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

Infinity is not a number at all it is merely the absence of an end. Saying that k is infinity is not valid. The glimmer of hope that you see is merely the fact that 1-1/k calculated in an infinite number of ways would yield an infinite number of results, however infinity does not do the impossible. The only other argument you could make is that the universe does not actually divide like math does. For example when a decaying radioactive isotope gets to less than one atom the mathematical model collapses and the atom just decays. However the truth of that matter is very much the same. Lets say that if you were counting in atoms, but due to the strings that make up the subatomic particles you are limited to an absolute calculation in (for the sake of argument) lets say the .000000000001 place. In this case the farthest possible you could go while describing atoms in a 1/k function is .999999999999. If you cant go any farther due to it not existing then the only logical step is to reach 1.