[jonsen]

The first is an infinite series:

  9/10 + 9/100 + 9/1000 + ... + 9/10^n + ...

The second is not?!

[oconnor663]

I mean you could if you want to:

1/10 + -9/100 + -9/1000 + -9/10000 + ...

But I just meant them as series, not necessarily as sums.

[jonsen]

Or

  1 - 9/10 - 9/100 - ...

or

  1 - ( 9/10 + 9/100 + ... )

So it becomes circular:

  0.00...1 = 1 - 0.999...

(In math a series is a sum:

https://en.m.wikipedia.org/wiki/Series_(mathematics)

[oconnor663]

Woops, you're totally right, I think I should've said "sequence".