine a body of water
This board is 90+ IQ only

>>12292875
89.999... here

>>12292939
So you are exactly 90 IQ and therefore not allowed here because this board is 90+ IQ only

>>12292950
90+ means ≥90

>>12293003
no it means 90+ε

>>12292791
Purposeless.

>>12293115
Porpoiseful.

>>12289109
e is literally defined by an infinite sum

>>12289143
your set is essentially the same as {1,2,3,...} the set contains ALL FINITE NUMBERS but infinity itself isn't a member of the set. .999.... is an infinite decimal.

>>12294388
No, you have it backwards: e is literally a number.
Every infinite sum that adds up to e is defined to have a limit equal to the number e, not the other way around.

>>12292471
That's true. 0.AAA... - 0.999... = (10/11-9/10) + (10/11^2-9/10^2) + ... > 0
How will onefags ever recover?