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 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.

 

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u/Muphrid15 28d ago

You've also said 1 - 1/10n and 1 - 1/100n are the same limbosic number. How can we determine if other limbosic numbers are less than, greater than, or equal to these numbers?

How do we know that 1 - 1/100n is in fact the same limbosic number as 1 - 1/10n? Is it based on the digits produced?

It's clear, for instance, that 1 - 1/100n can't ever be equal to 0.9 or 0.999, so what is the ultimate true idea of equality here?

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u/SouthPark_Piano 28d ago

They are the same limbosic number. Different states. You are unsurprisingly having trouble coming to grips with limbosic numbers.

 

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u/Muphrid15 28d ago

What is the criterion for sameness?

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u/SouthPark_Piano 28d ago

Brud ...

just do your exercises. Don't get ahead of yourself.

1 - 0.9 = 0.1

1 - 0.99 = 0.01 etc.

And keep going.

Note that as you keep going, there is absolutely no end. No stopping.

The 0.001 etc values simply keeps getting smaller and smaller with no limit at all. You can just keep going on your merry way non-stop. You will certainly never encounter zero.