>>12038102Well there is a method of proof that's exactly this. Proves something for every natural number by going one number after another recursively.
0.999... is not that different from induction. For any arbitrarily large n, the sequence 0.999(n) (forgive the shitty notation) lies in an open neighbourhood of 1, and no other number. Given a number x between 0.999(n) and 1, there s some m>n such that 0.999(m) > x > 1.
So the limit uniquely approaches 1.
Never to reach it I get it. It's but the intersection of all such neighbourhoods.
Where does it say it's length is static? Aleph_0 is not a real number. It's a spook of some weird manipulation of set theory.
