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9889074 No.9889074 [Reply] [Original] [archived.moe]

Let me get this straight. 0.999... is really really really really really really really really really really really really really really really really really really really really close to 1 so we just say it equals 1 but it isn't ACTUALLY 1. right?

>> No.9889078

What's the number between .999... and 1?

>> No.9889081

0.9999 is not well defined. The sequence of partial sums 9/10+9/100+...9/(10^n) converged to 1, but there is no number represented by 0.999

>> No.9889083

>>9889074
No.
> really really really really really really really really really really really really really really really really really really really really close
This implies that you believe eventually the 9s end. The 9s don't end. It isn't "really close" to 1 -- the 9s don't end at some point leaving a space between the last 9 and 1.0. The 9s never end. It's equivalent to 1.

>> No.9889090

>>9889078
that's like asking what the last digit of pie is. It's impossible to know but it exists.

>> No.9889097

>>9889090
i meant pi the number.

>> No.9889099
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9889099

>>9889090
>that's like asking what the last digit of pie is
>pie
I knew this was a troll, but you might wanna try a little harder next time if you want to have fun fucking with people
Watch some NJWildBerger and start parroting what he says, then come back with this argument

>> No.9889105

>>9889099
>>9889097
easy to get them confused because of the its association with pies and pie day

>> No.9889200

>>9889074
haha OP this meme is so funny xd

>> No.9889218

>>9889078
(1 + 0.999...)/2
Your move brainlets

>> No.9889229

>>9889081
>0.9999 is not well defined
It is perfectly well-defined as
[math] \displaystyle \frac{9999}{10000}[/math]
Lrn2repeating-decimal fgt pls

>> No.9889238
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9889238

>>9889218
got em

But seriously, how does adding 9’s infinitely ever change the place value of the previous 9’s? If they must be repeating, then the number doesn’t ever truly exist, and it is never complete. Yet 1 is complete, so the equality does not hold.

>> No.9889249

0.999... is a convergent infinite sum that converges to 1. While it's true that for any finite n, 9/10 + 9/100 + 9/1000 + ... + 9/10^n is strictly less than 1, the limit of the sum converges to 1.

>> No.9889264

>>9889249
Why don’t we say that a vertical asymptote touches the curve? How can we say that an infinite limit implies that a goal can’t be completed, and then say the exact opposite?

>> No.9889276

>>9889264
Because an asymptotic curve makes sense. 0.999... only makes sense as the limit of a sequence and that limit happens to be 1.

>> No.9889288

>>9889276
I see no difference. The vertical asymptote is a limit just as 1 is. Either we say that 0.999... can never equal 1 and that an asymptote is never touched or we say the opposite for both. If a vertical asymptote is at x = 1, how can only one statement be true?

>> No.9889289

>>9889074
The problem is that you're thinking of infinite decimal strings as the canonical form of the real numbers. We don't define real numbers as decimals, but using some construction like equivalence classes of Cauchy Sequence or Dedekind Cuts. It can them be shown from there that we can represent reals as infinite decimal strings (0.999... denoting the Cauchy sequence 0.9, 0.99, 0.999, etc for example). This representation is not unique.

>> No.9889313

>>9889289
what?
its simple

The number between 0.999... and 1 is

0.999... + 0.000...1

>> No.9889317

>>9889238
For 0.999... to be less than 1, the 9's have to stop somewhere.
Since by definition they don't stop,
0.9...=1

>> No.9889321

>>9889238
Numbers aren't a process, they just are. They're not in 'the process of completing' any more than 1 is in the process of completing all the zeroes it has after the decimal place, like 1.00000....

>> No.9889324

>>9889317
Even if they don’t stop you haven’t proven that they ever equal 1, only that the gap between 1 and 0.9 is always getting smaller. The gap would never disappear if the 9’s never stop. If the gap disappeared, then the 9’s would have a reason to stop.

>> No.9889328

>>9889324
The gap between 1 and 0.999... becomes zero. Prove me wrong.

>> No.9889332

>>9889288
Repeating decimals are defined by the limit

>> No.9889335

>>9889074
What is 1/3 in decimal form? What's that times three?

>> No.9889336

>>9889313
How about this?
.999... + 0.000...12

>> No.9889342

>>9889083
how can 1 divide itself into bits eternally? The universe isn't infinite

>> No.9889344

>>9889328
That’s like saying a curve eventually touched its vertical asymptote. If the gap ever became 0, then the previous 9 would be separate from 1, and that gap will be bigger at the previous 9, and so on, until reach 0.9, meaning there are a finite amount of 9’s.

>> No.9889347
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9889347

>>9889344
>Implying curves don't touch their asymptotes

>> No.9889348

>>9889321
numbers represent reality

>> No.9889356

>>9889348
ur mums so fat she isn't even a number

>> No.9889360

>>9889335
Why is 1/3 so weird? 1/4 gives you a clear cut answer but 1/3 doesn't. What's the matter with 3?

>> No.9889361

>>9889347
I would use the same gap argument that you ignored to show that curves don’t touch their asymptotes

>> No.9889370

>>9889361
What number is 1/(1 - 0.999...)? You should be able to calculate that just fine if there's a number there.

>> No.9889377

>>9889370
It can not be represented by a number, it is always increasing. Not infinity, but approaching infinity. 10^10.....

>> No.9889380
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9889380

>>9889347
>Not recommended

>> No.9889386

>>9889377
So is 1 - 0.999... not a number either?
Or is it a number that you can take the reciprocal of and get something that isn't a number?
What other not-a-numbers exist in this not-a-number system of yours?

>> No.9889392

>>9889090
>It's impossible to know but it exists.
That's not how infinity works.

>> No.9889397
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9889397

>>9889392
>he believes in infinity

>> No.9889398

>>9889386
0.999... isn’t a number and it has no purpose. We live in a finite world with clear distinctions. Infinity is an invention

>> No.9889400

>>9889398
It is a number, and its purpose is to confuse brainlets like yourself.

>> No.9889408

>>9889400
If it had any useful application then you would have provided it. Another problem I have is with Zeno’s paradox. Mathematicians “solved” this problem by saying 1/2 + 1/4 + 1/8 converges to 1 or however they wanna word it. The fact is this sum never equals 1, so you cannot, in fact, reach 1 with the above process. How can we still walk from one side of the room to another? Because there is no such thing as an infinitely small distance and even if there were, we humans can obviously not move at such a small distance.

>> No.9889413
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9889413

>>9889408
I did provide a purpose. It's a great litmus test for sifting out Wildbergers like yourself.

As for your paradox: You're more content with the idea that we teleport from point to point rather than get there smoothly?

>> No.9889418

>>9889074
No its 1

>> No.9889425

>>9889413
We have to teleport. Any smooth movement would consist of infinite moments, and any subset of that would contain infinite moments, ad infinitum. The finite cannot contain the infinite. And an infinitely small distance cannot actually exist, because if it did, and you could measure it, then there would be a smaller distance than that. So if you say that you moved through an infinite amount of distances, how large were those distances? They can’t be infinitely small, but if they were any bigger, then you would have moved an infinite distance.

>> No.9889426

>>9889090
No it doesnt exist


why do i always fall for this brainlet b8

>> No.9889430

>>9889425
>The finite cannot contain the infinite
How many numbers are there between 0 and 1? I'll wait for you to count them.

>> No.9889441

>>9889370
You need to go to a different number system (like projective line) to define 1/0 as a number of that number system. it certainly isnt a real number

>> No.9889447

>>9889430
Mathematically, there is no limit to how many numbers there are between 0 and 1. This only means that there is no largest finite amount, not that there is an infinite amount. I can cut the distance into however many regular pieces I want, but it must be a finite distance and there must be finite pieces. At no point does it magically become infinite.

>> No.9889448

>>9889324
>let's pretend that infinite is finite

>> No.9889458

>>9889447
>must always be finite distances
What's the next smallest number after 0?

>> No.9889460

>>9889458
Undefined

>> No.9889466

>>9889342
Who care about the universe, we are talking math here not physic.

>> No.9889469

>>9889074
I'm a brainlet

So pls, dont shame me

But...

1/3=0.33333......

0.33333333....*3=0.99999.....

1/3*3=1=0.9999.....

Is that slightly correct?

I study law, so I don't know wtf im doing here

>> No.9889480

>>9889448
>what is contradiction
>>9889458
>What's the next smallest number after 0?
In reality, the answer is 1. If I cut an apple in two, it is not one apple cut in two, but now two halves of an apple. There is a fundamental unit for space and time, and all objects are composed of large amounts of these units. A larger apple is said to be one apple, although it’s parts are greater in number than the smaller apple. Anything that can be divided was composed of multiple parts to begin with.

>> No.9889487

>>9889458
This ones easy. Epsilon.

>> No.9889493

>>9889480
In fractional form, such as in 1/4, 1 is just a placeholder for whatever must be divided by 4. It is the fundamental unit. So a number like 1/10^1000 only exists to portray a relationship between two quantities, but it is not a true quantity itself. So if I were to answer your question about what is the smallest fraction, then I would have to know the greatest amount of units that exist in the universe. I believe that number is finite, but no matter, I can conceive that the number is greater. But I can not conceive of an infinite number, so there is no limit to that greatest number, but it can’t be infinite. Only 0 is infinite.

>> No.9889537

>>9889408
>there is no such thing as an infinitely small distance

uh, zero

>> No.9889564

>>9889090
it doesn't

>> No.9889571

>>9889408
> Because there is no such thing as an infinitely small distance

As an absolute no, there isn't. But there can be where there is an equally infinitely large distance to counterbalance it and drive the difference to 0.

You could ask why the 2 don't eliminate each other into nothingness and to this i will answer there is probably an infinite structure that holds the 2 together allowing them to interact in ways that won't eliminate each polarity.

>> No.9889579

>>9889571
I just realized, in an infinite universe scenario, the neutral structure skeleton that holds the 2 forces together not allowing them to destruct cannot be neutral, it has to either have a positive or negative value to it and this would shift the balance of infinity.

Infinity doesn't seem to exist indeed. Unless we go outside the universe and claim that holding structure is "god" itself, but then we can start claiming anything really.

We live in a finite universe.

>> No.9889580

>>9889579
>cannot be neutral
And I just realized again, neutrons exist. So it is possible. The universe might be infinite.

this is bumfuckery. fuck it, im a brainlet, im not trying anymore

>> No.9889606

>>9889090
No it's 1

>> No.9889610
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9889610

>>9889397
>he doesn't believe in [math]/bbb{R}[/math]

>> No.9889896 [DELETED] 

>>9889074
If astrophysicists think both [math]\pi[/math] and [math]\e[/math] both equal 3, then I guess anything is possible.

>> No.9889898

>>9889074
If astrophysicists think that [math]\pi[/math] and [math]e[/math] are equal to 3, then I guess anything is possible anon.

>> No.9889900
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9889900

>>9889074
>really really close to 1

Two numbers are different if they differ by a FINITE amount.

Pick ANY finite distance that differentiates between them and it will be CLOSER than the distance you chose.

Since they do not differ by ANY finite amount they then must be identical.

>> No.9889904

>>9889900
Is a vertical asymptote at x = 1 ever touched by the curve approaching from the left?

>> No.9889908

>>9889904
>ever touched

Implies NO finite distance exists between them... yes!

>> No.9889919

>>9889908
Then there exists a point on the curve at x = 1. Since it approaches the asymptote exponentially, it will move away from it exponentially. Starting from the first point where the curve meets the line, we can trace the curve backwards, and the gap between it and the asymptote will ever increase until we reach y = 0. We could do this in a finite amount of time, which contradicts the nature of an asymptotic curve. Also, for the graph 1/ 1-x, you’re admitting that the graph can yield a point at x = 1, so we can divide by 0, which is impossible.

>> No.9889928

>>9889919
>the first point

There is NEVER a first point, where they meet.

STOP thinking in the finite!!!!

>> No.9889930

>>9889099
I've got a little butthurt actually

>> No.9889932

>>9889928
Then there isn’t a point at all

>> No.9889934
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9889934

>>9889932
>Then there isn’t a point at all

Excellent... you are learning!

>> No.9889949

>>9889934
If there is no point of intersection, then it never touches.

>> No.9889962

>>9889949
>it never touches.

Why are you incapable of understanding that to say "it touches", implies that there is no FINITE distance between them.

If they do not "touch" then there IS a finite distance between them.

There is NO finite distance between them, so they are equal.

Infinite and finite are totally different ways of thinking. You live in a finite world so EVERYTHING you know follows rules you understand.
You need to open your mind to the infinite.

>> No.9889964

>>9889083

you ABSOULUTE FUCKING retard fucking trying to sound smart, at the same time contradicting yourself.

>>the 9's never end
>> its equivalent to 1

it will literally never be equivalent to one, the whole definition of 0,9999infiniterepeat is that no matter how many 9's you add, you'll NEVER reach 1.

it'll just be very close to one.

>> No.9889967

why are yall letting yourselves get hung up on physical analogies about the number line

it's fucking pointless

>> No.9889976

>>9889962
>You need to open your mind to the infinite.

For example, you can count all the rational numbers (There is a unique cardinal number you can assign to each rational number).

The cardinal numbers are a subset of the rational numbers.

This seams contradictory (and it IS in a finite world), but is easily to show works in the infinite.

>> No.9889983

>>9889447
>This only means that there is no largest finite amount, not that there is an infinite amount.
You're getting warmer, bucko. Now apply that argument to the question of summation of [math]\sum_{n=1}^{+\infty} \frac{1}{2^{n}}[/math]

>there is no smallest finite distance between (1/2 + 1/4 + ...) and 1
That's the whole point of summation, if there is no smallest finite distance, then that implies that the distance is zero.
Here, I'll prove it to you.

[eqn]
\textrm{Let } a, b \in \mathbb{R}. \\
\textrm{If } \forall \epsilon > 0 : |a - b| < \epsilon, \textrm{then } a=b. \\
\\
\textrm{Proof:} \\
\textrm{Assume the contrary, that } a \neq b. \textrm{ That would imply } |a-b|>0. \\
\textrm{Let } \epsilon = \frac{|a-b|}{2} > 0. \textrm{ Then follows: } \\
|a-b|< \epsilon = \frac{|a-b|}{2} \Rightarrow \\
\Rightarrow |a-b| - \frac{|a-b|}{2} < 0 \Rightarrow \\
\Rightarrow \frac{|a-b|}{2} < 0 \Rightarrow \\
\Rightarrow |a-b| < 0 \\
\textrm{Which is a contradiction, so our assumption that } a \neq b \textrm{ is false.}\\
\textrm{Thus, } a=b. \\
[/eqn]

>> No.9889989

>>9889962
>open your mind to something that doesn’t exist
0.999... isn’t a number, it only represents a continual process. You can’t say that it contains an infinite amount of 9’s, only that there is no limit to how many 9’s you can add. At no point will the 9’s ever equal 1. You cannot conceive an infinite process as something that becomes actual; it is never-ending, never complete. A circle cannot have an infinite radius, or it would no longer be a circle. A finite distance can not contain infinite intervals, or it would no longer be finite. If we conceive 0.999.. in the most natural way possible, that is, fractions, then we would realize that as we increase the numerator, we also increase the denominator. At no point does the numerator ever become equal to the denominator. Infinity is a broken concept that is completely misused and causes contradictions and paradoxes. There is no use for this thinking. We can use methods of exhaustion without ever conceiving of a quantity that is infinite.

>> No.9889992

>>9889964
You are the retard here

>> No.9890001

>>9889976
Fractions aren’t truly numbers, only relationships between numbers.

>> No.9890005
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9890005

>>9889964
> no matter how many 9's you add

that's why infinity's definition states that it is larger than any real number

infinity is not a number, it's an unbounded value

>> No.9890006

>>9889983
0.999... isn’t a REAL number, though.

>> No.9890015

>>9889989
At some point, you will learn what a limit is. I suggest you revisit this issue when you do.

>> No.9890016

>>9890005
>infinity is not a number
>infinity is an unbounded value
You’re correct that it is not a number, but it also isn’t a value. (What’s the differences between an unbounded number and an unbounded value?)
It only means that there is no limit to the values which we can conceive. But every value we can conceive is finite.

>> No.9890021

>>9890016
>unbounded number
no such thing

>> No.9890022
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9890022

>>9889992
no retard. no retard. You're the retard

>> No.9890032

Let me show the nonsense of 0.999... once and for all. There exists a city, such that, for every 10^n amount of people, there is a 10^(n-1) amount of people who have brown hair, and 1 person with red hair. As n is unbounded, the amount of people with brown hair is approximated by 0.999...

If there are 10 people, then one will have red hair. If there are 100, then 1 will have red hair. No matter what the population is, there will always be one person with red hair.

>> No.9890034

>>9890032
>>9890032
****(10^n) -1

>> No.9890046

>>9890021
Correct. And 0.999... isn’t an unbounded number, but an unbounded relationship between a numerator and a denominator. Their difference is always 1, but the numerator is always increasing.

>> No.9890057

>>9890032
Your problem is that you don't grasp the mathematical concept of "infinity". It's not a really really really big number, it's exactly what makes 0.999... equal to 1.

>> No.9890093

>>9890057
Show me a practical application where 0.999... equals 1, or where the validity of this statement can be used for another practical application. It is more accurate, and just as practical, to say that for any 10^n, where n can be any finite number (no limit to how large it can be), there exists a relationship of 10^n -1 to the whole.

>> No.9890134

>>9890093
OK... you are obsessed with nomenclature.

Please express in the NEXT number after 1.0000...

----

OK now you begin to understand why
0.999... = 1.0

>> No.9890154

>>9890093
That's the thing, there is no practical application. The mathematical notion of infinity is an abstract construct. You're having trouble understanding it because you want to understand it in a physical sense. There is no infinity in nature.

>> No.9890162

>>9890134
The next number after 1 is 2. The number after 0 is 1. All “numbers” between 0 and 1 are relationships between a part and a whole. So the smallest fraction after 1 is simply dependent on the denominator, since the numerator is always 1. But there is no limit to how large the number can be, so there is no limit to how small the fraction can be. Since there will always be a 1 in the numerator, the part never equals 0. Similarly, with 0.999... there will always be a difference of 1 between the numerator and the denominator. Write out the differences as you increase n:

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......

How does this ever magically become 0?

But all this is only true abstractly. It has not been proven that there exist an infinite amount of units in the universe, so there could be a limit to how small a single unit could be to the total amount of units in reality.

>> No.9890171
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9890171

>>9890162

I
I am
I am overwhelmed by your stupidity.

>> No.9890178

>>9890006
>III The Completeness Axiom
>If a non-empty set A has an upper bound, it has a least upper bound.

Yeah, 0.999... is a real number.
It's the least upper bound of a set [math]\{a \in \mathbb{Q}|a<1\}[/math].

>> No.9890186

>>9890171
Nothing I have said is inconsistent, or contradicts reality. If I did, you would have pointed it out, instead of insulting. Convenience is not always accuracy.

>> No.9890201

>>9890178
0.999... is (10^n - 1) / (10^n)
where n has no limit

If a fraction is unbounded in both the numerator and denominator, how can the fraction’s value be bounded? Its value is always increasing, but it is bounded because it will never become the whole. The part 0.999... will never become the whole, 1.

>> No.9890203

>>9890186
>or contradicts reality

That is your problem.

The infinite DOES contradict finite reality.

In a finite world a subset can not map to the super-set, but in the infinite it CAN (Cardinal numbers to Rational numbers).

>> No.9890222

>>9890203
There are more rational numbers because you are simply taking actual numbers and arranging them, part to the whole. Given only the integers 1 and 2, we can form the rational numbers 1/1, 1/2, 2/1, and 2/2. Given 1, 2 and 3, then we can form 1/1, 1/2, 1/3, 2/1, 2/2, 2/3, 3/1, 3/2, 3/3.
>but 1/1, 2/2, and 3/3 are the same!
Not in reality, they are not. 1 apple and 1 orange is distinct from 3 apples and 3 oranges, only the relation between them is constant. So for any number n of integers, there are n^2 + n rational numbers.

>> No.9890254

>>9890222
Are you implying the the rational numbers are uncountable?

They are countable. Look it up, it is a very simple elegant argument.

>> No.9890269

>>9889074
In traditional mathematics 0.999... == 1. In Wildbergian Mathematics 0.999... doesn't exist because you cannot compute it. Any number that cannot be computed doesn't exist as a number, only as an intermediate representation that might be helpful when combined with another intermediate representation so long as the combination, somewhere down the road, produces a computable number.

>> No.9890271

>>9889989
This is the exact part you get hnfunny with. Learn more calculus to keep you sayjng stupid like "number is process" shit

>> No.9890284

>>9890254
I only said that there are more rational “numbers” than natural numbers, which I proved. Given a finite set of natural numbers, there are more rational numbers. Although an infinite set is illogical and inconceivable, even then, every natural number could form a relation with every other natural in the set, which would be just as large as the list of numbers themselves. All rational numbers with the numerator 1 would already be equal to the set of natural numbers, and we haven’t used 2 as a numerator, so it is clear that the set of rationals will always be greater.

>> No.9890287

>>9890154
Much math is construction instead of reality.
infinity: not real
circles: not real
points: not real
...
not real, as in does not exist in nature.

>> No.9890295
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9890295

>>9890284

You are a troll!

>> No.9890302

I’m having trouble finding a way to make it a fraction but it works with 1,99999999999999 (which is basically 2):
19-1/9 = 18/9 = 2
So it must be the same way for 0,999999 i suppose

>> No.9890307

>>9890295
You are the one who has faith in something you don’t understand. But thank God you have axioms! Because anything is true if you define it how you want to.

>> No.9890325

>>9890307
>has faith in something you don’t understand

But I do understand it.

Your the one who thinks all the OTHERS are wrong.

>> No.9890351

>>9890325
10^n will always be greater than 10^n - 1
An infinite number cannot be conceived which makes this statement false. Why play with this cute notation of infinity when it makes no intuitive sense and has no application? It is true when we say that the limit of (10^n - 1) / (10^n -1) equals 1 but that doesn’t mean it will ever equal 1. It is unbound in its numerator and denominator values but bound in its fractional value, that is, the relationship will never equal 1. Magically transforming the number into an “infinite” one does not make the problem go away, and is hardly intuitive.

>> No.9890503

>>9890201
>The part 0.999... will never become the whole, 1
But it will, just watch

Lim n -> inf (10^n-1)/(10^n) = 1

Ta dah

>> No.9890506

>>9890284
>I only said that there are more rational “numbers” than natural numbers, which I proved
Define "more" in the context of infinite sets

>> No.9890515

>>9889342

1 doesn't even exist in the universe, so how is that relevant? In mathland we can do whatever we want as long as we're rigorous enough.

>> No.9890523

>>9889081
0.999.... is well defined. It's literally defined as exactly what you posted. The limit of the sequence of partial sums 9/10 + 9/100 + ... + 9/10^n

>> No.9890529

>>9890503
0.999... is unbounded in value, but bounded because it will never equal 1. Just because 1 is its limit does not mean it will equal 1. Again, this is like saying a vertical asymptote is a limit yet the function reaches it at infinity.

>> No.9890531

>>9890506
Rational numbers are 2 dimensional, whereas the natural numbers form a line. An infinite plane and infinite line are unbounded, but the plane is clearly larger.

>> No.9890534

>>9889360
It's magic and is the meaning of life.

>> No.9890659

Why is it harder to visualize Graham's number than infinity?

>> No.9890671

>>9890659
Good point. Everyone pretends to understand infinity when they really don’t

>> No.9890752

>>9890529
>unbounded
>bounded

choose 1

>> No.9890803

>>9890752
Both its numerator and denominator are unbounded, but since the numerator is always one less than the denominator, the fractional value is bounded. It will never equal 1

>> No.9890821

>>9890803
Yes. The fractional value will never equal one. The limit equals one, therefore 0.9...=1.

>> No.9890848

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.

>> No.9891141

>>9889218
0.9999.... = ( 1/2 + 1/4 + 1/8 + ...)

>> No.9891142

>>9891141
< 1

>> No.9891178
File: 971 KB, 480x360, 1532148461633.gif [View same] [iqdb] [saucenao] [google] [report]
9891178

these threads always bring the kek out of me
good bait op

>> No.9891188

>>9889342
Non sequitor

>> No.9891196

>>9889328

Not zero, just 1/∞

>> No.9891197

The question is flawed, "0.999999..." isn't a """"""number"""" per say

>> No.9891230

>>9889074
it depends on your axioms.

>> No.9891360

>>9889081
>>9890046
>Their difference is always 1, but the numerator is always increasing.
????

>> No.9891384

>>9891360
9/10
99/100
999/1000
Both values are ever increasing, but their difference is always 1. The relation between the part and whole is approaching its maximum, but it never actually becomes the whole.

>> No.9891467

>>9891384
not with real numbers, but with inf, sure

>> No.9891470

>>9891467
So 0.999... is not a real number?

>> No.9891474
File: 54 KB, 625x325, retard.jpg [View same] [iqdb] [saucenao] [google] [report]
9891474

>>9891470
number of 9's isn't

0.9...=1 so yeah, real

>> No.9892001
File: 20 KB, 534x236, limits.png [View same] [iqdb] [saucenao] [google] [report]
9892001

>>9891142
the "..." means that we are refering to the limit of the sequence.

>> No.9892057

>>9889081
Convergence is an invalid concept. The technicality is that a method will tend towards a limit. 9/10^n tends towards the limit of 1.

For different problems where the sum tends towards "infinity" in that it continues to grow, this is called divergence and considered unhelpful.

Mapping all possible integers from 0 to infinity to instead be real numbers between 0.9 and 0.999..., provides that convergence and divergence are actually the same identical concept, but disingenous people abuse convergence to have more weight and meaning over divergence. Divergence never comes close to reaching infinity, so 9/10^n comvergence also never comes close to reaching 1.

The truth is, convergence/divergence is an invalid method while dealing with infinity, because infinity itself is invalid.

0.999... × 10 ≠ 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... can't exist because you can't reach infinity in the first place either.

>> No.9892067

add the infinite 1 and you're good

>> No.9892071

close enough

>> No.9892075
File: 7 KB, 420x420, b36.png [View same] [iqdb] [saucenao] [google] [report]
9892075

>>9889074
If there exists a number close enough to infinity to be considered infinity, then there also exists a 0.999... value close enough to 1 to be considered 1.

Pretty sure there isn't a number close to infinity though.

>> No.9892080

[ 1 . 0 ]
-[ 0 . 9 ]
=
[ 0 . 1 ]


[ 1 . 0 0 0 ]
-[ 0 . 9 9 9 ]
=
[ 0 . 0 0 1 ]


[ 1 . 0 0 0 0 0 . . . ]
-[ 0 . 9 9 9 9 9 . . . ]
=
[ 0 . 0 0 0 0 0 . . . 1 ]

>> No.9892097

>>9892057
inf isn't a number
even the definition says "larger than any real number"

>> No.9892125

>>9889328
>The gap between 1 and 0.999... becomes zero. Prove me wrong.
no, the gap is infinity small.

>> No.9892141

there is no infinitely small number between 0.9... and 1, because they're the same number. they're two different representations of the same number.

the fact that they look different is an artifact of decimal rendering of numbers and you shouldn't read anything more into it than that

>> No.9892274

>>9892097
If inf isnt a value on the numberline between 0 to inf

Then 1 isn't a value on the numberline between 0.9 to 1

QED

>>9892141
[math]\frac{1}{3} > 0.\bar{3}[/math]

This isn't an artifact of decimals, this is just a brainlet issue left unmitigated.

Only if 1÷3 = 0.333... does 0.999...=1, but 1÷3 does not equal 0.333...

the real result of 1÷3, [math]\frac{1}{3}[/math], is larger than 0.333...
There is never enough work done in accumulating extra 3's in 0.333... to have a direct equality with [math]\frac{1}{3}[/math].

decimal representation artifacts are only because mathleticians of the past were too cucked to try figuring to better fix mathematics. Don't be a dumb cuck and let the retards turd smears continue into the future. Step up to the plate, use your brain.

>> No.9892339

>>9892274
>the real result of 1÷3, [math]\frac{1}{3}[/math], is larger than 0.333...
it's not though

>> No.9892355

>>9892274
>on the numberline
it's not on the numberline
anything on the numberline is a number (duh)

>> No.9892698
File: 25 KB, 505x461, GreatTeacher.jpg [View same] [iqdb] [saucenao] [google] [report]
9892698

>>9889074
there are two possibilities you are an undergrad or you are a real mathematicisn
1. undergrad
you don;t believe that 1 = 0.99999... because either you don't get limits yet
or
2. you are a mathematician, and you believe that there is a difference between aci, actual infinities and poi, potential infinities. And that these are different.

Since all irrational numbers are defined as limits of sequences (see definition or 'e' for ex), you believe the irrationals, and therefor the reals, depend on poi's and therefore "don't exist". From this you can prove that every uncountable ZFC set is a contradictory non-set. Therefore the world of mathematics is in a catastrophic "FOURTH CRISIS" and all butthurt foundational mathematicians have to start over from scratch.

3. You are an engineer and don;t give a shit about the distinction between aci and poi, and think the only crisis of mathematics is their rapidly growing irrelevancy,

>> No.9892705

>>9892698
Or,
4. They're working in a number system other than the real numbers, which allows for infinitesimals

For instance, in the surreal numbers, (1 - 1/infinity) is actually a definable number that's different from 1. (I'm doing some handwaving here, "infinity" is also a much more complicated concept in the surreal numbers, there's not just *one* infinity.)

>> No.9892759
File: 20 KB, 480x360, brain1.jpg [View same] [iqdb] [saucenao] [google] [report]
9892759

>>9892705
invent calculus using infinitesimals

infinitesimals fake news, use cauchy sequences instead

find out infinite sequences are fake news. return to infinitesimals.

Leibniz smiles

>> No.9892804

>>9892698
>a mathematician believes there is a poi, potential infinity.
No mathematician believes in retarded shit like that.

>> No.9892857

For those that don't actually understand why 0.999... = 1 :
[math] 1 \in \mathbb{R} [/math] is literally defined as the set of all Cauchy sequences of rational numbers such that [math] \lim_{ n \to \infty } a_{n} - 1 = 0 [/math] and the real limit of every such sequence is also 1 by the definition of an equivalence class. The number 0.9999... is the limit of one of such sequences and therefore, it's also 1.
For the baiters:
>inb4 you're using 1 to define 1, your reasoning is circular xd
I'm not. The 1 we used to define the real 1 is the set of all ordered pairs of integers (a, b) such that a=b.
>inb4 I don't believe in infinity so your reasoning is invalid xd
Do point out where in the post I used infinity. Hint: a limit to infinity doesn't actually use infinity. With the rigorous definition of a limit, you can have limits "to infinity" even if you're a ultrafinitist.

>> No.9893117

You guys are fucking stupid, let me explain. If you write out .99999... if you theoretically kept writing 9s it would never = 1, because you'd die first. Let me give some mathematicalproof for you brainlets.

.999... = .999... that is correct


.999... = 1 that is incorrect. .999999... cant' equal too things.

Let me give one final reason. .9999999... is irrational, irrational numbers can't be divided (because they can't be written in fraction notation) AND if you can divid .999..., but you can divide 1, that means .999 has a different value than one.

Ofcourse there are fake irrational numbers, like 5^300/1, which is irrational because no one could write that number out as a fraction youd die first, but it is theoretically possible. Why is this even ana rgumetn?

>> No.9893192
File: 82 KB, 842x792, 1532406500037.png [View same] [iqdb] [saucenao] [google] [report]
9893192

>>9892339
>[math]\frac{1}{3}[/math] isn't bigger than 0.333...

>> No.9893217

>>9889074
Nope.
Infinity as a value is equidistant from all real numbers.
[math]\infty - 84^217 = \infty - 1[/math]
There is no such thing as "close" to infinity, or "really close", or "really really really really really really really really close" .
Infinity is the only thing like itself. All real numbers are finite, but infinity is not; so there will never ever exist any real number that can be said to be "closer to infinity" than another number; so also there will never exist a depiction of 0.999... that can be said to be indistinguishable from 1.

>> No.9893235

0.98989898....=1
Prove me wrong

>> No.9893256

/thread

>> No.9893261
File: 30 KB, 311x429, 1527377973763.png [View same] [iqdb] [saucenao] [google] [report]
9893261

>0.999... is a real number
>infinity is not a real number
>0.999... has properties of infinity
This is what a university maths education gets you.

It just gets you retarded.

>> No.9893311

.98989898989898... = 98/99 < 99/99 = 1

>> No.9893315

>>9893235
>>9893311

>> No.9893321

>>9893311
>98989898989898... = 98/99
Prove it

>> No.9893322

>>9893235
0.98989898... < 0.99 < 1

>> No.9893338

>>9893321
[math]0.98... = \frac{100-1}{100-1}(0.98...) = \frac{98.98... - 0.98...}{99} = \frac{98}{99}[/math]

>> No.9893583

The sum of all real, terminating numbers is larger than the sum of all real, non-terminating numbers.

>> No.9893632

>>9889989
>represents a continual process
no it doesnt

>> No.9893638
File: 9 KB, 211x239, 1513971000563.png [View same] [iqdb] [saucenao] [google] [report]
9893638

>>9893632

>> No.9893642

>>9890162
Reading your post is like watching the archer episode where he keeps struggling with ideas that are repeated to him and when asked which part he has a problem with he just says "core concept I guess".

>> No.9893654

>>9893117
>t. trump university graduate

>> No.9893669

>>9892857
Most people easily understand that 0.999... =/= 1. Its only "math majors" who would argue otherwise. But their arguments can be easily pulled apart so they aren't really convincing the masses. A limit is not an equality of a function over any amount of iterations, while convergence/divergence are also feasibly invalidated by the disingenuous attempt to exclaim that convergence is useful towards finding a value, yet divergence invokes negatory nullifying claims that a value tending towards infinity can't be explicitly useful; where the irony lays on the fact convergence is just the literal same process as divergence except with a real number limit. Ultimately, even withstanding faith in convergence, its retarded to say [math]\sum_{n=1}^{\infty} \frac{9}{10^n} = 1 [/math] in lieu of the more honest and accurate statement that [math]\sum_{n=1}^{\infty} \frac{9}{10^n} = 0.\bar{9}[/math]
A limit can be a real number, and if you're trying to say the limit can't be 0.999..., you're just admitting that 0.999... is not a real number.

mathematicians are actually conditioned to be retarded through their bastardized curriculum they call an education, and I do not envy them.

>> No.9893670
File: 641 KB, 600x826, 1520818653109.png [View same] [iqdb] [saucenao] [google] [report]
9893670

>>9893638
Referring to a number as a "continual process" makes you either a mathlet or near illiterate. Take your pick.

>> No.9893671

>>9893669
1/10^n < 1/9
2/10^n < 2/9
3/10^n < 3/9
4/10^n < 4/9
5/10^n < 5/9
6/10^n < 6/9
7/10^n < 7/9
8/10^n < 8/9
9/10^n < 9/9
0.999... < 1

>> No.9893680

>>9893671
1÷10^n = 1÷9 < 1/9
2÷10^n = 2÷9 < 2/9
3÷10^n = 3÷9 < 3/9

fractional numbers need not be converted to decimal to be useful, but its important to note that a repeating decimal value is not a valid number value and the fractional representation should be used instead.
Therefore 1/3 × 3 = 1
but 1/3 = 0.333... × 3 = 0.999... =/= 1

>> No.9893685

>>9893670
You must first prove that it’s a number instead of assuming that it is. Just because you see digits does not mean it’s a number
>>9893671
9/10^n isn’t 0.999...
9/100 is a form of 9/10^n, for example

>> No.9893731

>>9893669
>all of this verbal diarrhea just to express you don't understand what convergence is
Convergence is not an operation or a process. It's a property some sequences have and divergence is simply not having that property.

>its retarded to say [math] \sum_{n=1}^{\infty} \frac{9}{10^n} = 1 [/math]
Then surely you can find [math] \epsilon > 0 [/math] such that for all natural N, there is some n>N such that [math] | \sum_{n=1}^{\infty} \frac{9}{10^n} - 1 | \geq \epsilon [/math].

>the more honest and accurate statement that [math]\sum_{n=1}^{\infty} \frac{9}{10^n} = 0.\bar{9}[/math]
You, impossibly stupid man. I said this is true in the post you're replying to. In fact, it's the whole fucking reason I gave for why 0.999...=1.

By the way, this is the only time I dissect your shitty rethoric in order to find something barely resembling an argument. Either learn to express yourself or fuck off.

>> No.9893732

>>9893685
9/inf is not though. So there is no inherent easily understood intent derived from [math]\sum_{n=1}^{\infty} \frac{9}{10^n}[/math] in how it is supposed to equal 1. Its just repeating 9's. Overlines and ellipses do not mean the entirety of an infinite process has been concatenated, cause that would aim to treat infinity like a real, finite number. The symbology only exclaims a repeated pattern exists, with absolutely no indication for how many significant digits are required for an equation. Like how [math]\pi[/math] means "pi", but not "3.14159" or any fixed amount of digits.

Just as we can say 3.14159 is a good approximation for pi, we can also say thay 0.99999 is a good approximation for 0.999..., and just as any greater extension of digits in pi does not arbitrarily increment previous digits (3.14, 3.141, 3.1415, 3.14159, ...), so does any greater extension of digits in 0.999... not arbitrarily increment previous digits (0.9, 0.99, 0.999, 0.9999, ...).
Therefore 0.999... is a unique identity for a unique number that is not 1, but this number is not intelligenty crafted outside of [math]\sum_{n=1}^{\infty} \frac{9}{10^n}[/math]

>> No.9893734
File: 7 KB, 233x250, 1526961671180.jpg [View same] [iqdb] [saucenao] [google] [report]
9893734

>>9893731
Kek. Enjoy your school debt.

>> No.9893738

>>9893734
Ran out of bait?

>> No.9893742

>>9893731
You say 9/10^n converges to 1.
You say 10^n diverges to infinity.

these are the same single and identical process. You could just as easily say that the sum 10^n converges to an arbitrarily large real finite number in some n amount of iterations. To diverge and converge are the same mechanical process. Converging to 1 on 9/10^n is no more or less meaningful than diverging to infinity with 10^n, and there are infinitely many ways to either converge to 1 (or ANY given number) and also diverge to infinity.
x/(x+1)^n converges to 1 for infinitely many integer x's, and x^n diverges to infinity for infinitely many integer x's too.

You change the numberline when you have a limit. If 1 is the limit, that 1 then becomes the equivalent of infinity on an unresricted numberline. You will have as many divisions above 0 you want, but you will never increment to 1 on this limited numberline, no more than you could increment to infinity on an unrestricted numberline.

Convergence and divergence are the same exact identical method and your brainwashing runs deep if you think I'm lying to you or don't know what I'm talking about.

>> No.9893775

>>9893742
Convergence and Divergence are via the function of a limit. They are the same process, but with a different parameter. If the limit is any real number, its considered convergence. If the limit is infinity, its considered divergence. This is the problem though, since converging on infinity is explicitly just as meaningful as diverging to infinity based on the definition of infinity itself. Its not a bad thing to "diverge" to infinity, else it would be a bad thing to "converge" to any real number. Its not a good thing to "converge" to any real number, else it would be a good thing to "diverge" to infinity. The ultimate value of the parent function monitoring convergence and divergence relies heavily and explicitly on infinity being well defined, which it isn't, but even if it were, means the function itself is not necessary or beneficial towards acquiring any further truthful answer. Instead of revealing unknown information in an equation, it instead only acts to transform the equation into an alternate rendering yet fundamentally leaving the equation unchanged.

Its not really a valid maths thing.
Wir können auf Deutsch sprechen, aber dies ändern die Problem nicht. Es ist nür übersetzung und nie änderung. Die Problem kommt von ob sie kennst Deutsch, just as your problem comes from if you think you can trip anyone up with unnecessary and unhelpful math terminology that doesn't aim to solve a problem any better than it was already solved more simply before.

>> No.9893781

>>9893742
My god, you're dumb. First, 9/10^n converges to 0, not to 1. With that out of the way: No, it's not the same single and identical process because convergence is not a process, it's a property. Get this through your thick skull because I don't like to repeat myself. The rest of your post is dismissed because you don't understand this simple fact.

I'm still waiting for you to find that epsilon that proves [math] \sum_{n=1}^{\infty} \frac{9}{10^n} [/math] doesn't converge to 1. Don't think I forgot about that.

>>9893775
>If the limit is any real number, its considered convergence. If the limit is infinity, its considered divergence.
HAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHA no.

Ok, you pair of geniuses. Since convergence and divergence are the same thing, tell me to which number does the sequence (-1)^n converges. It should go to infinity, right?

>> No.9893789

>>9889074
>0.999...
Define the "..." part

>> No.9893791
File: 112 KB, 953x613, 1=.999....jpg [View same] [iqdb] [saucenao] [google] [report]
9893791

>>9889074
>2 DAYS OLD
HOLY SHIT SAGE AS FUCK

>> No.9893800

>>9893781
Surely you ought to have known i was talking about sum 9/10^n.

Like worst case scenario you should have been able to gleam that by context.

>> No.9893802

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

>> No.9893817

>>9893802
[math]\frac{1}{3} \neq 0.\bar{3} \\ \\ \ frac{1}{3} > 0.\bar{3} \\ \\ \frac{1}{3} × 3 = 1 \\ 0.\bar{3} × 3 = 0.\bar{9}[/math]

>> No.9893855
File: 86 KB, 384x313, s4dTtBy.jpg [View same] [iqdb] [saucenao] [google] [report]
9893855

[math] 0.3 < \frac{1}{3} \\ 0.33 < \frac{1}{3} \\ 0.333 < \frac{1}{3} \\ 0.3333 < \frac{1}{3} \\ 0.33333 < \frac{1}{3} \\ 0.333333 < \frac{1}{3} \\ 0.3333333 < \frac{1}{3} \\ 0.\bar{3} < \frac{1}{3} [/math]
deal w/ it.

>> No.9893859

>>9893855
>let's pretend finite is infinite

>> No.9893860

>>9893817
oh shitlatexman, always entertaining,
like looking at a dog playing the piano

>> No.9893871

>>9893855
https://www.wolframalpha.com/input/?i=(0.3...)-1%2F3

deal w/ it

>> No.9893921

>>9893859
Who are you quoting?
you seem to have overlooked some key information in the post.

You know, like the sequential incrementing of 3's.

Get some fucking glasses cause there were six fucking lines detailing the method of ever increasing 3's, and the post is only nine lines total.

>> No.9893929

>>9893921
>six fucking lines
actually seven, each finite
(boy you suck with numbers)

and the last line is infinite
you're pretending infinite is the same as the finite examples, retard

>> No.9893943
File: 48 KB, 540x720, 1529915845665.jpg [View same] [iqdb] [saucenao] [google] [report]
9893943

>>9893929
Christ you're dense.
No, six.
There are srven lines of 3's. Six of them are increasing after the first.

The eighth line is an extension of the previous seven lines, and also where your brain seems to be fucking up. Just what do you think the overline in [math]0.\bar{3}[/math] means? I get the idea you think it means "infinite", as if the symbology were meant to imply the entirety of an infinite value has been accounted for.

So really, you're the dumb motherfucker who is
> pretending infinite is finite

Incrementally increasing the amount of 3's (established in the first seven lines), is the equivalent of [math]0.\bar{3}[/math] and the purpose of its overline, being to keep increasing the amount of 3's.

>> No.9893950

>>9893943
>The eighth line is an extension

It's something totally different, retard

>> No.9893970

>>9893950
0.333... DOESN'T mean "infinite 3's"

0.333... MEANS "repeating pattern of 3's"

There is NO implied or explicit statement on the AMOUNT of repetition present. The symbology only holds as shorthand against attempting to actually write an inane amount of 3's.

0.333... is an extension of the work as follows:
0.3
0.33
0.333
0.3333
0.33333
0.333333
0.3333333
. . .
if we know more and more 3's will be appended, then we can just write
" 0.333... " or "[math]0.\bar{3}[/math]", both suffice as symbols for the same singular ideology.

>> No.9893981

>>9893970
bullshit
infinity is larger than any real number

2(1+2+3)
vs
2(1+2+3+...) which seems less than (1+2+3+...)

infinity changes everything, if you don't get that,
you're nothing but a monkey playing with pebbles

>> No.9893982

>>9893970
[math] \pi > 3 \\ \pi > 3.1 \\ \pi > 3.14 \\ \pi > 3.141 \\ \pi > 3.1415 \\ \pi > 3.14159 \\ . . . \\ \pi > \text{ any decimal representation of pi} \\ \frac{1}{3} >
0.3 \\ \frac{1}{3} >
0.33 \\ \frac{1}{3} >
0.333 \\ \frac{1}{3} >
0.3333 \\ \frac{1}{3} >
0.33333 \\ \frac{1}{3} > \text{any decimal representation of 1÷3}[/math]

>> No.9893984

>>9893970
>0.333... DOESN'T mean "infinite 3's"

>shit i just pulled out of my ass, lookie-lookie

>> No.9894018
File: 710 KB, 1080x1669, 2018-05-13 23.40.03-1.png [View same] [iqdb] [saucenao] [google] [report]
9894018

>>9893871
>wolfram alpha is never wro-

>> No.9894031

>>9894018
>shitposters are ever right

>> No.9894032

>>9894018
>let's pretend finite is infinite

>> No.9894061

>>9889074
0.9999.. Going on forever is 1

>> No.9894074 [DELETED] 

Four tres two uno

[Will.i.am:]
Listen up y'all 'cause this is it
The beat that I'm bangin' is delicious

[Fergie:]
Fergalicious definition make them boys go loco
They want my treasure so they get their pleasures from my photo
You could see me you can't squeeze me
I ain't easy I ain't sleazy
I got reasons why I tease 'em
Boys just come and go like seasons

Fergalicious (so delicious)
But I ain't promiscuous
And if you were suspicious
All that shit is fictitious
I blow kisses (muah)
That puts them boys on rock rock
And they be lining down the block
Just to watch what I got
(four tres two uno)

So delicious
(it's hot hot)
So delicious
(I put them boys on rock rock)
So delicious
(they wanna slice of what I got)
I'm fergalicious
(t-t-t-t-t-tasty tasty)

Fergalicious def—
Fergalicious def—
Fergalicious def— ["def" is echoing]
Fergalicious definition make them boys go crazy
They always claim they know me
Comin' to me call me Stacy (hey Stacy)
I'm the F to the E R G the I the E
And can't no other lady put it down like me

I'm fergalicious
(so delicious)
My body stay vicious
I be up in the gym just working on my fitness
He's my witness (oh wee)
I put yo' boy on rock rock
And he be lining down the block
Just to watch what I got
(four tres two uno)

So delicious
(it's hot hot)
So delicious
(I put them boys on rock rock)
So delicious
(they wanna slice of what I got)
I'm fergalicious
(hold hold hold hold hold up check it out)

[Vamp:]
Baby baby baby
If you really want me
Honey get some patience
Maybe then you'll get a taste
I'll be tasty tasty
I'll be laced with lacey
It's so tasty tasty
It'll make you crazy

[Will.i.am:]
T to the A to the S T E Y girl you're tasty
T to the A to the S T E Y girl you're tasty
D to the E to the L I C I O U S
To the D to the E to the to the to the
Hit it Fergie

[Fergie:]
All the time I turn around
Brother's gather round
Always looking at me up and down
Looking at my (uh)
I just wanna say it now
I ain't trying to round up drama
Little mama I

>> No.9894078

No its 1 0.999... is literally just another way to write 1

>> No.9894084

>>9889090
> it exists.
I don't think you understand what an irrational number is

>> No.9894119

>>9894032
You need to stop pretending infinite is finite, it's weird. Also learn how to greentext.

>> No.9894120

>>9894119
>i'm an asshole and have no argument

>> No.9894121

0.9999... is 1.
I guess:
4/9=0.4444...
5/9=0.5555...
9/9=0.9999...=1

>> No.9894124

>>9894120
Yes, you are. Thats also not how you're supposed to use greentext.

Just save us all the grief and go back to >>>/r/eddit

>> No.9894137

>>9894124
>Thats also not how you're supposed to use greentext
try again retard

>> No.9894148

Any infinite decimal can be represented by a fraction of two whole numbers. For example:
x = 0.6969...
100x = 69.6969...
99x = 69 <- We can do this because there are both infinite 69s at the end of both numbers
x = 69/99
If you don't believe me, just type it into the calculator.

So what is 0.999...?
x = 0.999...
10x = 9.999...
9x = 9
x = 1
And so we just proved 0.999... is 1.

>> No.9894149

>>9893800
Oh, yes, I did know. Doesn't make it right, though. If we let these little mistakes go unnoticed, then we end up with people who believe 0.999... is different from 1. I'm still waiting for you to find that epsilon, buddy.

>> No.9894202

>>9889074
0.999... is 1 and 1 is 0.999...

>> No.9894219

>>9893192
It's not.

>> No.9894277

>>9894148
This is disingenuous.

3.33 × 10 is not 33.33
the same number of significant digits remains after the multiplication.
3.33 × 10 = 33.3
there are three 3's in 3.33, and still three 3's in 33.3

The kind of wrongmath perfomed on repeating decimals like 0.999... ×10, to produce 9.999..., is just flat incorrect. It aims to artificially invent and inject an extra significant digit.

So if you disingenuously attribute the repetition to instead invoke an infinite amount, when amount is never an issue and an infinite amount has no intelligible value, you're ultimately faced with [0.nnn...] where there are 'infinite' n, but transforming it into [n.nnn...] where there are 'infinite+1' n.
If you want to call this method valid, you immediately forfeit the ability to give people shit for believing in a number 0.000...1, cause you're saying its fine for an extra value to come after infinity, which just means that if [0.999... × 10 = 9.999... and 9.999... - 0.999... = 9] is true, so it must also be true that [0.000...1] is a real number, ironically providing as much evidence in the contrary that 0.999... isn't 1, for as much evidence you're claiming 0.999... is 1.

>> No.9894287

>>9894277
>disingenuous
>you're saying its fine for an extra value to come after infinity
Anon has a very good point, but then chooses to out himself as just a sad brainlet.

>> No.9894293

>>9894148
>any infinite decimal can be represented by a fraction of two whole numbers
Just like the decimal representation for π can be represented by the fraction 22/7, presumably.

>> No.9894366
File: 81 KB, 337x376, yum.png [View same] [iqdb] [saucenao] [google] [report]
9894366

>>9894277
Mr. Wildberger,
Take your own council, your argument isn't going to change no matter how many times you repeat it.

>> No.9894371

3/3 = 1
1/3 = 0.33333...
3*(1/3)=3*0.33333...
3/3=0.99999...
1=0.99999...

>> No.9894375
File: 94 KB, 866x900, 1512784797225.png [View same] [iqdb] [saucenao] [google] [report]
9894375

>>9894366
math is not a sequence of events that must be repeated and only used verbatim as your professor taught you. Its just a language, and languages evolve.

>> No.9894681

>>9894277
what is 9.9.../10

is it =1 , <1 or >1?

>> No.9894691

>>9889074

0.9... is just a shorthand for an infinite sum. and this sum, if calculated, is 1.

>> No.9896194

>>9889078
>What's the number between .999... and 1?
it's circular reasoning to think "there's no number between .999... and 1 therefore they're the same number and they're they same number because there's no number in between them." It's a priori.

What is the first number that comes after .333...? If it must be the same because there's no number in between then by convention the next number that comes after that (the 3rd # after) is also the same because there's no number in between since the first two "are equivalent". You can quickly see this pattern never stops and breaks down the number system if we decide "if there's no number in between then the two numbers are the same"

>> No.9896234

>>9896194
>first number that comes after .333...
1/3

>> No.9896502

>>9894681
9.9/10 = 0.99 <1
9.99/10 = 0.999 <1
9.999/10 = 0.9999 <1
9.9999/10 = 0.99999 <1
9.99999/10 = 0.999999 <1
9.999999/10 = 0.9999999 <1
9.9999999/10 = 0.99999999 <1
9.999.../10 = 0.999... <1

It always holds less than one. Doesn't matter how many 9's are there.

>> No.9896507

>>9896502
>let's pretend finite is infinite

>> No.9896508

>>9896502
ok, is the answer larger than 0.9?
how about 0.99?

>> No.9896510

>>9896507
Who are you quoting?

>> No.9896513

>>9896502
>9.999.../10 = 0.999... <1

ok fine, so shifting left/right works

x=0.9...
10x=9.9...
9x=9
x=1

qed

>> No.9896515

>>9896508
Play your game with someone else. I take it no one ever does, right?
Maybe stop playing your dumb game then?

Learn to communicate, or just stop posting.

>> No.9896516

>>9896510
Momodou Bello N'Jie

>> No.9896526

>>9896513
No. There isnt an obvious connection between the post you're responding to and your takeaway from it. The No is for shifting, btw.

Are you schizophrenic or something though?

>> No.9896528

>>9896507
What particular qualities about the “infinite” would show his post to be incorrect? I fail to see how this infinite sequence somehow breaks from the logic of the finite and magically breaks the pattern that is understood by intuition.
>>9896513
>infinite sequences can multiplied and added like any other number
C I R C U L A R

>> No.9896530

>>9896526
>No is for shifting

direct quote from your post:
9.999.../10 = 0.999...

>> No.9896533

>>9896530
Except it’s not. He said 0.999.. is less than 1 just as 9.999... is always less than 10. The value preceding the decimal does not matter in this argument. You should be able to prove it without poorly established manipulations.

>> No.9896542

>>9896533
>He said 0.999.. is less than 1 j
that is just m-muh feelings guess
The relation he wrote, i.e.
9.999.../10 = 0.999...
stands

>> No.9896543

>>9896528
>infinite sequences can multiplied and added like any other number
>C I R C U L A R
You missed that the assumption is "shifting works". Which somehow has a meaning from the context.
That "infinite sequences can [be] multiplied and added like any other number" is the conclusion.
You want somebody to educate you on what "circularity" means?
Protip: it does not mean that the conclusion is radically different from the assumption.

>> No.9896545

>>9896528
>>infinite sequences can multiplied and added
yes, sometimes
>like any other number
no, you have to be careful that there is good pairing
in this case there is, every 9 in 0.9... has a buddy in 9.9...

>> No.9896553

>>9896543
You’re treating a so-called infinite quantity as if it’s complete, as if it can be multiplied and subtracted by and from finite quantities. This logic has not been established.
>You missed that the assumption is "shifting works".
Prove this relying on some anon’s post. How would a mathematician prove this?

>> No.9896564

>>9896530
Hm. You're retarded.

I crafted that 9.999... number over iterative steps. I did not instantiate x=0.999..., then multiply it by 10, like you did.
I see where you fucked up.
See >>9892057

My 9.999... number is not the same as 0.999...×10
Lets show the work, starting with bases
My: 9.9
X: 0.9

>My
>1} 9.9
>2} 9.99
>3} 9.999
>4} 9.9999
>5} 9.99999
>...}
> 9.999...

>X
>1} 0.9
>2} 0.99
>3} 0.999
>4} 0.9999
>5} 0.99999
>...}
> 0.999...
for every same iteration between My and X, they both have the same amount of 9's after the decimal place. Towards their futures, My @ 9.999... & X @ 0.999... both have the same amount of 9's after the decimal point.
My - X = 9
but 10X has one less 9 after the decimal than My, because thats how "shifting" actually works.
My = 9.999...999->
10X= 9.999...990->
(0.99 × 10 = 9.90)

My-10X = 0.000...009->

You might do yourself a favor to realize no "infinite" value is ever used, ever, for any application, ever. Its always to some arbitrary but finite point.

>> No.9896571

>>9896564
>You're retarded.

Quoting you is retarded.
You know, that's something I can live with, frankly.

>> No.9896572

This whole thing is an argument of metaphysics rather than just math.
The TRUTH (as in this is the truth and if you disagree you will never be right so shut the fuck up) is that THIS UNIVERSE IS NOT FUNDAMENTAL and there is an INFINITE PLATONIC REALM wherein all the forms of everything reside. Until you accept this your dumb ass is never going to understand the real numbers.

>> No.9896579

>>9896564
>My 9.999... number is not the same as 0.999...×10

So shifting right works, but shifting left doesn't?

>must be a right wing nut, he even babbles on and on and on like pink jabba

>> No.9896581

>>9889074
No, it exists and is a representative of the same number.

>> No.9896588
File: 132 KB, 1500x1100, 1500445463367.jpg [View same] [iqdb] [saucenao] [google] [report]
9896588

>OP

>> No.9896591

>>9889264
That's the difference between finite and infinity. At any finite step, they don't touch. At infinity, they do.

>> No.9896596

>>9896553
>You’re treating a so-called infinite quantity as if it’s complete, as if it can be multiplied and subtracted by and from finite quantities.
I wasn't "treating" anything other than your obvious lack of logic. Certainly none of your ridiculous "infinite quantities".
>Prove this relying on some anon’s post. How would a mathematician prove this?
You never have to prove an assumption before you can derive whatever follows logically from it, jeezus.
Anyway, you can only prove "shifting works" if you are given a clear definition of what that is supposed to mean. If you would be kind enough to explain to me precisely what it means *to you*, then I shall prove it for you, or explain to you why it is wrong.

>> No.9896600

>>9896572
That is a stupid comment. You do not have to "understand" real numbers. Even if you do not "understand", you can just follow the axioms. A computer can do this easily, without being smart in any way.

>> No.9896601

>>9889238
You're confusing decimal expansions with numbers. There are, in some poorly-defined sense, "more" decimal expansions than numbers. 0.999... and 1 both refer to the same mathematical object, they just have different representatives.

>> No.9896617

>>9896571
Infinity isn't for your use. Deal with it.

A number like [0.000...1] shouldn't bother anyone unless they misunderstand the applications of math or the meaning behind the symbology of 'repeating'. Any irrational decimal will be used up to a finite, real point. [0.999...] doesn't mean "infinite nines"; it means "as many real nines as you need". Doing any math with this value will always come to a finite point.

So the ellipses in [0.000...1] doesn't mean something to come after the infinite. It means there are as many real 0's as needed, followed by a 1.

Infinity is not well defined. Infinity is not meant to be used. At best, it is not considered an actual number, and at worst it pretends to be "the greatest number, greater than all other", which in that very definition makes it finite because it is a ceiling that can't be surpassed, much as there is a finite distance between your floor and the ceiling above.

Infinity is nonsense.

>> No.9896619

>>9896591
Bullshit. That’s literally saying that infinity multiplied by 0 is equal to 1. This level of baseless belief rivals religious fundamentalists

>> No.9896623

>>9896591
>at infinity
Never happens. Never has happened. Never will happen. You're treating infinity as finite if you can "arrive at" it.

>> No.9896634

>>9896619
stop making up shit

>> No.9896636

>>9896623
_at_ infinity =/= arriving

>> No.9896638

>>9896634
Consider the function 1/x.
If the curve touches the asymptote “at infinity,” then x = 0, and y = infinity. Then 1/0 equals infinity, and 0(inf) = 1.

>> No.9896647
File: 475 KB, 670x623, 1517284858323.png [View same] [iqdb] [saucenao] [google] [report]
9896647

>>9896636
And now you're just going to struggle with the english language in lieu of learning something you should have been able to figure out on your own.

Whatever.

>> No.9896649

>>9896647
arriving = fiddling with real numbers

at inf = not a real number

>> No.9896653

>>9896638
>at infinity,” then x = 0
top kek

>> No.9896655
File: 77 KB, 540x726, C9F3768C-2C91-4834-9E33-97B39C4A5A0B.jpg [View same] [iqdb] [saucenao] [google] [report]
9896655

>>9896649

>> No.9896657

>>9896649
May as well just use potato in lieu of infinity, then. You're not doing math if you're not dealing with numbers.

>> No.9896660

>>9896657
arithmetic no, math yes

>>9893981

>> No.9896663

>>9896591
There exists no point where they touch. For if there did exist a point, it would be a finite distance from 0.

>> No.9896667

>>9889983
I would just deny the premise in which '2' is taken to be a permissible divisor for every pair numbers (e.g. the case in which the numerator is |1 - .999...|); '0' is likewise an impermissible divisor. .999... is the closest possible number to 1 in the sense that 2 is the closest possible natural number to 3 that is also smaller than 3.

Your "proof" just begs the question, like all proofs of 1 = .999... do.

>> No.9896670

>>9896655
not the correct definition of infinity,
would be my guess

>> No.9896674

>>9896660
This post ( >>9893981 ) you're referencing doesn't make sense.

>> No.9896680

>>9896674
wanna bananna?

>> No.9896683
File: 10 KB, 150x247, Justin_Trudeau_G20_2015.jpg [View same] [iqdb] [saucenao] [google] [report]
9896683

>>9896680
>doesn't know how to spell banana

>> No.9896698

>>9896683
doesn't know how to cute-talk to stupid creatures

>> No.9896701

>>9896698
This is an 18+ site, bucko

>> No.9896707

>>9896591
>>9896649
This just provides that infinity is an imagination number. Its not a real number, and further has no relation to real numbers. It is not larger, or smaller than real numbers, because it has no relation to real numbers, no more than potato is larger than 42.

So infinity is just an imaginary point where something unrelated to all numbers might happen.

>> No.9896709

>>9896667
>Your "proof" just begs the question, like all proofs of 1 = .999... do
Even proofs that use a precise definition of a quantity ".999..."? I am pretty sure that you are clueless as to what such a definition might be, and you surely would not want to see a proof that starts from it. It would go against your retarded agenda.

>> No.9896710

>>9896701
go away then

>> No.9896713

>>9896707
>has no relation to real numbers

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

>better luck next time

>> No.9896716

>>9896502

Prove that if [math] a_{n} [/math] is a convergent sequence such that [math] \forall n \in \mathbb{N} a_{n} < 1 [/math], then [math] \lim_{n \to \infty } < 1 [/math].

>> No.9896718
File: 165 KB, 800x800, 1524043147486.jpg [View same] [iqdb] [saucenao] [google] [report]
9896718

>>9896713

>>9894018

>> No.9896721

>>9896680
new to /sci/ here. Is /sci/ usually this fucking retarded or is everyone here trolling each other?

t. Applied Math Ph.D student

>> No.9896722

>>9896716
Holy shit. I really fucked up the latex. Sorry.

Prove that if [math] a_{n} [/math] is a convergent sequence such that [math]
( \forall n \in \mathbb{N} ) a_{n} < 1 [/math], then [math] \lim_{n \to \infty } a_{n} < 1 [/math].

>> No.9896725

>>9896722
Do your own homework.

>> No.9896728 [DELETED] 

>>9896718
>9894032

>> No.9896731

>>9896725
If that is his homework, his teacher is trolling/retarded because that statement is false.

>> No.9896732

>>9896725
If you can't prove that, then
>>9896502 is meningless.

>> No.9896734

>>9896718
>>9894032

>> No.9896751
File: 85 KB, 1300x1090, cartoon-illustration-happy-house-holding-sale-sign-white-background-30151016.jpg [View same] [iqdb] [saucenao] [google] [report]
9896751

>>9896713
... could you define what you believe the words "an unbounded quantity" mean?

>> No.9896754

>>9896731
It's not my homework and I know it isn't true (a_n= 1–1/n) but >>9896502 used that statement as an argument for 0.9...=/= 1 so I'm asking him to prove it.

>> No.9896760

>>9896751
any time you count on it being bounded, you fail

>> No.9896764

>>9896709
What is a "precise" definition as opposed to a regular definition?

>> No.9896766

>>9896734
The image just throws Wolfram under the bus for being a shitty calculator. Wolfram is not an arbiter of truth. You may as well just link to a blogspot webpage with some other retarded definition of infinity on it.

I don't know why you keep posting about infinite is finite or whatever.

>> No.9896771

>>9896760
Can you describe how a number, for example the number 100, is "bounded"?

How is 100 bounded?

>> No.9896772

>>9896766
>Wolfram is not an arbiter of truth
well thank god we have you
top kek

>> No.9896777

>>9896771
it isn't greater than every real number

>> No.9896782
File: 42 KB, 479x720, UvGfe7Y.jpg [View same] [iqdb] [saucenao] [google] [report]
9896782

>>9896772
Indeed. Top k-Underflow[]+ek.

>> No.9896790

>>9896777
Every number isn’t greater than every real number, because for any n, there is
n + 1. Therefore that which is unbounded cannot be a number or quantity.

>> No.9896791

>>9896777
Hm.

So... you don't actually know what wolframs definition for infinity means?

Its ok ya know. Its just a brainlet filter.
The point is the definition is meaningless nonsense.

>> No.9896795

>>9896790
>a number
ok
>quantity
nope

>> No.9896796

>>9896790
kek, then infinite cardinals are not larger than finite cardinals, and therefore infinite sets do not have more elements than finite sets.

wow

>> No.9896797

3/3 =1

>> No.9896801

>>9896791
pretty sure it's more than 100

>> No.9896802
File: 455 KB, 1200x800, 05-10-2017_Infinity-1.png [View same] [iqdb] [saucenao] [google] [report]
9896802

>>9896795
infinity is imagination, bro. Its just imaginary. Its fantasy. Its a cartoon. Don't take it do seriously, it's not REAL.

>> No.9896810

>>9896802
aka math

if it's too much for you, stick to arithmetic

>> No.9896811

>>9896795
A quantity is that which can be increased or diminished, per Euler.

>> No.9896813

>>9896801
Is potato more than 100?
...or maybe potato is less than 100?

>> No.9896817

>>9896813
>maybe potato is less than 100
nonono that's your iq

>> No.9896818

>>9889078
What's the number between 1 and 2 in the integers set? If there's nothing in between, it means it's the same?

>> No.9896819

>>9896810
Lmao. Calm down bro, stop taking it so seriously. Infinity isn't real. Everythings alright, its just a joke.

>> No.9896820

>>9896811
try again

https://math.stackexchange.com/questions/216061/euler-and-infinity

>> No.9896821

>>9896796
That does not follow at all. Show your reasoning

>> No.9896824

>>9896818
what is countable vs uncountable
lrn2crawl before trying to walk

>> No.9896828

>>9896819
so you're bad both at math and humor
go back to >>>/x/

>> No.9896838

>>9896828
I didn't come up with the joke bro. I'm just seeing you treat infinity as if it were really important, like you're taking it too seriously. Just thought i'd reach out and remind you that infinity isn't real and its just a joke. Take a breather man.

>> No.9896844

>>9896838
still not funny

>> No.9896845

>>9896821
1. Numbers can only be smaller than other numbers.
2. Because they are bounded, finite cardinals are numbers.
3. Because they are unbounded, transfinite cardinals are not numbers.
4. Therefore, a finite cardinal cannot be smaller than a transfinite cardinal. (1, 2, 3)
5. Finite sets are measured, in terms of how many elements they contain, by finite cardinals.
6. Infinite sets are measured, in terms of how many elements they contain, by transfinite cardinals.
7. Therefore, a finite set cannot be said to have less elements than an infinite set. (4, 5, 6)

>> No.9896847

>>9896845
>1. Numbers can only be smaller than other numbers.
nope, all are smaller than infinity

>> No.9896857

>>9896847
Your "infinity" fits straight up my butthole. Which proves that it is even smaller.

>> No.9896859

>>9896847
wew

I bet you think "wew" is smaller in quantity than "230985092538" just because it has less letters, don't ya?

>> No.9896864

>>9896857
major ass huh, just as i thought

>> No.9896867

>>9896859
the key word here is "only"

>> No.9896869

>>9896845
All unbounded sets can be shown to contain a finite set within it, with an unbounded set after that. The only relation between any infinite set and a finite set is that the former is greater than the latter. Supposing that the set of integers between 1 and 10 is less than an infinite set more-so than the set of integers 1-100 is to assume that the finite can be subtracted from the infinite, which is absurd.

>> No.9896878
File: 137 KB, 323x454, 1396400124828.jpg [View same] [iqdb] [saucenao] [google] [report]
9896878

>>9896844
infinity isn't real. This isn't the joke.

>> No.9896891

>>9896878
haha ok you're funny.
happy?
>go away

>> No.9897010

>>9889074

Correct.

>> No.9897060

>>9889074
Nigga, it's just a convergent infinite sum

>> No.9898024

>319 posts


Jesus Christ.

>>
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