Let 0.999..9= lim(n->∞) (3*3*(11..1))/(5*2)^n
If 0.999..9=1, can we conclude that (3*3*(11..1)) equals to (5*2)^∞?
If 0.999..9=1, density property is false.
--
1/3≈0.333...x (never divides completely, non-zero remainder always exists)

--
What if A≡Σ(n=1,∞) 9/10^n = .999..9, what is the 3rd decimal digit?
Note that A is DEFINED exactly .999..., not 1.
Repeating decimal is irrational BY DEFINITION.

wij wrote :
> Let 0.999..9

Explain this notation please.

On Wednesday, December 8, 2021 at 5:36:39 PM UTC-8, FromTheRafters wrote:
> wij wrote :
> > Let 0.999..9
>
> Explain this notation please.

You are only irrational if you repeat forever different...
We have to measure PI...

On Thursday, 9 December 2021 at 09:36:39 UTC+8, FromTheRafters wrote:
> wij wrote :
> > Let 0.999..9
>
> Explain this notation please.

Already shown. Which one bothered you?

"repeating decimal" is actually an ambiguous term, but we are not there yet.

On 12/8/2021 5:32 PM, wij wrote:
> Let 0.999..9= lim(n->∞) (3*3*(11..1))/(5*2)^n
> If 0.999..9=1, can we conclude that (3*3*(11..1)) equals to (5*2)^∞?
> If 0.999..9=1, density property is false.
> --
> 1/3≈0.333...x (never divides completely, non-zero remainder always exists)
>
> --
> What if A≡Σ(n=1,∞) 9/10^n = .999..9, what is the 3rd decimal digit?
> Note that A is DEFINED exactly .999..., not 1.
> Repeating decimal is irrational BY DEFINITION.
>

no. A repeating decimal expansion pattern is always a rational number.

torsdag 9 december 2021 kl. 00:32:15 UTC+1 skrev wij:
> Let 0.999..9= lim(n->∞) (3*3*(11..1))/(5*2)^n
> If 0.999..9=1, can we conclude that (3*3*(11..1)) equals to (5*2)^∞?
> If 0.999..9=1, density property is false.
> --
> 1/3≈0.333...x (never divides completely, non-zero remainder always exists)
>
> --
> What if A≡Σ(n=1,∞) 9/10^n = .999..9, what is the 3rd decimal digit?
> Note that A is DEFINED exactly .999..., not 1.
> Repeating decimal is irrational BY DEFINITION.

Everything is wrong here.
1: you assume only finite decimals constantly
2: You assume it is an algorithm that defines, it isnät
3: INFINITE means NO LAST so you cannot write like 0.999...9, it is just 0.999.... because THERE IS NO LAST ONE!
4: repeating decimals are RATIONAL YOU MORON!

On Wed Dec 8 15:32:08 2021 wij wrote:
> Let 0.999..9= lim(n->) (3*3*(11..1))/(5*2)^n
> If 0.999..9=1, can we conclude that (3*3*(11..1)) equals to (5*2)^?
> If 0.999..9=1, density property is false.
> --
> 1/30.333...x (never divides completely, non-zero remainder always exists)
>
> --
> What if A(n=1,) 9/10^n = .999..9, what is the 3rd decimal digit?
> Note that A is DEFINED exactly .999..., not 1.
> Repeating decimal is irrational BY DEFINITION.
>
* No. That is wrong. The definition of 'a rational number' is a number that is equal to a ratio of integers.
An 'irrational number' is a number that cannot be expressed as a ratio of integers.

You must have missed that lecture.

earle
*

On Wed Dec 8 17:38:19 2021 "mitchr...@gmail.com" wrote:
> On Wednesday, December 8, 2021 at 5:36:39 PM UTC-8, FromTheRafters wrote:
> > wij wrote :
> > > Let 0.999..9
> >
> > Explain this notation please.
>
> You are only irrational if you repeat forever different...
> We have to measure PI...

*
In addition to the obvious definition of 'pi'
Pi is also the ratio of log(-1) to sqrt (-1).

This was proved by A. de Morgan in about 1790.

earle
*

On 12/11/2021 7:28 PM, Earle Jones wrote:
> On Wed Dec 8 15:32:08 2021 wij wrote:
>> Let 0.999..9= lim(n->) (3*3*(11..1))/(5*2)^n
>> If 0.999..9=1, can we conclude that (3*3*(11..1)) equals to (5*2)^?
>> If 0.999..9=1, density property is false.
>> --
>> 1/30.333...x (never divides completely, non-zero remainder always exists)
>>
>> --
>> What if A(n=1,) 9/10^n = .999..9, what is the 3rd decimal digit?
>> Note that A is DEFINED exactly .999..., not 1.
>> Repeating decimal is irrational BY DEFINITION.
>>
> *
> No. That is wrong. The definition of 'a rational number' is a number that is equal to a ratio of integers.
> An 'irrational number' is a number that cannot be expressed as a ratio of integers.
>
> You must have missed that lecture.
>
> earle
> *

agree, each is a rational, 9/10, 9/100, 9/1000, ...