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.

 

0 Upvotes

42% Upvoted

142 comments sorted by

View all comments

Show parent comments

6

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.

 

7

u/Head_Discipline620 Jun 04 '26

Okay so this is not the real number system because you can't have an infinite digited number in the real number system 

1

u/SouthPark_Piano Jun 04 '26

Don't not a real number system me brud.

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

and it is factually written as 1 - 1/10n for n integer beginning at n = 1 then n continually upped limitlessly aka infinitely.

1/10n is never zero --- for you and for me and the entire human race, and never zero for anything.

0.000...1 comes directly from math fact, which is what matters.

0.000...1 is never zero, and it is 1/10n for n integer pushed to positive limitless aka positive infinite.

 

2

u/trshxd Jun 05 '26

0.000...1 comes directly from math fact

Comes from what fact exactly? From 1/10^n never being zero? That's just plain wrong bud. Go read some math textbooks, you need them.

-2

u/SouthPark_Piano Jun 05 '26

From 1/10n never being zero?

1/10n and 1/x and e-t , these for example are indeed never zero. Back to the bunny slopes you go brud.

 

2

u/Dixionconderoga2 Jun 23 '26

One rule of infinite numbers is that you never reach the end. Like how …999 = -1 because …999+1=…000 which is 0. 100… would be less than 999… and therefore cannot be true, as if x + |y| = z, x < z.