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8797338 No.8797338 [Reply] [Original] [archived.moe]

0.999~ ≠ 1

And it never will....


>> No.8797348

True, but I don't know what that tilde is supposed to mean. 0.999..., however, does = 1.

>> No.8797350

its all about the last 1

>> No.8797391
File: 132 KB, 960x732, 1446645658580.jpg [View same] [iqdb] [saucenao] [google] [report]

It's one way to display an unending repeating string. Also no. You will never reach your dream. It is mathematically impossible. Don't try using a glitch in our current system to justify it.

>> No.8797419

not a glitch lol

>> No.8797435

Is glitch.

>> No.8797534
File: 114 KB, 596x600, 1330032919880.jpg [View same] [iqdb] [saucenao] [google] [report]

>Can't grasp interresting mathematical concepts
>Get stuck for years debating whether [math].\bar{9} = 1[/math]

Sad is the life of a brainlet.

>> No.8797540

Do you even math, bro?

[math] 0.999... = 0.333... \cdot 3 = \frac{1}{3} \cdot 3 = \frac{3}{3} = 1[/math]

>> No.8797594

>[math]0.333... \cdot 3 = \frac{1}{3} \cdot 3[/math]
nice circular reasoning

>> No.8797620

Whole number
Almost only counts with explosions and bowling...

>> No.8797629

So you really don't understand math, do you? You apparently don't understand what circular reasoning is.

>> No.8797662
File: 157 KB, 449x624, Picard_with_hair.jpg [View same] [iqdb] [saucenao] [google] [report]

So think of 0.999... as a distance and 1 as the destination. No matter what you do, you can never reach that destination. Saying 0.999... = 1 means you cheated and reached out to smack your destination because its utterly right there forever. That doesn't mean you actually reached it if you stuck to the original distance.

Think another way, it is literally the exact opposite of the speed of light in that you are virtually frozen in place...moving but never reaching.

>> No.8797665

What the fuck are you blathering about? Your metaphor is both terrible and wrong.

>> No.8797682

Or just beyond your comprehension

PS: It is.

>> No.8797686

Aww shit

All math since Newton BTFO

How will limitfucks ever recover?

>> No.8797687

No, it's just bad. 0.999... is just a notational variant of 1. Both are completely equal. This can both be shown arithmetically.

>> No.8797691
File: 106 KB, 953x613, 0.999 = 1.jpg [View same] [iqdb] [saucenao] [google] [report]


>> No.8797693

Approaches 1 is good enough for me.
My emphasis is combinatorics and related shit though, couldn't care less

>> No.8797723

So what's 1 - 0.999... ?

>> No.8797738

obviously 0.000...

>> No.8797758

Ok so I have a question. 0.333... equals 0.34, right? And 0.34 * 3 is 1.02. How is this possible?

>> No.8797760

That's what I thought. That would make them equal I guess

>> No.8797775

>0.333... equals 0.34, right?
No it doesn't. That is an approximation.

>> No.8797788

>Zeno's paradox.
Oh wow.

>> No.8797789

>mathematically impossible
There is no contradiction in 0.999... = 1 but there is in 0.999... + 0.000...1 = 1 for the Real set

Try to actually put some effort into learning real maths and stop being a fucking disgusting sensing-type brainlet

>> No.8797811

also for two different real numbers to not be equal, there must exist another real number in between those two numbers, but since numbers of the form 0.000...n do not exist in the real number set, there are no real numbers greater than 0.999... AND less than 1

>> No.8798143

There are. [math]\rm 0.aaa..._{11}[/math] is greater than [math]0.999..._{10}[/math].

>> No.8798184

they are actually equal

>> No.8799321

Ok, so if it's a distance and 1's the destination, what's the error from your distance to destination?



>> No.8799326

"glitches" are real. If our current axioms and definitions imply that 0.999...=1 (which they do), then it is what it is.

If you prefer a different set of axioms and definitions where 0.999... =\= 1 then I would be curious to know what they are.

>> No.8799327

0.000...1 is nonsensical. It implies an infinite chain of zeroes but it has an end? Thats a contradiction. Thiw number cannot exist

>> No.8799391

let me explain to all the brainlet why 0.999 =/= 1
1/3 =/= 0.333
why? because you cannot divide 10 by 3 therefore even if you have indefinite amount of 3 following it will not be equal to 1/3. You cannot express 1/3 in base 10.

>> No.8799398

You are a mongoloid. Good to see mathematical illiteracy is still widespread today.

>> No.8799410

First of all, 0.999... is a rational number since it only consist of a repeating decimal. Thus, it must have a quotient to represent it. Since it can't be directly represented by a quotien, it must be equal to something that can be represented as a quotient.

It can be represented as the infinite sum below.
This is the geometric series seen below with a=9 and r=1/10.
The solution to this geometric series is seen below, when the summation is done to infinity and |r|<1
We insert the given numbers for the representation of 0.999... and get that it is equal to one.
Even though limits have been used, it can be argued that 0.999...=1 because it has to be equal to something that can be represented as a quotient, because it is by definition a rational number and can't be represented as a quotient in and of itself.

>> No.8799411

then how can you have an infinite string of 9's?

In ordinal arithmetic there is the concept of "infinity plus one".

why can't we imagine infinitely many 0's followed by a 1?

>> No.8799416

Because this implies that the series is not infinite, since it has an end after which you place a 1. It makes no sense to talk about an infinite series of 9's with a 1 at the end, since there is precisely no end to the series. A concept like 'infinity plus one' may make sense when for example you are speaking of the cardinality of a set, but it makes none in this context.

>> No.8799426

OP is right. Also, the set of all rationals is greater than the set of all integers.

>> No.8799429

>kid who says infinity is a number

>> No.8799440

Infinity can be treated as a value. In fact, some infinities are greater than other, for instance [math] \aleph_0 < \aleph_1[/math]. It baffles my mind that you would discuss the concept of infinity on a message board dedicated to math and science when you don't even seem to know what is taught in a first year math course.

>> No.8799446

>the set of all rationals is greater than the set of all integers
Sometimes b8 is far too obvious.

>> No.8799473

And of course, there are only finitely many primes.

"0.9.. /= 1"ers: Learn about equivalence classes of limits of rational series or about Dedekind cuts. If this is too hard, you might enjoy:

>> No.8799484
File: 66 KB, 554x400, 1489000646449.png [View same] [iqdb] [saucenao] [google] [report]

easy proof:
suppose .99999... and 1 are distinct real numbers
now b/c real numbers are dense you should be able to find some x s.t. .999999... < x < 1
no such x exists
.99999... and 1 are not distinct
they are equal

>> No.8799488

what about 0.999.................10

>> No.8799502

Previous comments have addressed this already.
Note that I've advised your caretaker that you are on the internet without supervision again.

>> No.8799521

>ye bruh i bright infinity is number
>mathematical illiteracy
it's like you are saying infinity is a natural or real number, which it is not
0.33... is only but an approximation of 1/3

>> No.8799525

No. Go back to school.

>> No.8799528

Finally! SOMEONE who knows what they're talking about!

>> No.8799554

Suppose you tell me that .9999 is not equal to 1 because it is different by .0001. I will agree, and say that the number actually has another 9, and so is .99999. Then you will say "Aha! It's still off by .00001!"

It is clear that this process will continue forever.

I think there are arguments for either side:
---You could say that no matter how many 9s I add it will never be 1. This is true.
---I could say that the difference between .999... and 1 can not be a number greater than 0. This would also be true.

I think it comes down to physical interpretation, which is why mathematics was created in the first place. From a physical standpoint, there's no denying that .999....is equal to 1 in every sense of the word equal (and if you have some threshold for how close two numbers must be for you to allow them the adjective "basically equal," that threshold will surely be surpassed).

>> No.8799629
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Have you stopped to think that the problem isn't that the original statement is wrong, but that the math used to prove it is wrong is flawed because we don't yet fully understand math? Hence our current understanding tells us something that is in reality impossible?

>> No.8799649

>the math used to prove it is wrong
Math as such is not something that can be wrong, at least not in the sense you are implying. You can make mathematical errors, but there is no true math as opposed to false math. Mathematics is simply finding conclusions that necessarily follow from a set of axioms. Whichever axioms you choose is entirely up to you. From the axioms we traditionally accept, [math] 0.999... = 1[/math]. You could develop a mathematical system in which this is not the case.

>> No.8799685
File: 477 KB, 500x280, 1336955935818.gif [View same] [iqdb] [saucenao] [google] [report]

I question that. You may be perfectly correct, but you also may not be. I feel like we are still stuck in the dark ages of our understanding and that math is not as universal as we like to assume.

>> No.8799697

I feel like we are still stuck in the dark ages of our understanding

what makes you think that?

>> No.8799716

This simple equation and the fact that people think it is wrong because of our current evolution of math that can claim otherwise...

>0.999... ≠ 1

>> No.8799861

let x = .999...
therefore 10x = 9.999...
10x - x = 9.999... - .999...
therefore .999...=1

where did i make a mistake?

>> No.8799889

that's what I'm saying

>> No.8799906


The real question is

[math] 0.000... = 0 [/math]

>> No.8799910

ITT OP is a brainlet and can't accept a fact with countless proofs

saved you guys some time

>> No.8800198

>An open set is the same thing as a closed set!

>> No.8800215

>computers using floating points to approximate decimals: .999~ = 1
>EEs modelling electrical wave forms in real life: pi = 1
>Astrophysicist measuring the energy of a blackhole jet: 100=1

heh, I laugh at your analysis and pure math.
(as a math grad I understand your pain but do not share it cuz physics>math imo)

>> No.8800216

If .999 = 1 why don't they just write 1?

check and mate

>> No.8800243

The problem is that the so called "Reals" aren't real, which means any arithmetic or math done with them is pointless and retarded.

>> No.8800456
File: 6 KB, 225x225, kek.jpg [View same] [iqdb] [saucenao] [google] [report]

[math] 0.333...[/math] and [math]\frac{1}{3}[/math] are not sets dummy.

>> No.8800466

Assume 0.9999... != 1
OP is a faggot
Contradiction, therefore 0.9999...=1

>> No.8800496

>he doesn't understand limit theory

>> No.8800534

Weird how that works

>> No.8800601

>he misapplies limit theory.

>> No.8800623

No further proof for existence of infinity needs to be made other than existence of one.

>> No.8800647

The limit as the number of digits approaches infinity is equal to one. By definition. That's what limits are for.

>> No.8800900

.333... equals 1/3
.666... equals 2/3
.999... equals 3/3

>> No.8800906

If the sum of all positive integers equals -1/12 then math must be somehow broken

>> No.8800951

But dude they're different numbers

>> No.8800976

Or you don't understand mathematics.

>> No.8800997

Thank you.

>> No.8801002


>> No.8801040


>> No.8801260

Just saying: Hyperreals work, and 0.999... can be seen as shorthand for 1 - ε, which isn't 1.

>> No.8801285

>physical interpretation
>why mathematics was created in the first place
This is why schools should have history of mathematics as a required class.

>> No.8801683

>working with hyperreals

>> No.8801937

>he doesn't understand .99999.... =/= 1 isn't an integral part of limit theory for open sets

>> No.8802363

Why does rounding infinitely long numbers blow everyones minds
We do the same thing with pi and i never see people bitching about it

>> No.8802395

Because this one is not about rounding, it is _literally_ the same.

There are several non-standard analysis concepts, but come on, Hyperreals, Surreals, etc. are barely ever used.

>> No.8802412

its close enough to 1 that nobody gives a shit about the infinitesimally small bit at the end so we just call them the same

>> No.8802415


>> No.8802422

But this isn't actually true in the sense of the word sum that you know

All of these misunderstandings, whether it's the -1/12 meme or the 0.999 =/= 1 meme or a billion other things is just people applying their grade school level of understanding to concepts that are addressed by real math.

>> No.8802952

>its close enough to 1 that nobody gives a shit about the infinitesimally small bit at the end so we just call them the same
No, it is just one. That's how the real numbers work.

>> No.8803624

1/3 = 0.3 recurring
2/3 = 0.6 recurring
3/3 = 0.9 recurring = 1


>> No.8803626

sounds like you don't "fully understand" basic fractions and decimals mate

>> No.8803677

for what purpose? 0.9~ is equal to 1.0 for 98% of practical uses.

>> No.8803879

0.999... + 0.0...1 = 1
0.0...1 = 0
0.999... + 0 = 1
0.999... = 1

>> No.8803969

A simple proof:
X = 0.\bar{9}
10X = 9.\bar{9}
10X - X = 9.\{bar} - 0.\bar{9} = 9\
10X - X = 9X
X = 1

>> No.8803995

\(X = 0.\bar{9}\)
\(10X = 9.\bar{9}\)
\(10X - X = 9.\{bar} - 0.\bar{9} = 9\)
\(10X - X = 9X\)
\(X = 1\)

>> No.8804001

Easy: not formating apparently
X = 0.999
10X = 9.999
10X - X = 9.999 - 0.999 = 9
10X - X = 9X
X = 1

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