Incorrigible mainstream ignorance and stupidity: 1/3 = 0.333... implies 9 = 10.

All you need to do is consider the partial sums:

333... : s(n) = (10^n - 1)/3
999... : s(n) = 10^n - 1
0.999... : s(n)= 1 - 1/10^n
1000... = 999... + 0.999... : s(n) = (10^n - 1) + (1 - 1/10^n)=(10^n - 1/10^n)

So,

333... / 999... = (10^n - 1)/3 -:- (10^n - 1) = 1/3

In the above, we don't even care about n because both 333... and 999... are well defined, so no need for taking any limit. The conclusion is immediately evident.

333... / 1000... = (10^n - 1)/3 -:- (10^n - 1/10^n)

= [1/3 - 1/(3x10^n)] / [1 - 1/10^2n]

In the above, we have to take the limit in order to get 1/3. And why does this happen? Because the limit of 0.999... is 1.

Thus we take limits and we end up with 333... / 999... = 333... / 1000... implying that 9 = 10.

Thanks to Euclid for his brilliant proposition in helping to debunk your delusions. Chuckle.

Tsk, tsk. You can't get any more stupid than this!

Link to sci.math discussion so you can see how many morons still refuse to be corrected:

https://groups.google.com/d/msg/sci.math/szb6MwmmRrY/u-58VOB8DgAJ

Link to applet used in video:

https://drive.google.com/open?id=1jWjsFDY2j-Pb6UJv3O-ePIYT1WiIsbgg

Article which proves 1/3 has no measure in base 10:

https://drive.google.com/open?id=1o5kcWvU35tdt_SY83UFnXZAlsKBAsSYH

Link to my free eBook:

https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO/view

Euler's worst blunder : S = Lim S

https://www.linkedin.com/pulse/eulers-worst-definition-lim-john-gabriel/

There is a contributor on sci.math called Konyberg who is kindly disposed toward 0.333... and 0.999... as most of you fucking idiots would probably be too. BUT, the objects 333... and 999... which are valid series, produce exactly the same result:

333... : s(n) = (10^n - 1)/3 [A]
999... : s(n) = 10^n - 1 [B]

0.333... : s(n) = (1-10^(-n))/3 [C]
0.999... : s(n) = 1 - 10^(-n) [D]

[B] -:- [A] = 1/3
[D] -:- [C] = 1/3

See? Identical results. Why do you think [A] and [B] are not valid?