/sci/ - Science & Math

yes

No

maybe

i dont know

If you want

Sometimes

It's plausible

>>8688734
Define how much smaller than 1 it is.

>>8688825
an infinitesimal

>>8688734
Yes.

>>8688734
Yes it is

>>8688734
suck my dick you retarded troll, nobump btw

>>8688734
Depends.

Is 0.9999999... = 0.999...999 ?

>>8688742
>>8688743
>>8688744
>>8688745
>not followed by "can you repeat the question"
0/10

>>8688734
0.99999999...=x
9.99999999...=10x
9=9x
1=x
Thus, 1=0.99999...

You could also define the sum of 9/(10^n) for n=1 to infinity, and then prove that that sum converges towards 1

Is 0.999.... + 0.000...1 = 1
or = 1.000...1

Is a banana an apple? No, it's a banana

>>8688879
Is is a shipost? How do you get from 9.9999... = 10x to 9 = 9x.
Looks like youre preupposing.0.9999... = 1.

>>8688917
subtract x from both sides dipshit

>>8688917
0.9999999999..... = x
9.9999999999..... = 10x
9.9999999999..... - 0.99999999... = 10x - x
9 = 9x

>>8688734
Whoever made this picture is a fucking retard. Making a Nazi themed pic and cba to even look up how the fuck to write Sieg Heil properly? sad af senpai

Of course not you stupid asshole. Its just so close that |1 - .99999...| < e for any e > 0.

>>8688922
9.9999... ( - 0.9999...) != 10.9999.... ( - 0.9999...)
9 != 10

Are you usually this autistic or is it just this once?

>>8688925
9.9999... - 0.9999... = 9
10.9999... - 0.9999... = 10
9 != 10

>>8688945
Why are you posting on /sci/ if you don't know how to do arithmetic?

>>8688925
1.1 = x
11 = 10x
11 - 0.1 = 10x - x
11 = 11x
1.1 = 1

Am I shitposting yet?

>>8688962
yup

>>8688949
9 == 10?

>>8688978
At one point you replaced 10x with 10.9999...
See the problem?

>>8688982
But 10x - x != 9, 10x - x = 10

>>8688991
dude.
10x does not mean "ten plus x" it means "ten times x".
So if you got 10 x and take one x away, you are left with 9 x.

>>>/b/sqt

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

>>8688907
But what if you have an infinitely long banana. It could turn into an apple after awhile

The fact that these threads still get responses from people believing that so many posters here would actually be that stupid amuses me.

Just stop responding to obvious shitposting and read some better threads.

>>8688734
If by 0.999999... you mean 3*1/3 yes
If you mean the summation to infinity of 9*10^-k starting from k = 1 no
>It's equivalent!
No, limit doesn't mean it's equal, means it get closer and closer

>>8689013
But 1/3 != 0.333...
It's only an approximation.

>>8688991
>10x - x = 10

kek is this bait?
or are you an engineer?

>>8688734
No, think about it.

If 0.99999... = 1 then lets try to go deeper down the rabbit hole.

Think about it. What is the number
0.89999999999999...

Wouldn't it just be
0.999....

so it is also 1?

Now lets go even deeper
1 = 0.9...
= 0.89...
= 0.889...
= 0.8889...
But then we can repeat this process forever so
=0.888888...

So now 1 = 0.888888... ????????

Really makes me think why retards think 1 = 0.99... when it is so obviously fallacious.

>>8689498

[math]
0.8999... = 0.999... - 0.1 \\
= 1 - 0.1 \\
= 0.9
[/math]

>>8689501
No, you stupid. lets follow your amazing logic again.

0.9999... - 0.1.... = 0.99999... - 0.9..... (because 1 = 0.999... SUPPOSEDLY) = 0

Amazing. Tell me, at which state university did you get your degree in mathematics?

>>8689511

[math]
0.999... - 0.1 = 0.999... - 0.0999... = 1 - 0.1
[/math]

Stop embarrassing yourself

>>8689513
The reason you are getting that error is because you are unknowingly doing an infinite number of computations when in reality you can never do that.

Uh... have you taken analysis!

>>8688734
This has to just be a criticism of the number system. 0.99999... is 0.0000...;...0001 smaller than 1. Should every time x is solved for, you write eg. x = 6, 5.9999...? No, of course not. Those are two separate values. Unless if theres some magic nth number hidden at the end of base 10 between 9 and 0 that forces infinitly repeating decimals to always round up we have a problem here. There is something fundementally flawed here and it should be dealt with.

[math]
\frac{1}{9} = 0.111... \\
\frac{3}{9} = 0.333... \\
\frac{7}{9} = 0.777... \\
\frac{9}{9} = 0.999... [/math]

What else does [math] \frac{9}{9} [/math] equal to?
That's right, 1 (one).

Actual proof by another anon here: >>8688879

>>8689516
(Not that guy)
>Uh... have you taken analysis!
You, clearly, have not, for >>8689513 is exactly right.

>>8689531
Yeah yeah. Crazy people always think they are right.

I think you should go back to introductory analysis to see where your mistake is.

>>8689549
>Yeah yeah. Crazy people always think they are right.
Evidently.

>>8689560
>Evidently.
Indeed.

>>8688879

this is an extremely dumb proof desu. You can't multiply an infinite number by 10 and expect the maths to work out. By multiplying you're implicitly removing a digit somewhere down the line so 9.99999... isn't the same number of 9's as .99999... according to someone who believes .999... =/= 1.

The only proof that makes sense without begging the question is by proving there is no number between the two values and thus that they are essentially the same value. Everything else can be explained away as simply math tricks.

>>8689519
>Should every time x is solved for, you write eg. x = 6, 5.9999...?
Well, you CAN write it that way and it would still be true, but why would you do that?

>>8689569
>Everything else can be explained away as simply math tricks.
All of mathematics can be explained away as simply math tricks if you are looking for an excuse to disregard an argument you don't understand. That doesn't make it wrong.

>>8689569
>9.99999... isn't the same number of 9's as .99999...
Yes it is.

Infinity + 1 = Infinity.
Infinity + Infinity = Infinity

It's always the same quantity of 9's.

>>8689569
Yep, this all breaks down to believing that infinitely large hotels are good analogies.

https://en.wikipedia.org/wiki/Hilbert's_paradox_of_the_Grand_Hotel

>>8689569
>By multiplying you're implicitly removing a digit somewhere down the line

HAHAHAHAHAHAHAHAHHAHAHAHHAHAHAHAHHAHAHAHAHAHHAHAHAHHAHAHAHAHAHHAHAHAAHHAAHAHAHAHHAHAHA desu

>>8688734
sure you can manipulate the math to get .999...=1 but it doesn't make it true.
Nothing is perfect, including math

>>8689585
>sure you can prove it
>but that doesn't make it true

>>8689578

I'm not saying 1 doesn't equal .9999... I'm saying if you already believe that it doesn't then this isn't a sufficient proof to change someone's mind.

(1 - some infinitesimal) = x
10 - 10(infinitesimal) = 10x
10 - 10(infinitesimal) - (1 - infinitesimal) = 10x - x
9x = 9 - 9(infinitesimal)

x = 1 - infinitesimal, back to where you started

what you should be proving is that an infinitesimal value of .00000000...1 doesn't exist not using algebra tricks to sidestep the question

>>8688962
2nd line to 3rd line is wrong

You subtract .1 from left side and x from the right. And x = 1.1 not .1

>>8689591
>what you should be proving is that an infinitesimal value of .00000000...1 doesn't exist
Well, it's pretty obvious that it doesn't exist. You are putting an end to an infinite series, making it finite.

>>8688734


AHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH


AHHHHHHHHHHHHHHHHHHH


AHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH

AHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH

>>8689569
https://www.youtube.com/watch?v=TINfzxSnnIE

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

>>8688734
.999... = Reality
1 (reaching 1 from zero) = Fantasy, imagination, simulation, virtual environment.

Seriously sci, if a 0x0x0 singularity blew up by expanding by the smallest unit of distance ("infinitely" small), it would take "infinity" to get to one unit (we're not there yet). Are all of you anti-Zeno? Did you hear of paradoxes, and specifically Zeno's paradox?

I'd say it's "effectively" (as if) equal but it'd be better to calculate it, if possible, as 1. The inequality--exactly--is the difference presented above.

You retards give me one """"proof"""" of this bullshit that doesn't rely on fallacious decimal approximations of fractions and I'll stop laughing at you.

>>8689771
>fallacious decimal approximations of fractions
explain why that is true.

>>8689771
What is the actual decimal form of 1/9 then?

0.999... is not even a number
literally kill yourself

>>8689802
>>8689824
'converges to' is not the same as 'equal to'

>>8689826
>pi isn't a number
>1/3 isn't a number
>you are not a faggot

>>8689834
Then, can you mathematically prove that .999... isn't equal to 1?

>>8689855
you're basically too stupid to deserve a (You) but really thanks for the laugh

>>8689879
Thank you for proving my point anon.

How can .9999... equal both .99999... and 1 at the same time? It's one or the other, you can't have both

>>8689834
But "converges to in the limit" is.

>>8689895
>How can 0 equal both 0 and -0 at the same time? It's one or the other, you can't have both

>>8689895
[math] how can \frac{2}{4} equal both \frac{1}{2} and 0.5 at the same time? [/math]

>>8688745
can you repeat the question

>>8689895
Welp guess you can't be both a man and straight then, pick one faggot, are you a girl or a homo?

>>8688925
but that would equal

9=9.111111111x

REFUTED

>>8688734
1= 0.9 +0.1
1 (1/1) = 1 (1/3)- 0 (2/3)

Real numbers x and y are the same iff there are no rational numbers between them, as per the Dedekind construction of the reals.

How to finish?

>>8688734
Yes

T. Engineer

>>8689895
what are you doing on /sci/ TJ """""Henry""""" Yoshi

>>8690403
how is 0.999... - 0.999... = 0.111... ?

>>8688734

>>8691823
>non of these mentions the definition of real numbers which make it obvious beyond a sliver of a doubt that 0.99999...=1.

>>8688734
depends for what you need it.

>>8688734

No. There is an infinitely small number's difference between N and 1.

There are two infinities to think about here and they logically progress alongside eachother if we think about it where N's number of digits = RN's number of digits then we have this

At any definable set of digits within theinfinite set we see that N and RN's value is equal to 1.

0.999 + 0.001 = 1

This is the case at every single number of digits, as we are dealing with two infinite numbers which share the same sum.

So the infinite number, N and the infinite number RN sum to 1.

N - RN != N

>>8692166

N - RN would have to be true in order for N = 1

>>8692166

N - RN = N would have to be true for N to be 1. But RN is not 0.

>>8688734
>Is 0.9999999...=1?
No, the left side is equivalent to 1 - ε
Your task (should you choose to accept it) is to find the value of ε

>>8688734
0.99... = 0.33... X 0.33...
0.33... = 1/3
1/3 X 3 = 1

Simple conversion

>>8689585
>sure you can use math correctly to get unfalsifiable numbers
>that doesn't make it true

>>8688734
Almost

>>8688734
replace = with ≈ and it is true, however in terms of a floating point 1 > 0.9999999....

>>8688734
0.9999999... = 1.1111111...

>>8689498
0.8999...=0.9
>>8689477
What does "closer and closer" mean to you. You think infinite iterations means it can't be done? If you start with 0.9, "add" another 9 in the next second and keep adding 9s, each iteration halving the time it takes you to add a 9, you'll have infinite iterations within 2 seconds.
>>8689596
And 3rd to 4th. As he said, he's shitposting

>>8689578
>Infinity + 1 = Infinity.
>Infinity + Infinity = Infinity

both of these statements are false. you cannot perform arithmetic with infinity as doing so implies it is a bounded number. same with the repeating decimals.

>>8688870
The 9's at the end are arbitrary because there is an infinite amount of 9's before you get to the last three. So yes, they are the same thing.

>>8692166
Please read through a definition of real numbers.
1=0.9999.... is true by definition, as the differnece between the cauchy series [math]x_n=1[/math] and [math]y_n=\sum_{i=1}^n{9*\frac{1}{10^i}}[/math] tends (obviously) to zero, which is the definition for 2 real numbers equalling eachother.

>>8693407
>inb4 some retard saying "hurrr TENDS to 0, but is never actually 0"
>>8693392
They are not the sane thing because the first form is a valid form of a number, the other is not. There is no "end", it's infinitely long

You'd think it would be enough to just explain that zero is by definition an infinitely small number, but nooo.

>>8693085
What did I just read.
> 0.33... • 0.33... = 0.99...
You're joking, right?
Right?

>>8688734
YOU HAVE TO SAY THAT THE 0.00...1 DOES NOT EXIST.
Stop.
Please.

Haven't read the thread, so someone might have already given this example

> 1/3 = 0.333..
> 1/3 + 1/3 + 1/3 = 1
> 0.333.. + 0.333... + 0.333.. = 0.999..
> 0.999.. = 1

This is my favourite and comfiest proof

>>8692986
this is the best explanation for me
that number ε is 0.000...
so 1-0=1

You niggers should be able to solve this.