x = 5/9 is not 9/9. 5/9 = .55555...

You're proving that 0.555... equals 5/9 (which it does), not that it equals 1 (which it doesn't).

It's absolutely not the same result as x = 0.999... as you claim.

?
Where did you get 9x=5 -> x=1
and 5/9 is 0.555... so it checks out.

Quick maffs

Lol what? How did you conclude that if 9x = 5 then x = 1? Surely you didn't pass algebra in high school, otherwise you could see that getting x from 9x = 5 requires dividing both sides by 9, which yields x = 5/9, i.e. 0.555... = 5/9 since x = 0.555....

Also, you shouldn't just use uppercase X in place of lowercase x or vice versa. Case is usually significant for variable names.