Define:
x = 0.999...
Multiply both sides by 10
10x = 9.999...
Isolate integer part
10x = 9 + 0.999...
By definition of x
10x = 9 + x
Subtract x from both sides
9x =9
Divide both sides by 9
x = 1
x = 0.999...
Multiply both sides by 10
10x = 9.999...
Isolate integer part
10x = 9 + 0.999...
By definition of x
10x = 9 + x
Subtract x from both sides
9x =9
Divide both sides by 9
x = 1