I remember a junior high computer teacher explaining why 0.999... = 1 in a simple, elegant way in the 80's. Apologies in advance for any formatting weirdness.
Say x = 0.999...
That means 10x = 9.999...
9x = 10x - x
9x = 9.999...
- 0.999...
--------
9x = 9.000...
x = 1.000...
x = 1
