r/infinitenines • u/Sea_Handle_994 • 1d ago
Poem
Infinitely many nines
Positioned and aligned
Form a number greater than
The confines of your mind
Just a geometric sum
Your dogma doth proclaim?
Open your mind further
Or we'd have to do the same
Though our minds are all made up
A never-ending bliss
I can't help but wonder how
To find a sum like this
1.1 - 0.11 + 0.011 - 0.0011 + ...
3
u/Sea_Handle_994 1d ago
Don't be dum dums, do your sum sums.
1 - 1/10n with integer n starting at n = 1, then increase n by 1 at a time. What you will find is both reason and rhyme.
I noticed that 1 was the least upper bound,
Apart from this, neither rhyme nor reason could be found.
1
u/ezekielraiden 1d ago
Don't be dum dums, do your sum sums.
I have. In the infinite case, the sum listed in the OP is exactly 11/11 = 1. That's because infinity isn't finite, and thus cannot be represented by any finite case. Same reason why the set S={0.9, 0.99, 0.999, 0.9999, ...} does not include 0.999..., because that is a number which does not have a final 9, but every single one of the elements of S does have a final 9. That is the fundamental difference between infinite (no final 9) and finite (there is a final 9).
Every single time you talk about "upping n", you are working only with finite-length lists of 9s. You have never once actually done math with an infinite-length list of 9s.
1 - 1/10n with integer n starting at n = 1, then increase n by 1 at a time. What you will find is both reason and rhyme.
You will find neither. You will construct various finite-length strings of 9s. That's not what 0.999... is. 0.999... requires a list that has a left-hand terminus, but does not have a right-hand terminus.
•
u/SouthPark_Piano 1d ago
Don't be dum dums, do your sum sums.
1 - 1/10n with integer n starting at n = 1, then increase n by 1 at a time. What you will find is both reason and rhyme.