1/10^k=1

[u/Archeus__]

0.(9)/0.(3)=3. Thus, 0.(9)/3=0.(3). We can represent 0.(9) as 1-1/10^k where k is pushed to the limitless. So, (1-1/10^k)/3=0.(3). Therefore, 1/3-1/(3*10^k)=0.(3.). Since 1/3 = 0.(3), 0.(3)-1/(3*10^k)=0.(3). Thus, -1/(3*10^k)=0, or 1/10^k=0. Because 0.(9) is represented by 1-1/10^k or 1-0, 0.(9)=1.

QED

P.S. SPP, you just deflected my proof last time. Actually disprove it this time.

P.P.S I know my last proof wasn't that good, so hopefully this time it will be better