Timmah! on 25 September 2008
Yes. My rationale is as follows.
The number .999... goes on infinitely.
At every decimal place you add a 9, the difference between the decimal and the whole number becomes smaller by a factor of 10. (The difference between .9 and 1 is .1, The difference between .99 and 1 is .01, etc.)
Because of this, the difference .999... and 1 is infinitely small (since the difference shrinks by a factor of ten at every 9 after the decimal place, and this continues infinitely).
The only number that is infinitely small is 0, therefore the difference between .999... and 1 is 0.
If the difference between .999... and 1 is 0, then they have to be the same number.
