set N=.9(repeating)

if N=.9(repeating) then 10N=9.9(repeating)

10N-N=9.9(repeating)-.9(repeating)=9=9N

take 9N=9 and separate the N

9N/9=1

N=1

so... N=1 but N also = .9(repeating)
9N are 9*0.9(repeating)

you claimed 9N=9 that is wrong, because you claimed n=0.9 ... don't mix this ...

this is a little bit abstract but just keep an eye on the little things

so that is maybe your fault ;P

sincery spud