0.(9) ≠ 1

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

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

no
What kind of absurdity?

no

0.000...1 is not a real number.

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

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

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

see 1) "and what?"
see 2) and 3)

>I know nothing about math
It's okay user

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

>forgetting phenotypeposting

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.

...

now pls someone explain to me why:

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

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

...

[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*

not always
Why do not you understand this?

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

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).

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

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.

These are two different models and two different universes.

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

And "Original 0.(9)" = 0.99...9 ≠ 1

>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.

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

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]

>[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

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

Any undergrad book in analysis.

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

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))

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

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

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.

>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

suck (dick) and then (go) back

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

>>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

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

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

Are "pure math" threads not a thing anymore?

i suspect that 0.00...1 is ill defined

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]

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

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

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]

thanks

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