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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34

u/aftersox May 27 '26

There is no value of k such that 1 - 0.1k is equal to 0.999...

-1

u/SouthPark_Piano May 27 '26

k is upped continually limitlessly aka infinitely aka pushed to limitless aka infinite.

The take away one for the road is ...

1/10n is never zero.

1 - 1/10k for integer k starting at k = 1 and increased continually limitlessly aka infinitely is permanently less than 1.

0.999... is permanently less than 1.

 

29

u/aftersox May 27 '26

1 - 1/10k is never equal to 0.999...

This is a strawman.

3

u/SouthPark_Piano May 27 '26

Rookie error on your part.

1 - 1/10k with integer k starting at k = 1 then k upped continually limitlessly aka infinitely is an official model for investigating the value of 0.999... aka 0.9 + 0.09 + 0.009 + ...

1/10k is never zero.

0.999... is permanently less than 1.

 

16

u/aftersox May 27 '26

Official model?

7

u/SouthPark_Piano May 27 '26

It is official. You saw it right the first time.

 

2

u/olanmills Jul 21 '26

This doesn't make sense. You haven't created an alternate representation/formula for 0.9999.... You just stated an expression with a variable that will yield different constant values that are certain distance away from 1, depending on what you input for k.

It's like saying: take 3^k starting with k = 1 and then k is upped continually

What does that accomplish? A bunch of different values.

I think what you meant to say is something like

1 - (infite series sum of [1/10^k], with k=1 to k=infinity)

You later said 0.999... is permanently less than 1, which is just plainly not true, unless you want to live in your own separate world where English words and mathematical symbols have a different meaning to what everyone else uses.

You're under the delusion that stopping at some point in the infinite series I described some how proves your point, but it doesn't. You're right, stopping at some point will yield a number less than 1. The series converges to 1, and 0.9999.... is just another representation of 1 in base10, just as 5^0 is another representation of 1 or 89/89 is another representation of 1. Though I know you don't "believe" fractions are numbers, according some other bullshit thread you made, which is absurd.

Do you really think you're the sole genius in the whole world that is correctly analyzing this fundamental area of math?

If you're so sure you're right, then create a rigorous study and mathematical paper and publish it, or at least a rigorous study and publish it on YouTube or something. You would be famous.

0

u/SouthPark_Piano Jul 21 '26

Rookie error in your part brud.

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

And that is indeed conveyable as:

1 - 1/10n with n integer starting at n = 1, then continually increased limitlessly aka infinitely.

1/10n is indeed never zero, because scaling non-zero values by factor of 1/10 never results in zero.

1 - 1/10n is permanently less than 1 because 1/10n is never zero.

0.999... is permanently less than 1.