- #1
Fala483
- 8
- 0
Let f(n) be of the form F(1) = 0.999999 F(2) = 0.9999999 F(3) = 0.99999999 Etc
For arbitrary N >= 1
Let g(n) = f(n)^2
G(1) and g(2) end in 8
By linear relation all g(n) end in 8
Assume 0.999... = 1
0.999... X 0.999... must end in 8 per (4)
1 x 1 does not end in 8
By (5),(6),(7), contradiction
Therefore 0.999... = 1 is a contradiction
For arbitrary N >= 1
Let g(n) = f(n)^2
G(1) and g(2) end in 8
By linear relation all g(n) end in 8
Assume 0.999... = 1
0.999... X 0.999... must end in 8 per (4)
1 x 1 does not end in 8
By (5),(6),(7), contradiction
Therefore 0.999... = 1 is a contradiction