Originally posted by PatNovak
No, it is not philosophical, it is mathematical. And there is a correct answer.
There is no such number as 'infinity.'
Both of these statements cannot be correct.
For a start, I think we are disagreeing about what is or is not philosophical.
Edit: I agree that there is no such thing as index = infinity, but despite what you may say, that is definitely the question we are pursuing
You may be pursuing it, but I am not. I have already stated that there is no such answer because there is no such thing as index=infinity. Oddly enough you seem to agree with my premise but dispute the obvious conclusion.
(What is the value of the equation when the index = infinity is the only question at stake). That is why we can only approximate the answer, and the question of whether the answer in 1 or 0.999999999... is not mathematical, so it becomes philosophical at that point (because infinity is not a number, but an abstract concept).
Sorry, but philosophy doesn't automatically give you the right to throw logic out the window and say its OK. If something does not make sense, it wont make sense if you call it philosophy rather than mathematics.
Here is the correct mathematical formulation:
The sequence of partial sums that I gave previously is infinite. It includes numbers infinitely close to 1, but does not include 1. Or put more mathematically, for any number n less than 1, there exists a member of the sequence m, such that n<m<1. But equally true is the fact that for any member of the sequence o, there exists a number p such that o<p<1.
It does not have a member with index=infinity, nor does it have a member = 1.