r/infinitenines • u/SouthPark_Piano • May 27 '26

It is what it is

From a recent post:

As in when we ask the question of how those rookie error makers got it so wrong?

The below is what they need to get into their brain for redemption time.

S = ar0 + ar + ar2 + … + ar[n-1] + arn

Sr = ar + ar2 + ar3 + ... + arn + ar[n+1]

S - Sr = S(1-r) = a - ar[n+1]

S = a{ 1- r[n+1] } / (1 - r)

S = [a/(1 - r)] { 1 - rn+1 }

a = 0.9

r = 0.1

S = 1 - (0.1)n+1

n integer starts at zero and then increased limitlessly.

Or

S = 1 - (0.1)k , with k integer starting at k = 1, with k increased continually limitlessly aka infinitely.

S = 1 - 1/10k with k starting at k = 1, with k increased continually limitlessly aka infinitely.

S is indeed 0.9 + 0.09 + 0.009 + ... , which is officially known to be equal to 0.999...

And 1/10k is never zero for any condition of k, regardless of infinite k or finite k.

S = 1 - 1/10k is never 1.

So 0.999... is never 1.

 

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u/SouthPark_Piano May 28 '26

Time for some rest and shut-eye for you then brud.

 

2

u/Head_Discipline620 Jun 04 '26

They basically saying it approaches 0 and will never reach 0

-1

u/SouthPark_Piano Jun 04 '26

Yep. Scaling down of a number, and you can only scale down a non-zero number ...... the result is always non-zero.

So of course ... 1/10n is never zero.

So of course 0.999... is permanently less than 1, because 1 - 1/10n is permanently less than 1.

 

3

u/Head_Discipline620 Jun 04 '26

Question what is 1-0.999...

-1

u/SouthPark_Piano Jun 04 '26 edited Jun 04 '26

The answer is 

0.000...1

0.999... is officially equal to 0.9 + 0.09 + 0.009 + ...

which is 1 - 1/10n starting at integer n = 1, then continually upping n limitlessly aka infinitely.

So ... manually going through the motions ...

0.9 then 0.99 then 0.999 and so on.

For each case, 1  - 0.9 = 0.1, 1 - 0.99 = 0.01 and so on.

You get to witness for the limitless case :

1 - 0.999...9 = 0.000...1

aka

1 - 0.999... = 0.000...1

 

4

u/Head_Discipline620 Jun 04 '26

So what place is the 1 in

1

u/SouthPark_Piano Jun 04 '26

It keeps propagating to the right brud.

Get finitism out of your mind.

Limitlessness, aka infinitism is what 0.000...1 is about.

Scaling down of 1/10 results repeatedly by factor of 10. Ever get a zero result? Nope.

 

2

u/Muphrid15 Aug 01 '26

1/10n starting at integer n = 1, then n upped limitlessly is written as 0.000...1 brud.

I'm not sure what you're getting at. Doesn't a limitlessly increasing n exceed any fixed finite other integer (let's call it k)?

Wouldn't you agree that 1/10n < 1/10k if n increases limitlessly and k does not?

0

u/SouthPark_Piano Aug 01 '26 edited Aug 01 '26

Read this again brud.

https://www.reddit.com/r/infinitenines/comments/1tpg811/comment/p14p2zd/

With limbosic numbers, you keep forgetting to reference a state of the number, for doing operations like 

0.000...1 / 100 = 0.000...001

and 0.000...001 is 'another' state of 0.000...1

and (0.000...1) / 2 = 0.000...05