Umm - you don't need to go into calculus to prove .999999... = 1

Just go back to conversion of decimals to fraction in elementary school.

0.999999999999... * 10 = 9.999999999...

9.999999999999... - 0.999999999... = 9 = 9* 0.999999999999999

9/9 = (9*0.99999999....)/9 = 1

You can do the same thing to convert any repeating decimal to it's fractional expression. Taking at random 0.12345 ...

0.12345... * 100,000 = 12345.12345...

12,345.12345...-0.12345... = 12,345 = 0.12345.. * 99,999

thusly 0.12345... = 12,345/99,999 = 4,115/33,333.

CD. Or maybe in this case QED - <G>

CD