[ 3 / biz / cgl / ck / diy / fa / ic / jp / lit / sci / vr / vt ] [ index / top / reports ] [ become a patron ] [ status ]
2023-11: Warosu is now out of extended maintenance.

/sci/ - Science & Math

View post   
File: 2 KB, 160x99, IMG_0207.png [View same] [iqdb] [saucenao] [google]
8874142 No.8874142 [Reply] [Original]

Does 0.9999 ... = 1 ?

>> No.8874148

yes, it does.
they're different representations of the same number

>> No.8874149

only if the axeom of choice

>> No.8874151

>>8874142
Yes if all the nines are infinite and there is no other number in there.
No if there is a number somewhere in the 9 AND you actually use the scientific notation in order to actually know its exact value.

This is getting annoying.

>> No.8874153

>>8874151
>this is getting annoying

Never let them see you cry, sheesh.

>> No.8874155

>>8874149
>axeom of choice
The axiom of choice doesn't mean you can choose however you want to spell words

>> No.8874163

>>8874149
the axiom of choice has nothing to do with it

>> No.8874168

If you add 0.999... to 0.111... you get 1.111...

Which is the same as if you added 0.111... to 1.

>> No.8874177

unless you found the use of 0.00....1

it just the same shit
1=0.99999

>> No.8874390

>infinite significant figures
>one significant figure
no

>> No.8874396

>>8874390
>sigdigs
>math
absolutely not

>> No.8874400

>>8874396
>math
Not the topic.

>> No.8874468
File: 112 KB, 953x613, 1491507242712-sci.jpg [View same] [iqdb] [saucenao] [google]
8874468

>> No.8874513

For every purpose imaginable save one, 0.99999... = 1

The exception is shitty bait threads on /sci/

>> No.8874518
File: 58 KB, 603x452, meme n° 32.jpg [View same] [iqdb] [saucenao] [google]
8874518

>>8874142
Better question :
Is 0.9999999..... < 1 ?

Is 0,0000000000......1 > 0 ?

>> No.8874532

Only branlet writes 0.00...1

>> No.8874534

>>8874518
yes
yes

>> No.8874535

But then why doesn't 0.999999999999...998 = 0.9999999999999.... ?

>> No.8874541

>>8874151
It's not just this that is getting annoying. Sci is getting worse. Mods are needed or the quality of people posting will diminish. /b stands for bullshit.../sci stands for science...if /sci becomes /b then there is no /sci.

>> No.8874545

>>8874518
>>8874534
Does this imply that :
0,99999999.... < 1
And :
1/9 x 9 < 1

?

>> No.8874550

>>8874545
yes
no

>> No.8874555

>>8874535
>999999999999...998
is non-infinite.. the reason 0.99999.... = 1 has to do with it being a bounded infinity. Theorizing about it isn't going to help, check out the proofs.

http://www.purplemath.com/modules/howcan1.htm

>> No.8874587

>>8874535
A number with infinite 9's with an 8 at the end doesn't exist.

>> No.8874662

>>8874142
only if you post the question on /sci/ every fucking day

>> No.8874672

>>8874535
>0.999999999999...998
That is not a mathematical sequence.
> 0.9999999999999....
That is a mathematical sequence.

I don't know what you formally mean by the first thing. You're welcome to define your own math, but you're going to have to share definitions.

>> No.8874676

>>8874142
For the last time, no one knows. Godel's Incompleteness Theorem showed that it's impossible to fit all of mathematics within one logical paradigm, so we can't expect every mathematic transformation to be perfectly fungible with every other. It doesn't work that way.

>> No.8874680

>>8874155
>>8874163
Jokes on you, I wad only pretending to be retarded

>> No.8874692

{.9, .99, .999, .9999, ...}

>> No.8874724

>>8874149
If you take Laplace's Demon into consideration it all falls apart.

>> No.8874750

>>8874468
Why do they have to make it so fucking gaudy and complicated? Literally the only thing you need to know to convince yourself is that 1/3 = 0.333.... Three thirds make 1; three 0.333...=0.999....

Only a flat-earther would deny that.

>> No.8874888

No it does not, and I will argue this point to the death as soon as I finish me test.

>> No.8875031

>>8874142
>0.9999 ... = 1
Yes.

This is true by definition, anyone who claims otherwise doesn't understand mathematics.

>> No.8875035

>>8874888
>No
What is completion of metric spaces.

>> No.8875038

>>8874676
>>8874676
>>8874676
>>8874676
T H I S
H
I
S

>> No.8875053

>>8874676
This has nothing to with it, and you don't understand the theorem of Gödel.

Gödels theorem is only about consistency and up to now ZFC seems to be consistent.

And even IF it wasn't, 0.999...=1 would still be true in that axiomatic framework, because it is just part of the definition of the real numbers.

>> No.8875075
File: 145 KB, 898x960, hierarchy of weirdness.jpg [View same] [iqdb] [saucenao] [google]
8875075

>>8875053
>2017
>Not being able to prove your own consistency
C'mon

>> No.8875084

>>8875075
But that is exactly what Gödel proved, any complicated enough system can not prove its own consistency...

>> No.8875092

>>8875084
What is a joke

>> No.8875093
File: 24 KB, 365x479, 365px-Doron_Zeilberger_(circa_2005).jpg [View same] [iqdb] [saucenao] [google]
8875093

http://www.math.rutgers.edu/~zeilberg/Opinion146.html
Wow... /sci/ absolutely BTFO by an actual mathematician.

>> No.8875098

>>8875093
The ultra-finitism meme needs to die

>> No.8875104

>>8875093
(((Zeilberger)))

>> No.8875121

>>8875093
Aside from his rejecting of the axiom of infinity, nothing he said is actually wrong.
The meaning of math can never be truly objective anyway; that's why the "define X" meme is a thing.

>> No.8875163

>>8874142
Yep.
Hint: Rotate the given image 20 times.

>> No.8875213

>>8874142
>Does 0.9999 ... = 1 ?

The real number system does not have the ability to distinguish any difference between 0.9999... and 1. For that reason, the real number system "perceives" these two numbers as being equal.

However, the hyperreal number system can make a distinction between these two numbers, so it can "perceive" these two numbers as being nonequal.

Generally, mathematicians prefer to use the simplest number system possible to solve a given problem. For that reason, the real number system ends up being overwhelmingly used instead the hyperreals.

This causes the real number system to heavily dominate the textbooks, which creates the impression among many students that 0.9999... always equals 1. However, once students start learning about more advanced number systems, they see that the question is ambiguous, and can only be answered in the context of a specific number system.

---

By the way, the rational number system and the real number system share an interesting property: they both have cases where the same number can be represented using different digits. For example, the rational numbers 3/2 and 6/4 are equal, despite being composed of different digits. And in the real number system, 0.9999... and 1 are equal, despite being composed of different digits.

It might be considered "desirable" for a number system to have a perfect one-to-one correspondence between all possible digit sequences and all numbers. However, neither the rational number system nor the real number system have that "desirable" property.

>> No.8875217

>>8874468
>TEH MATH
Holy shit this image is ANCIENT

You guys have been shit posting about this topic since day one haven't you?

>> No.8875249

>>8874518
no
doesn't make sense

in short, seek help for your retardation

>> No.8875256

>>8874750
If you use duodecimal then 1/3 = .4, 2/3 = .8 and 3/3 = 1. Your "proof" only works in base-10. A proof that is base specific is not a proof at all.

>> No.8875270

>>8874142
do you want to machine something to 1" thick or 0.9999999999 thick? I think you are only competent enough for one of these options.

>> No.8875348

>>8875213
>The real number system does not have the ability to distinguish any difference between 0.9999... and 1
one starts with 0 one with 1. what a shitty system

>> No.8875500

>>8874468
I was never convinced of any proof until I saw the one on the right of this picture. Everything makes a lot more sense when you write

[math]0.999... = 9 . sum_{n=1}^{\inf} (frac{1}{10})^n = 1[/math]

"0.999..." is a stupid notation.
>nine nine nine dot dot dot amirite guise xD

>> No.8875506

>>8875500
[math]0.999 = 9. \sum_{n=1}^{inf} (\frac{1}{10})^n = 1[/math]

>> No.8875542

>>8875348
>one starts with 0 one with 1. what a shitty system

Well, mathematicians don't have a precise definition of what "shitty" means, so they don't say it like that.

Instead, mathematicians say that the real number system lacks the property of having a one-to-one correspondence between numbers and the digit sequences that represent them.

If that's an important property to you, then I would suggest using the natural number system instead.

It's very often the case that when you go to a more advanced number system, you lose one or more "desirable" properties. For example, when you go from the real number system to the complex number system, you lose the property of having a "less than" and "greater than" relationship between the numbers. If that property is important to you, then you'll have to avoid complex numbers. But it's usually not very productive to bitterly complain about how "shitty" the complex numbers are because they lack an ordering relation. A more mature attitude is to just accept reality and deal with it.

>> No.8875569

.99999.. doesn't exist in the IEEE754 floating point number system, the number you are looking for is 0.99999994, which does not equal 1.0, the bit pattern for the former is 00111111011111111111111111111111 whereas the latter is 00111111100000000000000000000000. Clearly not the same?

>> No.8875588

>>8875569
fuck off comp-sci tard.

>> No.8875975

>>8875217
It was made in 2014, but idiots have been around forever.