0.(9) ≠ 1

>>9146687
0,99...9 ≠ 0,(9)

>>9146687
GO fuck yourself only thread #76532 about this shit

>>9146687
0.000... = 0
0.999... = 1

>>9146706
Welcome to /sci/, pick your thread:
infinitesimals
/pol/ race raid
order of operations problem
IQ circlejerk
gorillapost

>using commas as decimal points

>>9146691
= of course
0.(9) = 0.99... only "9", so 0.(9) = 0.99...9 - inf of 9

>>9146712
0.00...0 = 0
0.00...1 ≠ 0
0.999... ≠ 1

0.00...0 ≠ 0.00...1
0.99...9 ≠ 1

>>9146773
>0.00...0 = 0
>0.00...1 ≠ 0
0.00...0 = 0.00...1 = 0.00... = 0

>>9146764
this would imply that 99 = 9 so no

>>9146687
>[math]0.000\dots1\neq0 [/math]
>[citation needed]

>>9146687
[eqn]
0.00\dots1=\lim_{n\rightarrow\infty} 10^{-n}=0
[/eqn]

>>9146781
no
What kind of absurdity?

>>9146778
no

>>9146794
0.000...1 is not a real number.

>>9146794
And what?

1)
0.(9) * 10 = 9.(9)
0.(9) * 9 = 0.(9) * (10 - 1) = 9.(9) - 0.(9) = 9
1 * 9 = 9
0.(9) * 9 = 1 * 9
0.(9) = 1

2)
0.9 + 0.1 = 1
0.99 + 0.01 = 1
0.999 + 0.001 = 1
0.99...9 + 0.00...1 = 1
0.(9) + 0.00...1 = 1
0.00...1 ≠ 0 =>
0.(9) ≠ 1

3)
0.(9) = 999.../1000...
1 = 999.../999... = 1000.../1000...
999.../1000... ≠ 999.../999... = 1000.../1000... =>
0.(9) ≠ 1

>>9146857
then 0.999...9 = 0.(9) is not a real number.

>>9146796
is 0,9...9 = 0,9...99 ?
is 0,9...9 = 0,99...9 ?

>>9146880
>>9146874
see 1) "and what?"
see 2) and 3)

>>9146877
>I know nothing about math
It's okay anon

>>9146903
>craziness of the crowd
It's okay anon
cause
man is a social animal

File: russian.jpg (19KB, 399x376px) Image search: [Google]

19KB, 399x376px

>>9146741

>forgetting phenotypeposting

File: 1491329822508.jpg (120KB, 1280x720px) Image search: [Google]

120KB, 1280x720px

>>9146687
>>9146691
>>9146764
>>9146773
>>9146778
>>9146874
Holy fucking shit stop putting numers at the """"end"""" of an infinite series of numbers you fucking retards, that's does't exist nor make any sense. My eyes are fucking bleeding.

File: 1497797476459.jpg (112KB, 953x613px) Image search: [Google]

112KB, 953x613px

>>9146687
now pls someone explain to me why:

>System.out.println(100*(25/100));
shows 0

>System.out.println((100*25)/100);
shows 25

>>9147120
>>9147079

>>9146687
[math]x = 0.\dot{9}[/math]
[math]10x = 9.\dot{9}[/math]
[math]9x = 10x-x = 9.\dot{9} - 0.\dot{9} = 9[/math]
[math]9x = 9[/math]
[math]x = \frac {9} {9} = 1 [/math]
[math]0.\dot{9} = x = 1[/math]
[math]\therefore 1 = 0.\dot{9}[/math]

*cough*

>>9147154
not always
Why do not you understand this?

>>9146687
1 = 10/10 = 9/10 + 1/10 = 9/10 + 10/100 = 9/10 + 9/100 + 1/100 = ... = 0.999...

>>9147029
It makes sense as 10^-n, where n approaches infinite. It isn't an infinite series, but is a number (which is equal to 0).

>>9146687
are you french? use periods fuckface I REFUSE to tolerate your retarded notation

>>9147170
1/3 ≠ 0.(3)
Because these are things from different universes. But these things are similar to each other. We mistakenly believe that this is the same thing.

>>9147199
These are two different models and two different universes.

"Imaginary 0.(9)" = "0.(9)" = 1 (your)

And "Original 0.(9)" = 0.99...9 ≠ 1

>>9146741
>no climate change denial and flat earth threads
lmao those are the best ones

so?

Man, I think any proof that 0.999... = 1 that doesn't mention the definition of the real numbers is not convincing.

>>9148193
assume the completeness axiom. therefore 0.999...=1

>>9146741
you forgot
>i shove my moms shampoo bottle up my ass while showering and while i was putting my own shit down the drain the shampoo bottle fell into the drain too.
>how long till the water needs to dissolve the plastic?

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

>>9148380
>[math]\frac{1}{3}=0.\overline{3}[/math]
>[math]3\cdot 0.\overline{3}=1[/math]
says who?

in the reals, the cauchy sequence converges
if you want to use infintesimals, then thats fine, but make it clear
thread over

>>9147120
25/100 is an integer and gets rounded down to zero. Try 25.0/100

>>9148672
Any undergrad book in analysis.

If you can't handle the arithmetic of convergent series you should be studying instead of shitposting.

>>9147236
are you dumb?

i just showed you BY DIRECT CONSTRUCTION that indeed 1 = 0.(9).

by entirely analog construction you get 1/3 = 0.(3)

i actually gave the BEST prove and yet everybody ignores it. pathetic.

"0.(3)" - we just mean "1/3" (it is not original 0.(3))
"0.(9)" - we just mean "1" (it is not original 0.(9))

>>9147120
You're working in ints not floats/doubles, so 25/100 approximates to 0, 100*0 = 0. Whereas In the other you have 100*25 = 2500, 2500/100 = 25

>>9148711
doesn't explain why 1/3=0.333...

>>9149065
0.333... is the usual representation for the series \sum^\infty 3*10^-n, which is a constant times a geometric series. It converges to 1/3. Again, read a fucking book sometimes, your popmath crap won't get you very far in life.

>>9149065
>doesn't explain why 1/3=0.333...
my god you fucktard JUST READ MY FUCKING POST WHERE I CONSTRUCTED YOU THE FUCKING REASON THIS EQUATION HOLDS TRUE.

1/3 - 3/10 = 10/30 - 9/30 = 1/30
1/30 - 3/100 = 10/300 - 9/300 = 1/300
1/300 - 3/1000 = ....

ergo 1/3 - (3/10 + 3/100 + 3/1000 + ....) = 0
ergo 1/3 = 0.(3)

you fucking scum

>>9146899
suck (dick) and then (go) back

>>9149078
>ergo 1/3 - (3/10 + 3/100 + 3/1000 + ....) = 0
ergo 1/3 - (3/10 + 3/100 + 3/1000 + ....) = -1/12
ftfy

>>9149107
>>ergo 1/3 - (3/10 + 3/100 + 3/1000 + ....) = 0
>ergo 1/3 - (3/10 + 3/100 + 3/1000 + ....) = -1/12
>ftfy
if i cannot add anything i at least wanna spout a meme

>>9149126
I-I-I'm s-s-sorry, senpai, I just tried to be funny

>>9149221
>I-I-I'm s-s-sorry, senpai, I just tried to be funny
be funny elsewhere

>>9146741
Are "pure math" threads not a thing anymore?

>>9146687
i suspect that 0.00...1 is ill defined

>>9149078
test
[math] \displaystyle
\begin{align*}
\frac{1}{3} - \frac{3}{10} &= \frac{10}{30} - \frac{9}{30} = \frac{1}{30} \\
\frac{1}{30} - \frac{3}{100} &= \frac{10}{300} - \frac{9}{300} = \frac{1}{300} \\
\frac{1}{300} - \frac{3}{1000} &= \frac{10}{3000} - \frac{9}{3000} = \frac{1}{3000} \\
\frac{1}{3000} - \frac{3}{10000} &= \frac{10}{30000} - \frac{9}{30000} = \frac{1}{30000} \\
&\cdots
\end{align*}
\\\Rightarrow 1/3 - (3/10 + 3/100 + 3/1000 + \cdots) = 0
\\\Rightarrow 1/3 = 0.\overline{3}
[/math]

>>9149879
yes, and he doesn't even make a difference between 0.00...1 and 0.00...01

>>9149955
what a beautiful post

No there are not two universes and it isnt false
... Is just bad notation that isnt really used. Use summ notation and the problem disappears

>>9149485
You seriously mean this thread?
People should argue with cauchy-sequences and the corresponding metric or some other real-line-topology stuff, define things and notations properly etc.
Or explicitly state that they are using some kind of infinitesimals and non-standard models.
But this thread... Jesus. "Math-board" my ass.
Look here, some more mathemagic-food for you guys:
[math]
0.(0) = 0.0...01 = \frac{1}{100...0} = 0
\Rightarrow
1=100...0 * 0
\Rightarrow
1=0
[/math]
...fight!

Proof that 0.9999...=1 with infinite sums
[math]\displaystyle 0.9999...=0.9+0.09+0.009+\cdots=\sum_{n=1}^\infty 9\times 10^{-n}=(9)\left(-1+\sum_{n=0}^\infty\left(\frac{1}{10}\right)^n\right)=(9)\left(\frac{1}{1-1/10}-1\right)=(9)(10/9-1)=(9)(1/9)=1[/math]

>>9148700
>>9149057
thanks

>>9146877
>then 0.999...9 = 0.(9) is not a true equation
FTFY