/sci/ - Science & Math

[Anonymous No.9889587]

Why is this possible? There is a fallacy within mathematics!

[Anonymous No.9889590]

0.999... Is meanigless.

[Anonymous No.9889597]

>>9889587
your just rarted

[Anonymous No.9889598]

>>9889590
I think you mean "useless"
Having two numbers represent the same number is retarded

[Anonymous No.9889600]

>>9889590
No it isn't.
Math represents reality. 0.999 is how much the whole (1) can break down and the above showcases it's infinite unless it's not.

What can make it not be? What is the final particle? Why can't we find it?

0.3333... is 1/3

Again, something finite. Why

Is math flawed? Or is the universe playing with us

[Anonymous No.9889609]

>>9889587
The logic in that proof is flawed.
It treats 0.999 as the unit (1) and not part of the unit. 0.999 is never the unit, but part of it.

How can we find what the tipping point from the decimal to the full, undivided unit is?

[Anonymous No.9889612]

>>9889587
convergence and continuity

[Anonymous No.9889615]

>>9889612
elaborate

[Anonymous No.9889617]

>>9889615
on basic precalc?

[Anonymous No.9889619]

....9999.0 = x /10
9999.9 = x/10 -x
0.9 = -9x/10 *10
9 = -9x /-9
x = -1

[Anonymous No.9889623]

>>9889587
You are assuming that every real number has a unique representation using decimals. It is wrong.

Any research on the decimal numeral system will tell you that. Why don't you try to do researches about it before making a stupid thread?

[Anonymous No.9889625]

>>9889598
Not really, equivalence classes are a proper way of constructing the real numbers.
>>9889600
You don't know what you are talking about.

[Anonymous No.9889632]

>>9889625
>You don't know what you are talking about.
I say you don't. Decimal is a unit as long as we define it as such. Since infinity isn't a thing, it all comes down to 1

>>9889623
How much can 1 fragment?

[Anonymous No.9889697]

>>9889587
>There is a fallacy within mathematics!
>fallacy
We don't say fallacy anymore, we say it's "problematic".

[Anonymous No.9889701]

>>9889697
>phallusy

[Anonymous No.9889712]

[Anonymous No.9889729]

>>9889712
this just proves mathematics can't adequately represent our reality.
Which means that our brains haven't evolved adequately to create a new tool to describe it.

[Anonymous No.9889732]

>>9889729
>our brains haven't evolved
speak 4 yourself m8

[Anonymous No.9889882]

>>9889732
you are an apelet

[Anonymous No.9889985]

>>9889617
>precalc
not precalc

[Anonymous No.9889986]

This basically shows how the decimal system has the big gay. That's all

[Anonymous No.9889987]

>>9889587
>There is a fallacy within mathematics!
No, there is a fallacy within your understanding of mathematics. The math itself is fine.

[Anonymous No.9890117]

>>9889987
really huh? how so?

[Anonymous No.9890125]

>>9889598
No, decimal expansions just aren't unique. Everyone, get this into your head.

[Anonymous No.9890135]

>>9889590
... if you wanna having sex with qt girl

[Anonymous No.9890137]

>>9889986
b-but other systems are the same
0,11111111 (binary) = 1

[Anonymous No.9890140]

>>9889598
1/3 2/6
[math]\mathbb{C}[/math] is retarded

[Anonymous No.9890145]

>>9889598
1/3 = 2/6
[math]\mathbb{Q}[/math] is retarded

[Anonymous No.9890146]

>>9890140
Both of those fractions exist in the real world. 1 blue marble and 2 red marbles, or 2 blue marbles and 6 red marbles. Only the relationship between the part and the whole is constant.

[Anonymous No.9890149]

>>9890146
4 red marbles*

[Anonymous No.9890197]

>>9889587
This assumes all infinities are the same.

[Anonymous No.9890217]

>>9889587
0,999... is by definition 9/10+9/100+9/1000+...
Now multiply by 10, you get 9/1+9/10+9/100+...

[Anonymous No.9890223]

>>9890217
(10^n - 1) / (10^n)
where n has no limit,
is approximated by 0.999....
But there will always be a difference of 1 between the numerator and the denominator.

[Anonymous No.9890244]

If you don't think 0.999... = 1 then you have a different idea of what 0.999... means, but 0.999... = 1 follows from the way real numbers and limits are defined. If you don't like it you are free to construct your own number system and see how it works out.

[Anonymous No.9890273]

>>9889587
you already set x = 0.999... you fucking moron

[Anonymous No.9890311]

>>9890223
Yeah, I agree, 0,999...9 is not 1, 0,999... however is.

[Anonymous No.9890315]

>>9889712
>An appeal to intuition:

>Take a bottle of water. Pour it into three glasses, so the amount of water is exactly the same in each glass. You know that 1/3 is o.333..., and that three sets of these will be 0.333... + 0.333... + 0.333... = 0.999...

>But this came from 1 bottle, so you know that 0.999... = 1

The real answer here is you can't divide evenly into 1/3rds. If you try to pour 1 glass into three bottles they can never be exactly even.

1 = 0.333 + 0.333 + 0.334
0.333... is just an abstract concept.

[Anonymous No.9890318]

>>9890315
>The real answer here is you can't divide evenly into 1/3rds.
*The real answer here is you can't divide ONE UNIT evenly into 1/3rds.

[Anonymous No.9890320]

>>9890273
and?

[Anonymous No.9890323]

>>9890311
As n increases, the difference between the numerator is shown below:

1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1.......

There are infinite 1’s, meaning there is never a difference of 0.

[Anonymous No.9890358]

>>9890323
Did you seriously type out like a hundred 1s to convince me that the fraction is never 1? I know that, 0,999... is not any of those fractions.

[Anonymous No.9890361]

>>9889632
Maybe it's a point that's infinitely precise, sort of like how the circumference of a circle has no final decimal point that we can currently think of without putting an end cap on it

[Anonymous No.9890403]

>_<

[Anonymous No.9890543]

>>9889615
0.999... isn't really a number you fucking retard, it's just shorthand for the convergent series 9/10^n. Now use a basic limit comparison test to show that the series converges to one.

[Anonymous No.9890551]

>>9889712
I'm pretty sure the first 2 "proofs" are circular /fallacious, only the infinite series one is a legitimite proof.

[Anonymous No.9890560]

>>9889587
so tl dr you do not agree that 1=0.999999999999999999999...................
well done writing the "proof" which serves no purpose at all

[Anonymous No.9890592]

ITT: Proof that "not one == one"

[Anonymous No.9890695]

>>9889587
Take x=.9
10x=9
10x=9+0*x
Now take x=.99
10x=9.9
10x=9+.9
Notice x does not equal .9 but .99

[Anonymous No.9890747]

>>9890695
your point being? 9 is defined and finite, 0.999.. isn't

[Anonymous No.9890938]

>>9889985
Yes it is

[Anonymous No.9891015]

>>9889587
Its false because step 2 is wrong and omits information for later steps.

0.999... × 10 [math]\neq[/math] 9.999...

there were already a maximum of an infinite amount of 9's in 0.999... , but 9.999... implies infinity+1 via
[x].[xxx...] 》
[1+].[inf..]

the correct way to think about it is just simplifying and doing the math on non-repeating.

>x = 0.999
>10x = 9.990
>10x - x = 8.991
>9x = 8.991
>8.991 ÷ 9 = 0.999
>x = 0.999

mathlet brainlet retards will try to say
>8.999...1 cant exist cause nothing can come after infinity!!!!
but they're gaslighting homos who forget that 0.999... cant exist because you can't reach infinity in the first place either.
Feel free to disregard them.

[Anonymous No.9892645]

>>9890244
>>9890318
1 + 1 + 1 = 3
3/3= 1/3 + 1/3 + 1/3

this is equivalent to:
Have a friend video record this on his cellphone:
take a shot glass. Fill it with vodka and dump it into a tumbler 3 times. take magic marker and mark of the level of vodka in the tumber. Drink vodka in tumbler (exhale to the right first).
Npw reverse the video sequence. You have just constructed 3rds.

[Anonymous No.9892658]

I become inordinately angry at these finitist threads. I can not contain the anger, after reading them I must either punch my couch or masturbate to relieve myself. Refrain from making them, please.

[Sage No.9892729]

>>9889632
This comment perfectly explains what I’ve been saying, retards btfo.

[Anonymous No.9892734]

>>9889587
0.9999...
Is a limit.

[Anonymous No.9892761]

>>9889587
this works because 0.9999... is finite. If it wasn't you could produce arbitrary conclusions from it. Also this only makes sense in R or at least Q, as in non-standard R, 0.999... could (awkwardly) stand for something like 1-d (which would again be 1 if you then strip the infinitessimal parts from it to project it into R).

[Anonymous No.9892776]

>>9892658
why not try punching your dick and jerking off your couch instead

[Anonymous No.9892797]

>>9889587
It is idiotic, but quite possible. Since x=.999... just means by definition that x is equal to 1, you get 10x=9.999... which is 10, again by definition.
If you do not agree, then please explain what you think that the notation x= .999... means, if not that x is equal to 1.

[Anonymous No.9893491]

>>9889729
>doesn't know about infinitesimal analysis
>calls others apelets

[Anonymous No.9893938]

>>9889587
you already defined x so you cant use marh this way to get x again... only if there is another value exp. X1 and x2 if im correct, please excuse me :)

[Anonymous No.9893958]

>>9889587
It isn't. It's just an intuitive explanation for brainlets.

[Anonymous No.9894601]

>>9889587
it just means that 1 - 0.999... = 0.
Duh

[Anonymous No.9894637]

>>9889590
Your life is meaningless

[Anonymous No.9895010]

every engineer knows 0.9=1 and 0.8=1
absolute state of mathfags

[Anonymous No.9895056]

>>9889600
0.333.. isn't 1/3 though, it's a limite actually, it tends toward 1/3 without ever reaching it because there is always a tiny bit missing.

For exemple : lim 1/n = 0 , so you might want to say with your notations lim 1/n = 1/9999999... = 0 (1)
implying that 1/99999..= lim 1/n , which is wrong because in (1), the thing on the right is a number and the things on the right aren't, they are kinda like a propriety of (1/n).

To sum up, it's a matter of mathematical objects, you should check whole series and analysis for more understanding on the matter.

[Anonymous No.9895119]

>>9895056
This. The limit of a thing is what defines it and differentiates it from what it is not. It is where it ceases to be. The limit of
(10^n - 1) / (10^n)
is 1, but the sequence itself is equal to 0.999...

If 0.999... were ever equal to 1, then what is preventing it from continually adding values and surpassing 1? The answer is that it can ever equal 1 in the first place.

If you construct an image within your mind, of one wall constantly moving towards another, which is still and 10 units from the first, and the first wall will always move 9/10 the distance between them, then you can imagine that, the second movement from 9 units to 9.9 units will be visually the same as from 0 to 9, but only at the smaller scale. If you only zoom in after every movement so that the two walls appear to be the same distance as in the beginning, then it will be clear that the process will never end, that the first wall will never reach the second. It is at this point where someone claims, “But you’re thinking finitely, you have to think in terms of infinity”
Well, do explain how an infinite number of movements will somehow allow the first wall to touch the second. I absolutely cannot see how anyone can believe that it is possible without drawing a veil over his own comprehension and pretending to know what he’s talking about.

[Anonymous No.9895162]

>>9895119
>If you only zoom in after every movement so that the two walls appear to be the same distance as in the beginning, then it will be clear that the process will never end, that the first wall will never reach the second.
Good point. You can even imagine that you never go past 9. Just add 9 to 0 and start back again infinitely times and you will supposedly end up at 10

[Anonymous No.9895222]

>>9890358
there arent 100

[Anonymous No.9895238]

>>9895119
This is a picture of why you're wrong.

[Anonymous No.9895250]

Think of every digit being a 3x3 box so you have nine squares. Once you fill in all of them, "adding" one more empties them and fills a square in the box on the left. So the first "number" is an empty box representing zero. So if you are at 9 and are going to ten, every box to the right needs to be filled to infinity. With .999... all the boxes are filled in to infinity. If you think there is a ...001 at the end, well that is filled in as well. There is no point past the decimal point that is not accounted for. There is no number between .999... and 1.

[Anonymous No.9895263]

>>9895238
>>9895238
>NP = s -1
This assumes the sequence x + x^2 + x^3... actually reaches N, which hasn’t been proved.

[Anonymous No.9895275]

>>9895263
It's easily provable that every point on ON can be uniquely mapped to a corresponding segment on or above it, for some power x^n, and vice versa, so the length of ON is fully exhausted by the sequence of lengths 1 + x + x^2 + ... and this sequence of lengths is fully exhausted by the length of ON, so they are equal.

This pic illustrates (an initial finite segment of) my mapping. You can't point to a single point of ON that isn't covered by the full mapping.

[Anonymous No.9895286]

>>9895119
[math]
x= \frac{1}{10} \\
0. \overline{9}=9x+9x^2+9x^3+9x^4+ \cdots \\
0. \overline{9}=9x \left (1+x+x^2+x^3+ \cdots \right ) \\
0. \overline{9}=(1-x) \left (1+\mathbf{x}+x^2+\mathbf{x^3}+x^4+ \cdots \right ) \\
0. \overline{9}=1-x+ \mathbf{x-x^2}+x^2-x^3+ \mathbf{x^3-x^4}+x^4-x^5+ \cdots \\
0. \overline{9}=1
[/math]

[Anonymous No.9895289]

>>9895275
>You can't point to a single point of ON that isn't covered by the full mapping.
N

[Anonymous No.9895308]

You're like a little baby, watch this

[math]\frac{2.\overline9}{3} \neq 0.\overline9[/math]

[Anonymous No.9895314]

>>9895286
>assuming infinite sums can be multiplied like any other number
You must show the intuitive nature of these infinite entities before you perform operations with them. For example, address the experiment in>>9895119

[Anonymous No.9895315]

>>9895289
Goes to P. And also has a length of zero.

[Anonymous No.9895320]

>>9895315
Scratch that, I meant P, which is the end of NP, as we’re trying to prove if s-1 actually reaches the end of NP

[Anonymous No.9895332]

>>9895320
NP = ON - 1 by definition because AN = NP (because it's a right triangle of gradient 1)
and ON = AN + 1. So you'd have to assert that the sum 1 + x + x^2 + ... doesn't exhaust ON to assert that s - 1 doesn't reach the end of NP, and that assertion is false.

[Anonymous No.9895341]

>>9895332
>and that assertion is false.
Because? How is it proved that sum exhausts ON?

[Anonymous No.9895351]

>>9895341
See here >>9895275
The lengths of the elements of the sum entirely cover all non-zero portions of ON. The special point N gets mapped to P and is a length zero segment so it contributes nothing to the total length of ON.

[Anonymous No.9895360]

>>9889619
>t. brainlet who can't subtract or multiply

[Anonymous No.9895361]

>>9895351
So now you must prove that P is reached by the sequence. This seems awfully circular

[Anonymous No.9895365]

>>9890551
>9890551
The first two examples are appeals to intuition retard. not proofs/

[Anonymous No.9895371]

>>9895365
It’s not intuitive that 10(0.999...) =9.99...
or that 1/3 = 0.333...

[Anonymous No.9895373]

>>9895361
You actually don't even have to do that. P is the only point that isn't reached by the sequence, but the only part of ON that is left uncovered as a result is the single point N. So unless you want to say that the single point N has some finite length, then you must say that the length of ON is the same as the length of ON minus the point N.

As to why the line ON and the line ON minus N have the same length, that starts getting into some interesting aspects of point set topology and measure theory. It turns out that lines have so many points that you can't change their length by only removing a finite number of points, or even a countably infinite number of points.

[Anonymous No.9895388]

>>9895314
what is 9.9.../10

is it =1 , <1 or >1?

[Anonymous No.9895392]

>>9895373
>P is the only point that isn't reached by the sequence
I agree
>but the only part of ON that is left uncovered as a result is the single point N
I also agree
>then you must say that the length of ON is the same as the length of ON minus the point N.
Points have no length, yes, it is the measurement between points that defines length. Remove all points between O and N and length is still the same. However, removing N removes an endpoint, and since intuition supports finite points and distances, there will be a loss of distance between N and the point that precedes it, which subtracts from the total length. If this were not so, then you could remove every point on the line and you would have the same length, which is absurd. For, if not, how many points would you have to remove, starting from N, until the length is changed? Whatever your answer may be, it is not supported by intuition. It is a mistake for people to be taught that lines are composed of infinite points, when it has never been demonstrated so.

[Anonymous No.9895394]

>>9895314
10pi=31.4159265...

show how that's wrong

[Anonymous No.9895403]

>>9895388
>what is 9.9.../10
I do not know, because I do not understand the nature of the problem. The notation is unfamiliar to me. I have yet to see it in action, in my mind, as something I can say I fully understand. If we were to refrain from vague abstractions and concentrate on a real form of this 0.999..., which we could understand geometrically, then maybe the problem could be approached. Until then, I will believe that this notation is an invention, a dream. For, after the decimal notation was introduced, how difficult would it be to stumble on the idea of an infinitely long decimal? But it was never shown how the decimal corresponded to reality, that it actually exists. If I were to return to some concrete approach, then I will imagine my two walls, one always approaching the other, 9/10 units at a time, but never reaching it. How can this movement be divided by 10 if it is infinite? Never mind that, I already know that after infinite movements the walls will never touch, so if the sequence were shortened—which I assume to be the meaning of dividing by 10– then I would confidently say that still, the walls would not touch.

[Anonymous No.9895406]

>>9895392
>If this were not so, then you could remove every point on the line and you would have the same length, which is absurd. For, if not, how many points would you have to remove, starting from N, until the length is changed?
I actually answered this. You can remove a countably infinite number of points and the length will remain the same. You have to remove an uncountably infinity number of points to actually change the length.

>Whatever your answer may be, it is not supported by intuition.
Your intuition and what the math says don't line up here. You can work with objects which better coincide with your intuitions, but you won't be working with the real number system anymore.

>It is a mistake for people to be taught that lines are composed of infinite points, when it has never been demonstrated so.
This is also incorrect. The real numbers form a mathematical model of a 1D Euclidean space. Every axiom of Euclidean geometry is satisfied by the geometry of real numbers.

You can argue all you want, but the length difference between ON and ON minus N is zero, as the only remainder is the single point N, which has no length.

If you want to create a number system based on geometry which allows for the line ON and the line ON minus N to stand for different objects and different "lengths", you're free to do so, and you can probably create a consistent system, but this system will not be the real numbers, and will have 'more points' than the real numbers. In the reals the lengths defined by the line segment ON and ON minus N are the same length, because single points have no length, so 0.999... = 1, that's just how the real numbers work.

[Anonymous No.9895408]

>>9895403
>I do not understand
retard

[Anonymous No.9895410]

>>9895394
That only seems to be an approximation, unless you can prove it is an equality.
Pi is equal to pi, and 10pi is equal to 10pi, but your statement has not been shown to be true. The decimal is never completed because we don’t understand it completely.

One knows that a perfect circle cannot be created on a grid. Could it be that our own reality is a grid, and the perfect circle is a human invention, never existing in reality?

[Anonymous No.9895418]

>>9895410
so which digit is wrong?
if you can't point which one is wrong, neck yourself

[Anonymous No.9895447]

>>9895418
I do not disagree with any of the first trillion digits of pi, because they have all been proven using finite methods. It is supposing that an infinite method exists, or that there exists such a true thing as a circle, that is wrong. If we lived in a world that allows circles, as it did straight lines, then we would not be arguing over math. All curves are approximations derived from a finite set of points.

[Anonymous No.9895455]

>>9895418
And it is fine to use these approximations, because they are true, but we cannot ever use equality.
0.999.... is approximately 1
Pi is approximately 3.14159265....
sqrt(2) is approximately 1.414...

There is no use for infinity

[Anonymous No.9895481]

>>9895447
>>9895455
>i have nothing

[Anonymous No.9895496]

>>9895447
>All curves are approximations derived from a finite set of points.
Hence, pi=4 in kinematic situations. All circles travels are cycloids.

Yes, if a circle was a straight line it's linear distance would be 3.14159... * 2 * R

[Anonymous No.9896163]

>>9890273
setting it to 0.9999 is just a shortcut for saying you set it to the infinite sum of 9/10+9/100+9/1000, as digit values are defined for the decimal system.


Similarly you can play the same game in base 2 and you will find the uncontroversial fact that 1/2+1/4+1/8+1/16... = 1, which is the number 0.1111... in base two


What you essentially do, is writing a shorthand for an infinite sum, that happens to have a nice limit.

or even simpler:
1+0/2+0/4+0/8+0/16= 0+1/2+1/4+1/8+1/16...

[Anonymous No.9896199]

>>9891015
>you can't reach infinity in the first place either
You're so stupid.

[Anonymous No.9896205]

>>9896163
>1/2+1/4+1/8+1/16... = 1
This hasn’t been proven, and makes no intuitive sense as seen in the 3rd paragraph here
>>9895119

[Anonymous No.9896230]

>>9896205
>This hasn’t been proven
top kek

[Anonymous No.9896249]

>>9896230
Its limit is obviously 1, but even an infinite sum will never be equal to 1. No one has yet addressed my thought experiment, basically Zeno’s paradox. To say that we can walk from here to there by infinite sums assumes that space is infinitely divisible, which hasn’t been proven, either. Try thinking for yourself

[Anonymous No.9896256]

>>9896249
>infinite sum will never be equal to 1

1 = 9/10 + 1/10
= 0.9 + 1/10
= 0.99 + 1/100
= 0.999 + 1/1000
:
= 0.9... + 1/inf
= 0.9... + 0
= 0.9...

[Anonymous No.9896274]

>>9896256
>1/inf = 0
Can you possibly prove this bold statement? It seems obvious to me, that with any two numbers greater than zero as numerator and denominator, the fraction will never be equal to zero. If 1/inf = 0, then does 1 = 0 x inf? You’re making the mistake of assuming 1/inf and 9.999... actually exist, completed, but then recognizing that an infinite number can’t be completed, then passing off its value to the next actual number. The truth is, 1/inf only represents 1/n, where n is unbounded. And for all n, 1/n is a finite number greater than 0. I hope your next argument won’t be so circular

[Anonymous No.9896328]

>>9896274
inf is unbounded, by definition

if the result would be >0,
then that would make inf bounded.

[Anonymous No.9896341]

>>9896328
1/inf is unbounded in the fact that the fraction can infinitely lose value, and never be able to be complete. This is why it makes no sense to speak of it as complete, because it has the power to always reduce itself even further. But if 1/inf = 0, then it is actually bounded and complete, which is hard to reconcile with the concept of infinity, indeed.

[Anonymous No.9896348]

>>9896341
stop treating inf as a real number
it's embarrassing

[Anonymous No.9896353]

>>9896341
>1/inf is unbounded
nope, inf is
lrn2read

[Anonymous No.9896367]

>>9896348
>>9896348
Yeah I’m not.
Gauss:
>... first of all I must protest against the use of an infinite magnitude as a completed quantity, which is never allowed in mathematics. The Infinite is just a mannner of speaking, in which one is really talking in terms of limits, which certain ratios may approach as close as one wishes, while others may be allowed to increase without restriction.
So as 1 as numerator and n as denominator, with n unbounded, then we have what you people call 1/inf, which just means that the fraction can get as close to zero as you like, without actually becoming 0.

You guys have no arguments at this point. Maybe you should take a break, and reflect on this alone, and see if everything you believe is actually true.

[Anonymous No.9896444]

>>9896274
1/inf is often shorthand for "limit of 1/n as n goes to infinity" and that limit is 0. Next, since inf is not a real number, you can't use real number algebra manipulations on it. For example, you can't go from 1/inf = 0 to 1 = 0 x inf. That's not allowed since inf isn't a number.

Also, you should note that a limit (when it exists) is a `complete' number. It's not an approximation. The approximations can be used to figure out what the limit is, but the limit of a convergent sequence is a number. That comes from the very definition of what \lim_{n\to\infty} a_n means.

If you want to argue that limits aren't numbers, then you're not arguing math. That's a philosophical argument that will not change anything inside, say, ZF set theoretic math. You could make your own different system of math where limits aren't `complete numbers' but that's not where we're currently working. We're arguing from ZF where limits are indeed numbers.

[Anonymous No.9896485]

>>9896367
>with n unbounded
there you go again >>9896348

[Anonymous No.9896486]

>>9895308
2.999 ÷ 3 = 0.999666...
2.9999 ÷ 3 = 0.9999666...
2.99999 ÷ 3 = 0.99999666...
2.999999 ÷ 3 = 0.999999666...
2.999... ÷ 3 = 0.999...

this checks out perfectly well. You did your math wrong.

[Anonymous No.9896489]

>>9896199
Lmao why the fuck did you take that as an insult and respond like this.

[Anonymous No.9896512]

>>9896485
Infinity means not complete, never ending. 1/inf doesn’t represent a rigid value, it’s always changing. And since it’s always changing, it doesn’t have a value at all, but approaches the value 0, because for every successive n you get closer to zero, but it is impossible for 1/n to be equal to zero. Increasing n forever will not change this fact. >>9896444
There’s a difference between 0 being the limit of 1/inf, and 0 being equal to 1/inf.

Since I don’t believe infinity actually represents a value, 1/inf is a meaningless statement, and we have to think in finite terms. Think about what you’re saying. The length 1, divided infinitely, yields 0. An infinite string of lengths of 0 equals 1. It takes faith to believe all this nonsense. It can’t be reasoned at all, only argued for in a circular fashion.

[Anonymous No.9896534]

>>9896512
>Infinity means not complete
lol, it means sooooooo complete
it's the most absolute complete you can imagine
there is a word for it too: unbounded

[Anonymous No.9896605]

>>9896534
If numbers never end, then the sum of all numbers never ends. It is always increasing, from finite to finite, and this process of always increasing is the infinite, not the sum itself. Since something infinite and endless never ends and is never completed, at no point will the sum also be infinite and endless. You think you understand infinity but you don’t. It is perfectly imaginable that I could keep adding numbers, although it isn’t actually possible, since I will eventually die. But, supposing I was immortal, and I had all the computing power in the world, and multiplied numbers for an infinite amount of time, never ending, then I will never reach this “infinity” that you treat as a value. Again, the process is infinite, but the result is not. You can’t just pretend that there will be a time when I have counted for an infinite amount of time, because that would imply that the endless has come to an end. In other words, there is no such thing as the sum of all numbers because the sum could never be completed.

[Anonymous No.9896629]

>>9896605
https://www.wolframalpha.com/input/?i=infinity
An unbounded quantity that is greater than every real number.

Inf isn't a real number
Even less it's a real number that grows

[Anonymous No.9896639]

>>9896512
That is not how it works.
You seem to be discussing about rational numbers. There is no rational number q with 1/q = 0. So you can say: let us consider all rational numbers together with new elements inf and -inf for which 1/inf = 1/-inf = 0. The obviously 1/inf "represents a rigid value" inasmuch as you consider 0 to be a fixed "rigid" number.
This is the typical scenario that happens in mathematics. I do not know what you mean by inf being "not complete" or "never ending".

[Anonymous No.9896646]

>>9896639
>>9896605

[Anonymous No.9896659]

LMAO. This thread reeks of philosophy majors larping as mathematicians. This is resolved in Analysis 0.1.

[Anonymous No.9896736]

>>9896646
I get that.
But discussing arithmetic that includes "new" elements like "inf" has nothing to do with limits of partial sums. I responded to misguided comments about the former use of "inf", not to misguided comments about the latter use.
If you insist on conflating all possible uses of "inf", then it is your own funeral. Just check any mathematical paper: if it contains any concept of "inf", then it is explained at the beginning of the paper what the author takes "inf" to symbolize *in the context of the paper". It could be just about anything, just like "x" could be the name of just about any real number.

[Anonymous No.9896917]

>>9896512
>limit of 1/inf
No no no no. You don't understand at all. I said that 1/inf is shorthand for "limit of 1/n". Like a nickname. If you replace "1/inf" for "limit of 1/n" then you get the equality 1/inf = limit of 1/n = 0 so 1/inf = 0. Your "limit of 1/inf" is gibberish and shows that you don't know any rigorous math. As I said before (and you completely ignored), you're trying to argue about infinity philosophically, not withing a well formed mathematical framework like ZF set theory.

If you want to argue the philosophy of infinity, please stop putting on airs of arguing actual mathematics. The concept of the infinite and infinity is well established in the system of math that we use now and it is not your interpretation.

[Anonymous No.9896952]

>>9896917
I agree that the limit is equal to zero, and the limit of 10^n-1 / 10^n is 1, or the limit of the sum 9/10^n is 1.
This all comes back to >>9896256
where it was not really shown that the infinite sum cannot equal 1. The limit equals 1, but that doesn’t mean the sum itself is equal to 1.

[Anonymous No.9896979]

>>9896952
>where it was not really shown that the infinite sum cannot equal 1.

The point there is that each line equals 1
It never drifts anywhere.
It's the opposite of 0.9... slowly approaching 1

[Anonymous No.9897190]

>>9896952
>The limit equals 1, but that doesn’t mean the sum itself is equal to 1.
No, that's exactly what it means. The definition of an infinite sum is "the limit of the partial sums". Since the limit of the partial sums is exactly 1, then the infinite sum is itself equal to 1. That's precisely the mathematical definition.

That is, 0.9... = limit of (9/10 + 9/100 + ... + 9/10^n). That limit exists and is equal to 1, so 0.9... = 1.

The post you quote is actually essentially correct. To make it a bit more rigorous, simply note that 1 = 0.99...9 + 1/10^n for any n. So we can take the limit as n goes to infinity of both sides. Now since 1 is constant with respect to n we get that its limit is 1. Thus 1 = limit (9/10 + ... + 9/10^n) + limit (1/10^n) = 0.9... + 0 = 0.9... which is the same as the post says.

[Anonymous No.9897206]

All these proofs hinge on the fact that 1/3=.333... when that is simply not true.....

[Anonymous No.9897221]

>>9897206
I'm sorry, you'll have to finish your post, the ... at the end in undefined.

[Anonymous No.9897224]

>>9896659
Considering its still taught that 0.999...=1, I'd wager no, you're not getting the right answer in any school approved curriculum.

[Anonymous No.9897238]

>>9897206
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.9897240]

>>9897206
No, it's much more natural to say that 1/3=0,333... is a consequence of 1=0,999... since the latter is much more obvious. or 1/9=0,111... if you're into geometric series.

[Anonymous No.9897339]

>>9889632
>>9892729
You know those crack pots who think they've come up with some grand theory physics and start sending out their "work" to physics professor in hopes of recognition? That's what both of you are doing but for math.

[Anonymous No.9898298]

>>9897238
Infinity is not a fucking number lmfao

[math]\frac{1}{\inf}[/math] has no more meaning than [math]\frac{1}{\text{potato}[/math]

there is no path of incrementing to infinity, therefore its not a number, and its not an object with any hard relation to numbers aka it isn't even necessarily greater than any number, because its not a fuckin' number.

Infinity is just imaginary.

[Anonymous No.9898301]

>>9897238
Infinity is not a fucking number lmfao

[math]\frac{1}{\infty}[/math] has no more meaning than [math]\frac{1}{\text{potato}}[/math]. There is no path of incrementing to infinity, therefore its not a number, and its not an object with any hard relation to numbers aka it isn't even necessarily greater than any number, because its not a fuckin' number.

Infinity is just imaginary.

[Anonymous No.9898303]

>>9898301
Whatever. The latex is right but sci is shit.

[Anonymous No.9898339]

>>9897240
Its not natural to say 1÷3 = 0.333...
Its just simple, based on bad assumptions. Is simple as grabbing a calculator, typing [1] [÷] [3] then hitting the [=] button. The action of manipulating a calculator is not math, its just pressing buttons. You think that because you're hitting the [=] button that the calculator is finding an equality, but it isn't. The calculator just prints howevermany 3's instantly. In math, you have to find your result yourself. You can do long division on paper for 1/3, and what you'll acquire is an answer that keeps growing.
0.3
0.33
0.333
0.3333
0.33333
And so the actual natiral way of thinking about the decimal solution to 1/3 is instead that, because there is always a remainder to continue dividing without any evenly divided finalized condition to denote absolute equality, the fraction 1/3 must be greater than the decimal 1÷3, aka
[math]\frac{1}{3} > 0.\bar{3}[/math]

Its not natural to think 1/3 = 0.333..., rather it is an artificial and baselessly oversimplified result.

[Anonymous No.9898353]

>>9898339
[math]\frac{1}{3} > 0.\bar{3} \\ \frac{1}{3} × 3 > 0.\bar{3} × 3 \\ \frac{3}{3} > 0.\bar{9}[/math]

1 > 0.999•••

[Anonymous No.9898388]

>>9898301
1/inf = 0

show a reference other than your cuckoo math that says otherwise

[Anonymous No.9898416]

>>9898388
absolute brainlet motherfucker

[Anonymous No.9898430]

>>9898416
>i have no argument

[Anonymous No.9898451]

>>9898303

[Anonymous No.9898459]

>>9898430
Christ man, how the fuck do you still not know how to use greentext? You're not supposed to put arrows in front of your own fucking part of the post unless you're paraphrasing a story.

Believe you me, its self fucking evident that you have no argument. You don't need to tell us about it.

[Anonymous No.9898481]

>>9898451

[Anonymous No.9898484]

>>9889712
> can’t divide a glass of water evenly into three parts
Which brainless Neanderthals believe this?

[Anonymous No.9898488]

>>9898459
>can't say anything meaningful so retreats to ad hominem
came up dry then. no big surprise.

[Anonymous No.9898493]

>>9898481
irish math?
do you hop around your computer without moving your hands?

[Anonymous No.9898517]

>>9898493
Wat

[Anonymous No.9898559]

>>9898517
https://youtu.be/W22gpBv00gg

[Anonymous No.9898689]

>>9898301
>aww shitlatexman stumbled again
'ere ya go
[math]
\dfrac{1}{ \text{potato}}
[/math]

[Anonymous No.9898787]

>>9898689
>>9898481
Heres your (You)

[Anonymous No.9898795]

0.999...=1

There is an inherent limitation in the so called real number decimal systems that numbers can be represented into two ways.

[Anonymous No.9899169]

>>9898795
a non terminating number can't be represented as a decimal you stupid fuck. how is that hard to understand? holy shit i'm actually appalled by the single IQ faggots on this board. i'm going to trace all your IPs and send a drone to shoot dildos at you.

[Anonymous No.9899238]

>>9899169
Giving a balanced and well justified opinion is a beautiful thing.
You should try it sometimes.

[Anonymous No.9899249]

>>9889587
x = 0.444
4x = 4.444
4x = 4 + 0.444
4x = 4 + x
4x = 4
x = 1

Basically everything becomes 1, awesome!!!11

[Anonymous No.9899250]

>>9889587
10x is not 9.999...

[Anonymous No.9899255]

>>9899249
>0.444 * 4 is 4.444

[Anonymous No.9899268]

1/7 = 142857/100000 + 1/7000000
= 0.142857 + 7*10^-6
= 0.142857142857 + 7*10^-12
= 0.142857142857142857 + 7*10^-18
:
= 0.142857... + 1/inf
= 0.142857... + 0
= 0.142857...

[Anonymous No.9899274]

1/7 = 142857/100000 + 1/7000000
= 0.142857 + 7*10^-6
= 0.142857142857 + 7*10^-12
= 0.142857142857142857 + 7*10^-18
:
= 0.142857... + 7/inf
= 0.142857... + 0
= 0.142857...

[The Lord No.9899280]

>>9889587
>Why is this possible?
it has to do with the "..." notation. If you write
x = 1 - epsilon

instead of
x = 0.999...

then there is no issue

[Anonymous No.9899297]

>>9899249

x = 0.444
x = 1

[Anonymous No.9899303]

>>9899250
what is 9.9.../10 ?
is it =1, <1 or >1 ?

[Anonymous No.9899660]

>>9898353
Correct

[math].\bar{3}<\frac{1}{3}<.333...4[/math]

[Anonymous No.9900073]

>>9898353
>>9899660

[Anonymous No.9900079]

It means two symbols can represent the same concept. There's nothing wrong with that, 2+2 and 2*2 both point towards the same concept.

[Anonymous No.9900325]

1 - 0.999... = 0.000...1
0.000...1 × [math]\infty[/math] = 1

[Anonymous No.9900542]

>>9891015
the absolute fucking state of sci

[Anonymous No.9900718]

>>9889587
0.999... does equal 1. That's not a fallacy in mathematics.

[Anonymous No.9900787]

>>9900718
Explain your reasoning

[Anonymous No.9900808]

There is insufficient reasoning to think [math]\sum_{n=1}^{\infty} \frac{1}{2^n} \text{ should evaluate identically as } \sum_{n=1}^{\infty} \frac{9}{10^n}[/math] without making some majorly retarded assumptions about the definition of what the [math]\infty[/math] symbol means, or what the contents of a concatenated string cut down by ellipses or an overline are.

Its explicitly disingenuous for sum 1/2^n to even be considered as 0.999..., much less considered 1. Its at least feasible for 9/10^n because this only has a string of 9's for every partial sum total, but the partial sum total for 1/2^n is like half 9's and half random bullshit numbers as a result of halving.

Infinity is shit and professors who refuse to stop teaching this completely non-functional and vague fantasy variable should be shot.

[Anonymous No.9900845]

>>9900808
look at this brainlet

[Anonymous No.9900866]

what fucking retard made this.

10x = 9+x

"subtract x from both sides"
fucking retards division and subtraction are basic arithmetic

[Anonymous No.9900873]

[math]0.999... = 1[/math]

There is no fallacy. They are *exactly* the same.
Just because they look different doesn't mean they are not. Remember, there are many ways to represent the same thing in math.

[Anonymous No.9900927]

>>9900873
Attempt to explain your reasoning

[Anonymous No.9900937]

0.999... = sum .9/(1..inf) = lim n->0 1-n = ...

The notation is only fallacious if you decide it is (...)

[Anonymous No.9901014]

>>9900325
nope

0.0..1 = 10^(-inf) = 0

0*inf is undefined, because it is equivalent to the 'unmovable vs unstoppable' meme and can't be made sense of

[Anonymous No.9901037]

>>9900927
proof of the
1/(1-x) formula:
https://youtu.be/XFDM1ip5HdU?t=5m40s

[Anonymous No.9901069]

>>9901037
These are some bad assumptions.

I honestly don't understand how pure mathematicians would consider themselves so intelligent while simultaneously being too brainlet to figure against asinine thinking.

"On and on, forever" immediately followed by "equals" is oxymoronic and paradoxical. You never get to final equivalence to equate an answer from "infinite" work, cause you're still stuck doing the work. Its a literal leap of the imagination to figure "unending" work can be ended, one way or another.

The rule is: don't stop
Mathematician solution: stop

its unironically default invalid.

[Anonymous No.9901070]

Daily reminder that this "proof" is just an optical illusion. By multiplying 0.999... by 10, we actually get an error.
>zero at the end that's produced hy multiplying any number by 10 magically disappears.
No logic to this claim.
>using a different number system to diaprove another system.
Flawed argument.

[Anonymous No.9901091]

>>9901069
Heres a joke

A mathematician driving to work stops in the middle of the highway. Cars and trucks go speeding by while honking. Soon enough, a police cruiser pulls up and a cop approaches the mathematician's car. The mathematician rolls down their window. The cop asks "whats the hold up?". The mathematician replies, "i'm a mathematician, officer. I'm already at work, so I don't need to drive any further". The cop laughs, "Everyone knows mathematicians don't have jobs."

[Anonymous No.9901092]

>>9901069
Look again. Instead of slowly crawling up toward a sum, the video makes sure that at each step the total is 1.
So a doubter like you has the burden of explaining why the total would ever drift off from 1.

[Anonymous No.9901093]

>>9901070
10 * 1.1 = 11
*poof* disappearing zero

[Anonymous No.9901105]

>>9901093
Jokes on you, as there was a decimal place before, the number of decimal places can't change.
>1.1 * 10 = 11.0
So the zero's still there, and since you cannot put an end to an infinite or a number that tends to another number, the multiplication by 10 invalidates any so-called "proof".

[Anonymous No.9901111]

>>9901105
you sure it isn't 11.000... ?

[Anonymous No.9901113]

>>9901092
0.9 + 0.1
0.99 + 0.01
0.999 + 0.001
0.9999 + 0.0001
0.99999 + 0.00001
Theres always a smallest part leftover.
And this is generous based on [math]\sum_{n=1}^{\infty} \frac{9}{10^n}[/math] rather than the video's [math]\sum_{n=1}^{\infty} \frac{1}{2^n}[/math], which provided their leap of logic in having final equality and an end to unending work in assuming an infinite'th iterative step is reached and that it is the final finite step (which is retarded), the solution would be an infinite amount of digits after the decimal where only half of them are 9's and the other half are various numbers.

You see, more often than not, mathematicians treat the "infinite" nature of a decimal as some hard buffer. They dont care that its 0.9999999...999957534...7536
they'll just call it "0.999..." and invent an arbitrary cutoff point where the pattern no longer holds true, so their reported result is instead a conveniently modified and shortened substring of the whole result.

[Anonymous No.9901117]

>>9901111
Nice quads.
Well, even in that case and if there was no previous decimal place, meaning multiplying by whole numbers, a zero is tagged on to the end either way. As such, it is still invalid to say 0.999... = 1.

[Anonymous No.9901120]

>>9901113
soo, when does the total drift away from 1 ?

n=100 or n = inf-100 or n=inf-1, or what?

give my that information
not some hand wavy mystical lecture

[Anonymous No.9901122]

>>9901113
In otherwords for 1/2^n, double over infinite work so all infinite digits of the result are 9's, but they'll say 2*infinity is "the same" as infinity, so they just end up throwing out anything related to intelligible arithmetic just to attempt saving face. They can't admit they're wrong, so its more likely than not they're always wrong.

Seriously its like watching a dog chase its own tail to try to get a mathematician to stick to one, single definition of infinity. They'll constantly redefine it and try to appear like they know more, but they're ultimately just telling bold faced lies. They know jack shit. They're conartists.

[Anonymous No.9901125]

>>9901120
Drifting has nothing to do with it. Your previous post was already acknowledging the whole of parts add up to 1. I didn't argue that.

[Anonymous No.9901126]

>>9901122
>one, single definition of infinity

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

[Anonymous No.9901131]

>>9901126
Learn to read. Just went over how mathematicians treat is as a real, finite number to assume an end to unending work occurs, allowing themselves a final solution to nfinite iterative work.

These definitions are at odds.

[Anonymous No.9901137]

>>9901131
hmm, W-A vs shitposter
no dilemma here

[Anonymous No.9901140]

Jesus fucking Christ I am sick to fucking death with this shit. It makes my fucking blood boil to see this kind of fucktardery!

Listen up cunts, because I am only going to fucking well say this once.There is fiction and there is fact. Furthermore there are two types of fiction. Self consistent fiction and inconsistent fiction.

This 0.999...= 1 bullshit belongs to the self consistent fiction variety. It does make sense within the fiction that is called infinity. It is self consistent with that fantasy. That doesn't mean it is fucking real. Its is not. Its is just a made up thing, like a fantasy world were elephants can fly and the fairy Godmother grants magical wishes.

Got that now? HAVE YOU FUCKING GOT THAT THROUGH YOUR DENSE FUCKING SKULLS YET????

Good.

NOW GO THE FUCK AWAY!

[Anonymous No.9901144]

>>9901140
[math]
\\ 0 < p < 1
\\
1 = p + (1-p) ~~~~~~\overset{1}{[\overbrace{=====p=====|==(1-p)==}]} \\
= p[x+(1-x)] + (1-p) ~~~~~~\overset{1}{\overbrace{\underset{p}{[\underbrace{=====x=====|==(p-x)==}]} ~~ + ~~ (1-p)}} \\
\\
\dfrac{x}{p-x}=\dfrac{p}{1-p} \Rightarrow x- xp = p^2 - xp \Rightarrow x=p^2 \Rightarrow (p-x)=p(1-p)\\
\overset{1}{\overbrace{\underset{p}{[\underbrace{=====p^2=====|==p(1-p)==}]} ~~ + ~~ (1-p)}} \\
\\
\dfrac{p^{n+1}}{p^n(1-p)}= \dfrac{p}{1-p} \Rightarrow \dfrac{p}{p}=1\\
\overset{1}{\overbrace{\underset{p^2}{[\underbrace{=====p^3=====|==p^2(1-p)==}]} ~~+ p(1-p)+(1-p)}} \\

[/math]

[Anonymous No.9901147]

the problem is that its wrong to assume 1/3=0.3333333... (repeating of course)

[Anonymous No.9901150]

>>9901147
>>9897238

[Anonymous No.9901151]

>>9901069

Amen brother. One day these asshats will pay for their crimes.

[Anonymous No.9901154]

>>9901120
Using infinity is the hand wavy bullshit.
How much more hand wavy bullshitting can you get than literally "we do this, the this, then YADA-YADA AND SO ON, and now we have this answer"
its the fucking underpants gnomes from south park
>1.) 1 + 2 + 3 + 4 + . . .
>2.) ?????????
>3.) [math]- \frac{1}{12}[/math] !!!!!!!
its all leap of logic bullshittery. Infinity isn't even consistent as a fiction like >>9901140 claims. Its like the Aristocrats joke, every fucking mathematician or method makes up its own infinity to solve its own problem. Its a fucking plot device. Its a fucking variable. Its vague poorly defined bullshit. Its hand waving, hell its even sleight of hand and misdirection. "NOW everyone, if you could please turn around" so the mathemagician can stoop down under the table and grab the rabbit he's going to "magically" pull out of his hat.

fuck off with this ". . ." shit.
If you have an answer, show your work. If you're playing around in fantasy land, don't leave it up to the student to figure, cause the student is paying for an education with real money, not make believe fantasy funbux. They expect valuable knowledge.

[Anonymous No.9901155]

>>9901154
>another hand wavy mystical lecture
kek

[Anonymous No.9901157]

>>9901150
you just showed that theres an arbirtary amount of ways 1/3 can be expressed, theres no proof that 1/3 will eventually become 0.333... (repeating ofc)

[Anonymous No.9901161]

>>9901157
it's not "becoming"
each line equals exactly 1/3

it is your job to show
at which line it suddenly isn't 1/3

protip: you can't

[Anonymous No.9901165]

>>9901161
No line is 1/3rd lmao
>1÷3 = 0.3333

[Anonymous No.9901168]

>>9901161
Oh wait i see what you did. You dumb bro.

Gj incrementing to infinity though. How'd you do that, if you don't mind me asking?

[Anonymous No.9901169]

>>9901155
Hey man, you don't have an arguement. Quit heckling.

[Anonymous No.9901171]

>>9889598

0.9999... is not a number. It's a shortcut representation for an infinite sum.

[Anonymous No.9901180]

>>9901161
are you retarded?
you just showed various combinations of fractions that equaled one third
and then claimed that proved 1/3=0.3...
and then asked me to disprove something you never proved in the first place

[Anonymous No.9901189]

>>9901165
>No line is 1/3rd
american education, folks

[Anonymous No.9901191]

>>9901171
[math]\sum_{n=1}^{\infty} \frac{\underline{9}}{1\underline{0}^n}[/math] is a pattern of "infinite" sums from 9/10^n, 99/100^n, 999/1000^n, to as many equal 9's and 0's desired, where [math]0.\bar{9}[/math] may arise as a "result". Otherwise, 0.999... isn't a real number and does not naturally arise from any normal arithmetic, but can render itself if mistakes are made during calculation, such as rendering 1÷3 as 0.333... then multiplying that decimal result by 3. There are real mistakes that can be made to come along 0.999..., otherwise it isn't a number that will exist in human-intelligible arithmetic. Just cause its not a normal number that would appear outside of calculus does not mean it equals 1, though.

[Anonymous No.9901192]

>>9901189
>someone attacks ur argument
>b-but ur stoopz :'(
if you cant even defend your argument semi seriously, just stop posting

[Anonymous No.9901193]

>>9901180
soo, which line is it, the one that doesn't equal 1/3

[Anonymous No.9901195]

>>9901180

Do you agree 0.3333... is the sum i : 0 -> inf : 3 * 10^(-i) ? In that case, let's call it S. Now from elemental calculus we know that sum i : 1-> inf : n ^( - i) equals n / ( n - 1) - 1 . from S, we can factor out the 3. so we get 3 * sum i : 1 -> inf : 10^(-i) = S. we take our known sum, and see S = 3 * 1/9 = 1/3. 1.e.d.

[Anonymous No.9901197]

>>9901192
you are the classic american idiot
take the third line for example
333/1000 + 1/3000
= 999/3000 + 1/3000 = 1000/3000 = 1/3

[Anonymous No.9901198]

>>9901191

>>9901195

look at my proof here. I rigorously have shown 1/3 to equal 0.3333..., only taking one simple equality that might not be obvious to all of us, but probving it through induction is easy.Do you disagree with any part of it? ;)
and yeah it's not a real number, if by number you mean a digital representation since "..." is not a valit part of those representation. If you meant the mathematical concept behind it is not a number... well then i have to assume pi is not either.

[Anonymous No.9901207]

>>9901198
[eq]\frac{1}{3} > 0.\overline{3}[/eq]
These are two different values. You cannot render the fraction [math]\frac{1}{3}[/math] in decimal. Shit just doesn't work. Theres always a remainder and always more 3's, there is never a final equality, so the decimal [math]0.\bar{3}[/math] is always missing a part from the fraction [math]\frac{1}{3}[/math], ergo the fraction has more information and is larger than the decimal. It doesn't matter how many 3's are present in 0.333•••, and thats what the "•••" stands for. Whether its one 3, ten 3's, or you never stop weiting more 3's, its never enough, because the value doesn't play well with decimal.

[Anonymous No.9901209]

>>9901207
[math]\frac{1}{3} > 0.\bar{3}[/math]

[Anonymous No.9901210]

>>9901197
>>9901193
>get called out for havign a stupid argument
>just make the same argument again
you cant ask me to disprove something you havent actually proven

[Anonymous No.9901212]

>>9901207

i never tried to. I explained that 0.33333.... does not denote a decimal representation but an infinite series ( thats what "periodicity" means, you can not express it in decimals, but you can produce a simple series in the form i provided). And the sum of this series is exactly 1/3. So how, for the love of god, can you argue the values are not the same? it doesn't matter wether I use 4 in an equation or 2 + 2 either.

Have you read my proof? I just constructed a simple and correct proof for my proposition, so either find an error in it, accept it, or continue being an irrational ( not accepting a correct mathematical proof is exactly that) idiot.

[Anonymous No.9901213]

>>9901154

Amen Brother!

I swear by Christ one days these scamming turd eating tardfucks will pay! One day they shall be dragged from their beds in the middle of the night to face JUSTICE! JUSTICE! In the SUPREME COURT OF REALITY!

There in front of a JUDGE they will be made to answer for their crimes!

"OH! AND NOW YOU ARE SAYING THERE ISNT JUST ONE INFINITY BUT MANY DIFFERENT TYPES OF INFINITY???? TAKE THIS CRAWLING PIECE OF LYING SCUM AWAY!!"

[Anonymous No.9901214]

>>9901210
I just proved that line#3 = 1/3
my claim is that any line is 1/3
stop bullshitting and give the line# that isn't 1/3

[Anonymous No.9901215]

>>9901209
Cool, what's the distance between 1/3 and 0,333...?

[Anonymous No.9901216]

>>9901213
seek help

[Anonymous No.9901218]

>>9901213

Okay so you claim there is as many real numbers as natural ones? prove it.

[Anonymous No.9901229]

>>9901215
x = [math]\frac{1}{3}[/math]

0.3 < x < 0.34
0.33 < x < 0.334
0.333 < x < 0.3334
0.3333 < x < 0.33334
0.33333 < x < 0.333334
0.333333 < x < 0.3333334

0.333••• < x < 0.333•••4
it wants a number to exist between 3 and 4 that can be rendered as 1 digit, not "3.5" or whatever. The true solution value to 1÷3 just does not exist in the decimal system.

If our writing system was a little different but still reliant in base-10, it might be acceptable to write the solution to 1÷3 as 0.3.5, or 0.3r1 for "remainder 1" which is basically how all children are initially taught division anyway.

1/3 is always greater than 0.333..., but thanks to fudging we can just as easily say [math]\frac{1}{3} \approx 0.333...[/math], but that takes careful observation to not intentionally mislead by mixing the approximation sign up with the equals sign.

[Anonymous No.9901232]

>>9901229

did you ignore the proof where i showed their equality? and by the way : 0.333....4 is not a sensible mathematical representation of anything.

[Anonymous No.9901235]

>>9901232
>0.333....4
It is 0.333... + 4/(10^inf) = 0.333... + 0 = 0.333...

[Anonymous No.9901239]

>>9901232
0.333... is not a sensible mathematical representation of anything either. Its a moot point. I'm just playing ball on the field here, I didn't build this retarded stadium.

0.333...4 really only doesn't make sense if and only if you disingenuously believe the "..." is shorthand for "cumulative total infinity", AKA "nothing can come after infinity". But if you use that definition, you're ignoring the fact nothing can reach infinity in the first place.

Ita easier to trust that "..." just means "an arbitrary finite amount to the authors discretion".
The infinity can't be taken in whole. It cannot be accounted for to completion. It cannot be grasped. This simple understanding can help by process of elimination for what "..." ought to truly stand for.

[Anonymous No.9901240]

>>9901239
>It cannot be grasped.
speak for yourself

[Anonymous No.9901244]

>>9901240
Well, you can imagine in your fictional daydream fantasy land that you may grasp infinity. Doesn't mean its really happening though. Doesn't mean it can really be reproduced either.

[Anonymous No.9901246]

>>9901235

sometimes to the power of "infinity" is not sensible either. powers are only defined for numbers. it's like saying 2 + infinity

[Anonymous No.9901248]

>>9901239

and besides : i just provided a clear and useful , stringent definition that exactly matches what we mean by this notation with the series i provided further up. And your whole argument against a rigorous, correct proof is "it's easier to trust that..." we are not talking about fucking god or unicorns here bit stringent mathematics. So to you the same choice i gave further up : a.) accept the correct proof and it's conclusion b.) invalidate it by actually finding a flaw in it. c.) do not accept a proof you assume to be correct, making you a babbling idiot, being the most irrational a human could be.

[Anonymous No.9901249]

>>9901244
>grasp
you can't "grasp" 159, the best I can visualise simultaneously in my head is 6 as a 2x3 array.
Doesn't that you can't do math with 159.

Same with infinity - the things you can do with it are crude, compared to a normal number. Like the difference between a pair of tweezers vs a sledge hammer. But some operations can be done if you're careful.

[Anonymous No.9901250]

>>9901248
>>9901195
The proof is invalid because it relies on infinity, which is a vague non-numerical concept. it wouldn't change a thing to replace "inf" with "etc."
this is not proof. This is the omission of work.

[Anonymous No.9901251]

>>9901250

So you deny the existence of infinite sets? How many primes are there?

[Anonymous No.9901253]

>>9901246
>it's like saying 2 + infinity
10^inf = inf
2 + inf = inf

no problem here
if you disagree, that's your problem
no reputable citation will agree with you

[Anonymous No.9901255]

>>9901249
There are [math]\color{red}\text{zero}[/math] real-world applications involving infinity. Its not tweezers. Its squinting your eyes with one eye shut and vocalizing sound effects while you pinch your fingers over someone in your frame of view as an attempt to squish their head.

Its fucking fiction.

[Anonymous No.9901256]

>>9901255
>Its not tweezers
of course it isn't you dolt,
infinity is the sledge hammer

[Anonymous No.9901258]

>>9901253

Strange. My algebra book agrees with me since +, defined on semigroups, is only ever defined for a, b that are in the set of the semigroup. Is infinity a natural number for example?

[Anonymous No.9901259]

>>9901140

you consider infinity a fiction. what is the biggest prime?

[Anonymous No.9901260]

>>9901258
>Is infinity a natural number for example?
>>9901126

[Anonymous No.9901261]

>>9901251
Infinity is not a number. The theoretical size of a theoretical set is nothing anyone can care about.

[Anonymous No.9901262]

>>9901260

i know this ;) i just wanted to show the absurdity of using infinity like it was a number by constructing a contradiction between "infinity is a natural number" ( which would be needed for natural number addition with it to work) and the peano axioms ;)

[Anonymous No.9901263]

>>9901216

>Being this retarded.

[Anonymous No.9901264]

>>9901261

wrong. E.g. Riemanns hypothesis cares deeply about it and large parts of Computer Science and Physics depend on it.

[Anonymous No.9901265]

>>9901262
>addition with it to work

if 2+inf=inf
then I'd say it doesn't "work"
but that's addition that breaks down, not infinity

if 2/0 doesn't work, do you that conclude that zero doesn't exist or that division broke down?

[Anonymous No.9901267]

>>9901264
No real world application relies on any definition of infinity.

[Anonymous No.9901268]

>>9901259

You.Just.Dont.Get.it.

Infinity is a self consistent fantasy. You can have as many primes as you want, because its consistent with the fiction. Its like asking how many flying elephants are there in flying elephant land.

[Anonymous No.9901269]

>>9901267

Is cryptography or lasers real enough for you?

[Anonymous No.9901270]

>>9901267
Just keep flipping those burgers bud

[Anonymous No.9901272]

>>9901268

Do you just disregard all formally correct proofs that lead to infinite sets?

[Anonymous No.9901273]

>>9901268
>hand waving intensifies

[Anonymous No.9901274]

>>9901265

I am not a finitist, i suppose you have the wrong guy. I just wanted to debunk this notion of "10^inf" being some piece of valid mathematics ;)

[Anonymous No.9901275]

>>9901269
Neither rely on infinity, brainlet.

[Anonymous No.9901279]

>>9901274
retard

https://www.wolframalpha.com/input/?i=10%5Einf

[Anonymous No.9901282]

>>9901275

The models leading to lasers rely on vector spaces with infinitely many dimensions and cryptography relies on the riemann hypothesis whose core function , the zeta function, itself is an infinite series. Were it not, the hypothesis were false and cryptography as we know it would break down since there was an easy algorithm to factorize prime numbers( of which there would, at this point, only be finitely many as well)

[Anonymous No.9901283]

>>9901279

you just did the equivalent of entering pi into your calculator and concluding "hah, pi is finite since the calculator only shows 10 digits!"

[Anonymous No.9901286]

>>9901283
shitposter vs W-A
yeah, I'll go with W-A

[Anonymous No.9901287]

>>9901286

read the wikipedia article on fields :)

[Anonymous No.9901288]

>>9901287
wikipedia vs W-A
yeah, I'll go with W-A

[Anonymous No.9901291]

>>9901272

You can prove anything when you live with Alice in Wonderland.

Are you trying to disprove the Cheshire cat didn't vanish leaving only behind its smile?

Within Wonderland, no you cant, because its a self consistent fantasy. But a fantasy none the less. No less than infinities, which assumes that infinities can exist. "Right, we will assume infinities exist, now lets prove they exist...Hurrah! They do! We proved it!" Jesus Christ. Its hocus pocus, nothing more.

[Anonymous No.9901294]

>>9889587
>10x = 9.999
fucking idiot

9.999 = 9.999

[Anonymous No.9901295]

>>9901291
>>9901273

[Anonymous No.9901296]

>>9901291

So you even disregard the school level proof of there being infinitely many natural numbers?

[Anonymous No.9901298]

>>9901282
Cryptography is about who has the source material and who doesnt. You obviously don't.
Mathematician's understanding of computers and computer calculation is truly abyssmal. Its all based in finiteness.

[Anonymous No.9901300]

>>9901298
>carefully avoids giving any detailed examples
kek, what an idiot

[Anonymous No.9901309]

>>9901274
You need the extended reals for measure, integration, monotone convergence, stereographic projection, etc.

The significance of these results are generally introduced around postgraduate analysis if you decide to pursue a career in mathematics.

[Anonymous No.9901310]

>>9901300
Crypto is about who has the locks and who has the keys. Contrary to mathematician belief, you do not need to know how to predict the value of the key. All you need to do is intercept it. Its all based on equations and the solutions to those equations. The key is part of the equation, and the lock is part of the equation. If you know the formula and you know either the lock or the key, you can reverse engineer by manner of fucking simple solving for X. Cryptography is more about speed than anything; it is not reliant on any mathematical factor of scrambling. Scrambling a communication is left to the end users, sending messages in code where the formulas to decrypt are stored clientside disconnected from any potential intrusion from the outside. You can intercept as many scrambled communications as you want, but unless you have the sequence for decoding they're worthless to you.

I've made my own encryption programs before. As with all secrets, they're only kept secret if they stay secret.

[Anonymous No.9901355]

>>9901310

have you ever heard of key exchange protocols or asymmetric cryptography or trap door functions? You seem to have a preeeetty naive view on cryptography. E.g. you can know the sha3 protocol, and you can know the hash, you can still not in any rational justifiable time get the to the hashed file. You can with e.g. diffie hellman key exchange exchange a secret key over an insecure line and even if someone can get all of it he still doesn't know the key. Just two small examples where the "key - lock -analogy" and "if you know one and the algorithm you can get the other" fails.

[Anonymous No.9901363]

>>9901258

So 1+2.3 doesn't add up because one is an integer and the second is a real number.
Your Fields Medal is in the mail.

[Anonymous No.9901427]

>>9901355
Kek.

an equation produces a result.
The equation can't run without being told how to run.
If its figured to run, its known to run.
This isn't cryptography. Its code talking. If you have the key, the code can be broken. If a key exists at all, it can be had.

This has nothing to do with computers or even math. Its only the protection of communicated knowledge, but communications can be intercepted. From hardware manufacturers to software programmers, its all people at the end of the day, and people make mistakes. People spill the beans. People communicate. In order to encode, you need the directions to do so. Whether those directions are already part of your system or sent as part of the key, because the directions exist, so does the ability to reverse engineer them. Its all bits. There are no secret inputs and outputs in a computer. If a computer can do something, it needs the directions. Any action has a reaction.

If I say 2+2=?
i'm communicating to you the direction. You're thinking about it. Its on your mind. Your brain computer is programmed to know what 2 is and what addition is. The knowledge already exists.

Computers are not gods in a box. They only do what they're told to do. You tell it to encode, it must also know how to decode to make any use of the encoding. If it knows, the directions and key exist on your system. Just gotta know where to look for them.

[Anonymous No.9901883]

.

[Anonymous No.9901887]

>>9897238
1/7 = 142857/10^6 + (7*10^6)-1
= 0.142857 + (7*10^6)-1
= 0.142857142857 + + (7*10^12)-1
= 0.142857142857142857 + + (7*10^18)-1
:
= 0.142857... + (7*10^inf)-1
= 0.142857... + 1/inf
= 0.142857... + 0
= 0.142857...

[Anonymous No.9901892]

>>9897238

1/7 = 142857/10^6 + (7*10^6)-1
= 0.142857 + (7*10^6)-1
= 0.142857142857 + (7*10^12)-1
= 0.142857142857142857 + (7*10^18)-1
:
= 0.142857... + (7*10^inf)-1
= 0.142857... + 1/inf
= 0.142857... + 0
= 0.142857...

[Anonymous No.9901901]

>>9897238

1/7 = 142857/10^6 + (7*10^6)^-1
= 0.142857 + (7*10^6)^-1
= 0.142857142857 + (7*10^12)^-1
= 0.142857142857142857 + (7*10^18)^-1
:
= 0.142857... + (7*10^inf)^-1
= 0.142857... + 1/inf
= 0.142857... + 0
= 0.142857...

[Anonymous No.9902466]

>>9889587
try again

[Anonymous No.9902525]

10 years later and /sci/ is still getting trolled by .999.. = 1

[Anonymous No.9902663]

>Another 0.999 thread
>The same discussion
>again and again
the absolute state of /sci/

[Anonymous No.9902698]

>>9889587
Mods really need to start banning these threads.

[Anonymous No.9902719]

>>9902663
It's a meme ya dingus. What other way of keeping the retards all in one thread do you suggest? It's called Dunning-Kruger. No better retard bait than making a thread for all of them to spout basic mathematics while also feeling high and mighty because they know algebra or how to compute a geometric series.

[Anonymous No.9902749]

>>9889597
>Irony

[Anonymous No.9902866]

>>9896736
sure this is important to partial sums. You can trivially rewrite 0.9, 0.99, etc. as 1 - 10^-n, which then has a fancy limit of 1.

[Anonymous No.9902871]

>>9902815
So that's nobody's walking sidewalk outside of my house, because (you) don't have evidence that any people outside of my house

[Anonymous No.9903105]

>>9901240
>lets pretend infinity is finite

[Anonymous No.9903360]

>>9892776
Nicely said anaon

[Anonymous No.9903933]

>>9899249
holy shit lmao

[Anonymous No.9904559]

>>9889587
Being too stupid to understand why .9 repeating equals 1 doesn't mean there's a fallacy in math. Fuck you. You're the retard for not understanding this result. You may as well argue that 6/3 and 2 are "obviously" not the same numbers.

[Anonymous No.9904567]

>>9889632
>Since infinity isn't a thing.
Tell me what the largest natural number is or GTFO.

[Anonymous No.9904574]

>>9890117
Take Calc 2.

[Anonymous No.9904579]

>>9889597
>your just rarted

[Anonymous No.9904587]

>>9899249
You forgot a step in between row 4 and 5, fucking retard.

[Anonymous No.9904589]

>>9900787
It's called Calc 2. Take it and then apologize for being retarded.

[Anonymous No.9904646]

>>9899249
>4*.4444...=4.4444
>4x=4+x => 4x=4

algebra 1 pls go

[Anonymous No.9904661]

>>9901258
there are other ways to define addition and exponentiation which to not have to take place in a set.

e.g. if 2 is a set of cardinality 2, and 3 one of card. 3, then the set of functions from 2 to 3 has cardinality 3^2. You can extrapolate other properties of arithmetic like this in Sets bc it has a notion of cardinality and is cartesian closed.

For example, we often use this abstraction of arithmetic when we say that P(N) has size 2^N (it's even standard notation).

[Anonymous No.9904666]

>>9901069
ok, but that's not how pure mathematicians think about it. 9.9... is just shorthand for a convergent series, which has very definite properties. If you think of reals as equivalence classes of decimal representations, the fact that [1.0]=[1]=[01]=[.9...] is no stranger than [6/4]=[3/2].

[Anonymous No.9904678]

>>9901207
this doesn't make any sense. That's just the definition of decimal representation. Would you say the same thing about 3 represented as 3.0000.....?

[Anonymous No.9904695]

>>9890273

>Start by declaring x as a value.
>Perform valid manipulations
>Find that x is equal to a “different” value
>Those two values must therefore be the same.

Is that hard to follow?

[Anonymous No.9904705]

>>9889712
>when you... have to convince every motherfucker
>define 0.999 as what you need it to be
Mathematics in the 21st century, ladies and gentlemen. If the Math doesn't work, just make it up.

[Anonymous No.9904738]

>>9889729
all this proves is that the decimal system doesn't give a unique representation to every real number. when your brain evolves to grasp this concept, there is your new tool.

[Anonymous No.9904741]

>>9904661
In axiomatic set theory, addition and exponentiation are defined as subsets of Cartesian products of sets. "Take place (with)in a set" isn't rigorous phrasing, but colloquially the operations take place within a set.

The set of functions of from any set to the empty set is empty. The cardinality of the empty set is 0, however 1^0 != 0. Therefor, the cardinality of A x B is not equal to the cardinality of the cardinality of B to the power of the cardinality of A, for all A and B. I'm not sure what you are trying to communicate.

The second equality P(N) = 2^N is true but describing it as an "abstraction of arithmetic" is imprecise.

>>9901258
There are other sets besides the natural numbers for which arithmetic is defined. The most familiar to include infinity being the extended reals. You would be correct in that the extended reals are not a semi-group, however the properties of a semi-group are not required for arithmetic.

[Anonymous No.9904751]

Sageru

[Anonymous No.9904757]

>>9904741
um, like all numbers 1^0=1 in arithmetic. And identically, the collection of functions o-->1 also has cardinality one. We don't want 1^0=0, just as they are not equal in arithmetic.

Ofc it's not precise. You can google cardinal arithmetic to find the precise definition easily.

Also,
>The set of functions of from any set to the empty set is empty. The cardinality of the empty set is 0, however 1^0 != 0.

It sounds like you are getting the direction of your arrows confused. The first thing you said was a statement about maps A-->o, which should correspond to 0^A, which, as expected, is an empty set of cardinality 0. The sentence you followed it up with is about sets of maps o-->A, which will always have cardinality 1.

The only funny business is 0^0, which has cardinality 1.

All I was trying to communicate is there is a sense in which 2^inf is interpretable if we are careful. the cardinality of AxB for finite sets is certainly the cardinality of A times the cardinality of B. We can take it as the definition for products of cardinalities for arbitrary sets.

[Anonymous No.9904782]

>>9904757
!= is a symbol for "not equal".

Cartesian products that include the empty set are empty. Functions are subsets of Cartesian products. All subsets of the empty set is empty.

The empty set had cardinality 0, therefor all functions to or from them empty set has cardinality 0.

You stated functions( 2 -> 3) = 3^2. Generally, this would be functions( A -> B) = B^A.

However, functions(1->0) != 0^1 and by counter-example the equality does not hold for all sets A and B.

>the cardinality of AxB for finite sets is certainly the cardinality of A times the cardinality of B

No, this property will not hold for the empty set which is finite.

2^inf is defined for the extended reals.

[Anonymous No.9904792]

>>9904782
>The empty set had cardinality 0, therefor all functions to or from them empty set has cardinality 0

False. The collection of maps to o has cardinality 0, corresponding to the arithmetic fact 0^A=0. The collection of maps from o has cardinality 1, corresponding to the unique empty function o-->A, which has cardinality 1, corresponding to the arithmetic fact that A^0=1. (Both match the arithmetic facts except in the funny case 0^0)

>No, this property will not hold for the empty set which is finite.

Also false. oxA=o, corresponding to 0*A=0 for all A.

I was responding to your message under the assumption that != means not equal.

sauce: https://en.wikipedia.org/wiki/Cardinal_number#Cardinal_arithmetic

[Anonymous No.9904801]

>>9904782
I think perhaps you are getting the fact that o-->A has an empty graph confused with the fact that this is still a well-defined function. https://math.stackexchange.com/questions/45625/why-is-an-empty-function-considered-a-function responds to this question.

[Anonymous No.9904815]

>>9904801
to clarify their point:

the set of functions B^A from your point of view is the collection of subsets of AxB (relations) which satisfy the "function condition": for all a in A, a is related to exactly one b in B. For B^o, this will include the subset o of oxB, since it satisfies the condition trivially. So, {o} is the set B^o, which has cardinality 1.

[Anonymous No.9904826]

>>9889587
no 9.9999999.../10 does not = 0.999999999... it = ~0.9999999999...

[Anonymous No.9904827]

>>9904815
also, .9999=1

[Anonymous No.9904864]

>>9904695

Show us more of your magic, oh mighty Wizard!

[Anonymous No.9904869]

>>9904559

Go back into your kennel, dog, what is being discussed here is far beyond your comprehension. Gnaw on a bone instead, there's a good boy!

[Anonymous No.9904873]

>>9902466

x = 0.999...

How convenient. Let x equal some number that can never be defined. A number that doesn't exist.Nice.

And these pompous little twats wonder why they are the laughing stock.

[Anonymous No.9905196]

>>9904589
Fucking godless retard.

[Anonymous No.9905201]

>>9904666
Repeating decimals have absolutely nothing to do with brainlet convergence. You acquire these values by simple long division. Stop trying to hijack basic terminology.

[Anonymous No.9905205]

>>9904678
3 is not a fucking equation, shitstick.
[math]\text{Go back to} \text{ reddit}[/math]

[Anonymous No.9905246]

>>9905196
found the home schooled jesusnut

[Anonymous No.9905399]

>>9904695
>manipulating infinity

[Anonymous No.9905508]

>>9905399
Keep tally on pairing and it's ok.

https://youtu.be/i7c2qz7sO0I?t=1m30s

[Anonymous No.9905631]

What the fuck is the point of mods if they dont trash these dumb shit threads?

[Anonymous No.9905636]

>>9889597

[Anonymous No.9905652]

>>9904826
>m-muh feelings
...and not one iota of proof was seen

[Anonymous No.9906074]

>>9905205
lmao ok if you need it spelled out then 3.000....=3.0

[Anonymous No.9906439]

>>9889587
its 1 minus an infinitely small part. so small... it might as well not be there.

[Anonymous No.9907236]

why not spent your valuable times to discovering greater things than arguing philosophically, math is a just tool, we like to make them uniform and formal but there is no "truth" or "profound beauty" whatsoever

[Anonymous No.9907307]

>>9905631
t. person who bumps the thread