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7015159 No.7015159 [DELETED]  [Reply] [Original] [archived.moe]

So if we divide a number for example a/b
then a/b*b=a

So what if we divide 1 by 100

we get 0.01

0.01*100 = 1

0.01+0.01+0.01...x100 = 1
now we substract 0.01
0.01...+ 0.01 x99 = 0.99

what if we make the number we divide by bigger?

1/10^100

then we get something like

0.000...1

Shouldn't still 0.000...1*10^100=1?

so 0.000...1+0.000...1 x10^100 = 1

now again we substract

0.000...1 + 0.000...11 x(10^100-1) = 0.999....

BUT!

isn't 0.999... = 1?

so then

0.000...1 + 0.000...1 x (10^100-1) = 1 ?
and 0.000...1 + 0.00...1 x 10^100 = 0.000...1 + 0.00...1 x (10^100-1)
but wouldn't that be false?
Are you saying 0.000...1 = 0?
but then 1/10^100 = 0 and 1/10^100*10^100=0 and not 1

I am legitimately confused.

>> No.7015162

>>7015159

Basic logic dictates that 0.99 repeating is less than one.

Mathematic logic can be "tricked" into resulting in the idea that 0.99 repeating is equal to one, only because "repeating" is an imaginary concept in the human mind. There is no such thing as an infinitely small number, so 0.99 repeating is just an idea, not a real number.

>> No.7015178

>0.000...1
Oh look, it's you again

Can't you just learn what a limit is and fuck off?

>> No.7015181

<span class="math">\lim_{x\to -\infty} 10^x = 0[/spoiler]
<span class="math">\lim_{x\to \infty} 10^-x*10^x = \lim_{xto \infty} 1 = 1[/spoiler]
<span class="math">\lim_{x\to\infty} -(10^x) + \sum\limits_{i=1}^x 9*10^-x = 0[/spoiler]

Now get the fuck out with this pleb shit.

>> No.7015222
File: 112 KB, 953x613, 0.999.jpg [View same] [iqdb] [saucenao] [google] [report]
7015222

>>7015159
Finally a use for this. Pic related.
Sage all day
Learn limits OP

>> No.7015231

<span class="math">\displaystyle
1 = \frac{3}{3} = 3 \cdot \frac{1}{3} = 3 \cdot 0.\overline{3} = 0.\overline{9}
[/spoiler]

>> No.7015251

>>7015162
I always thought basic logic dictated you know shit

>> No.7015390
File: 1.16 MB, 200x200, 1415190203704.gif [View same] [iqdb] [saucenao] [google] [report]
7015390

>>7015159
>0.000...1

>> No.7015445

>0.000...1
This can only have finite amount of zeros. If it had uncountable zeros the it would be
0.000... which is zero.

>> No.7015734

>>7015159
This shitty surface dwelling crap again?

N != Q

Go learn some number theory.

>> No.7015740
File: 50 KB, 700x400, periodicrationals.png [View same] [iqdb] [saucenao] [google] [report]
7015740

>> No.7015749
File: 830 B, 138x51, Barnett's Identity.gif [View same] [iqdb] [saucenao] [google] [report]
7015749

How do I use Barnett's identity to prove that 0.9999...=/=1

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