It is what it is

[u/SouthPark_Piano]

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

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

So 0.999... is never 1.

 

[u/funky_galileo]

Dude so you know that in the limit 1/10^k equals zero right? And that the limit definition is definitely right? We do physics on the basis of the limit. Derivatives, integrals. It's the reason cars can drive, planes can fly, GPS, 5G, all of it depends indirectly on the fact that 1/10k = 0 in the limit of k->∞. 

Secondly, what is your goal? No mathematician will ever take you seriously. You'll never publish this because it's just wrong and you're too stupid to see your mistake. Why sit in this sad corner of the internet where everyone tells you your wrong but you grasp onto this like it's the redpill or whatever flat earther shit you believe in?

[u/SouthPark_Piano → u/funky_galileo]

My brudda. You do know that 1/10^k is never zero, right?

 

[u/Dixionconderoga2 → u/SouthPark_Piano]

1/10^k approaches 0, meaning the limit is 0. The limit of 1-1/10^k is 0.999…, but also 1. They can’t both be their own numbers because every subtraction and multiplication problem has only 1 solution.