Infinity defeated

let

s = 1 + 2 + 4 + 8 + ...
s = 1 + 2(1 + 2 + 4 + ...)
s = 1 + 2s
s = -1
1 + 2 + 4 + 8 + ... = -1

discuss

s = 1 + 2 + 4 + 8 + ...
s = 1 + 0 + 2 + 0 + 4 + 0 + 8 + 0 + ...
s = 1 + (1 - 1) + 2 + (1 - 1) + 4 + (1 - 1) + 8 + (1 - 1) + ...
s = (1 + 1) (- 1 + 2 + 1) (- 1 + 4 + 1) (- 1 + 8 + 1) + ...
s = 1 + 1 + 2 + 4 + 8 + ...
s = 1 + s
0 = 1 ZOMG!!

Inconsistent'd