Fun with infinity

aye, so 0.99999999999999999 was a bad example. Try 1/x as x -> infinity then. That's a converging limit.

Yes while the above statement is occassionally useful, it has nothing to do with the infinity I originally talked about.

It doesn't converge to 1, it is 1, ryt? Sadly, infinity is a badass thing which is hard to understand sometimes.

It is a convergence if you take it as the limit of a sum... that is
sum (n = 0 to infinity) 0.1^n * 0.9
ie. 0.9+0.09+0.009+0.0009+...
or 0.9, 0.99, 0.999, 0.9999, 0.99999 etc. as n = 1,2,3,4,5,...

Of course using the simple rule of a/(1-r) where a is the first value and r is the geometric ratio, you see 0.9/(1-.1) = 1