omg new proof

Assumptions
If A = B, then
a)  A-B = 0
b) A = (A+B)/2 = B

If A > B, then
a)  A-B > 0
b) A > (A+B)/2 > B


Let A = 1, B = .999...9
a) A-B = 1-.999...9 = .000...1 =/= 0
b) (A+B)/2 = (1+.999...9)/2 = 1.999...9/2 = 1.999...95 < A

Therefore, .999...9 =/= 1

>>45
1 = 0.999...
Also, by your definition, the real numbers would be countable, pi would not be a real number, and the "set" of real numbers would be a different set* based on what base you choose! Talk about stupid.

* - by your definition, 1/3 is not a real number, since its decimal expansion, 0.333..., is infinite. But in base 3, 0.1 represents 1/3. Whoops!